Elementary ParticlesContents

Figure 1501 shows the size of the systems, which are governed by the rules in quantum theory. It starts from molecule with a size of 10^{7}cm to the hypothetical entity of string and membrane, which has a size of only 10^{33}cm. Figure 1502 shows a proton composed of two up quarks and one down quark. According to the superstrings theory, these quarks are loops of string or string attached to a membrane at the scale of less than 10^{33}cm, which is called the Planck scale  the smallest meaningful size (see Quantum foam).  
Figure 1501 Quantum Domain 
Figure 1502 String & Membrane 
Particle accelerators were invented to investigate objects with size less then 10^{12} cm. Accelerators are to particle physics what telescopes are to astronomy, or microscopes are to biology. These instruments all reveal and illuminate worlds that would otherwise remain hidden from our view. They are the indispensable tools of scientific progress. The earliest accelerators were simple vacuum tubes in which electrons were accelerated by the voltage difference between two oppositely charged electrodes. From these evolved the CockcroftWalton and van de Graaff machines, larger and more elaborate, but using the same principle. The modern example of this type of device is the linear accelerator, a sophisticated machine used in many scientific and medical applications. All such straightline accelerators suffer from the disadvantage that the finite length of flight path limits the particle energies that can be achieved.
The great breakthrough in accelerator technology came in 1920 with Ernest O.
Lawrence’s invention of the cyclotron. In the
cyclotron, magnets guide the particles along a spiral path, allowing a single
electric field to apply many cycles of acceleration. Soon unprecedented energies
were achieved, and the steady improvement of Lawrence’s simple machine has led
to today’s proton synchrotrons (PS), whose endless circular flight paths allow protons to gain
huge energies by passing millions of times through the electric fields that
accelerate them.
Until twentyfive years ago, all accelerators were socalled fixedtarget machines, in which the speeding particle beam was made to hit a stationary target of some chosen substance. But early in the 1960’s physicists had gained enough experience in accelerator technology to be able to build colliders, in which two carefully controlled beams are made to collide with each other at a chosen point. Several colliders exist around the world today, and the technology for them is by now well established. Colliders are more demanding to build, but the effort pays off handsomely. In a fixedtarget machine, most of the projectile particles continue the forward motion with the debris after impact on the target. In a collider, on the other hand, two particles of equal energy coming together have no net motion, and collision makes all their energy available for new reactions and the creation of new particles.
It is realized that the massenergy relation (E = mc^{2}) provides a new way to get information about particles. If particles could be made very energetic and then used to collide with other particles, some of their energy could be converted into the creation of previously unknown particles. When particles are produced in a collision, they are not particles that were somehow inside the colliding ones. They are really produced by converting the collision energy into mass, the mass of other particles. Which particles will be produced is partly determined by their mass  the lighter they are, the easier it is to produced them, other things being equal  and also by the probabilities calculated from the Feynman diagram.
Particle with energy about 1 Gev (10^{9} ev) is required to probe the structure inside proton. Higher energy is required for smaller system  about 1000 Gev is needed to probe into the quarks. The same amount of energy is required to create many of the hypothetical particles. Currently, the Fermilab's Tevatron has enough energy to produce the top quark (~170 Gev). Up to 14 Tev (10^{12} ev) will be available by the LHC (Large Hadron Collider) at CERN in 2007. Table 1501 below summarizes some features of the major accelerators in the world (all of them are colliders):
Accelerator  Colliding Particles  Total Energy  Major Accomplishment 

Stanford Linear Collider (SLC) in Palo Alto  electron, positron  100 Gev  provided first look at Z^{0} 
Large
Electron Positron Collider (CERNLEP) in Geneva 
electron, positron  200 Gev  discovered Z^{0}, W^{+ } in 1983; shut down in 2002 
Relativistic Heavy Ion Collider
(BNLRHIC) in Brookhaven 
heavy ions  200 Gev  created quarkgluon plasma (little Big Bang) 
Tevatron (FNAL) in Chicago  proton, antiproton  2 Tev  confirmed Z^{0}, W^{+ }, discovered top quark 
Large
Hadron Collider (CERNLHC) in Geneva 
protonproton; ionion  14 Tev  planned for 2007  LEP replacement 
Note 1: CERN = European Organization for Nuclear Research, BNL = Brookhaven
National Laboratory,
FNAL = Fermi National Accelerator Laboratory.
Note 2: Cosmic rays
are energetic particles come from outer space. Before the development of
particle accelerators, cosmic rays provided physicists with their only source of
highenergy particles to study. Although lowenergy cosmic rays are emitted from
the Sun, the origin of the highest energy cosmic rays is one of the outstanding
puzzles in astrophysics. These particles (mostly protons, but including heavier
atomic nuclei) have energies of up to 10^{8} TeV. We can only speculate
about the conditions at the source of the cosmic rays, because we know of no
standard object (supernova, pulsar, or even a black hole) that could easily
accelerate particles to such enormous energies.
Symbol Name, Electric Charge, # of Colour Charges Stability, Mass (in Mev) 
Generation 1  Electron Neutrino, 0, 0 Stable, < 0.0000022 
Electron, 1, 0 Stable, 0.511 
Down Quark, 1/3, 3 Stable, ~ 9 
Up Quark, +2/3, 3 Stable, ~ 5 
Generation 2  Muon Neutrino, 0, 0 Stable, < 0.19 
Muon, 1, 0 Unstable, 105.66 
Strange Quark, 1/3, 3 Stable, ~ 175 
Charm Quark, +2/3, 3 Stable, ~ 1350 
Generation 3  Tau Neutrino, 0, 0 ?, < 16.2 
Tau, 1, 0 Unstable, 1777.1 
Bottom Quark, 1/3, 3 Stable, ~ 4500 
Top Quark, +2/3, 3 Unstable, ~ 178000^{§} 
^{§}Latest measurement in 2004.
Enrico Fermi:
Hideki Yukawa:  

It has been mentioned in Topic 12 that the transition from classical to quantum mechanics can be accomplished either by the path integral method or by the more ad hoc "canonical quantization" such that the momentum p and position q are no longer mere numbers but are operator satisfying the commutative relation: pq  qp ~ h. The Schrodinger equation was developed and applied to the atomic and molecular system with great success. This formalism becomes increasingly inaccurate for phenomena in smaller domain where energy can manifest itself in a variety of ways, e.g., pair creation or particle moving at relativistic speed. Therefore, the Schrodinger equation has to be replaced by field equations such as the KleinGordon equation (for particle with no spin) or Dirac equation (for particle with spin 1/2). These field equations are invariant (unchanged) under a change of the spacetime coordinate system (Lorentz transformation). It is referred to as relativistic invariance, which ensures the validity of the field equation at relativistic speed. To account for the creation/annihilation of particles in high energy interaction, the field is considered to be an operator. It is expanded into Fourier series in terms of harmonic functions and coefficients. These coefficients are then subjected to some quantization rules. Depending on whether the particle has integer or half integer spin, these operators satisfy the commutation or anticommutation relations (for example: ab + ba = 1; the Pauli exclusion principle is guaranteed by quantization with the anticommutation relations for spin 1/2 particles). They are the creation and annihilation operators, which operate on state vectors describing the number of particles in different states. This is called the second quantization, which endows particle property to the field (field + second quantization = quantum field). Thus, in quantum field theory the particles are just bundles of energy and momentum of the fields, which constitute the basic ingredient. A more mathematically oriented description on Quantum Field Theory can be found in the appendix.
Before performing the second quantization, a field equation has to be available to describe the dynamic of the field. It is found that the field equation is equivalent to minimizing the "Action", which is now a function of the field and its first derivative. Since there is an infinite choice for the form of the "Action", some conditions are imposed to limit the arbitrariness. For example, the "Action" should be invariant (unchanged) under the operation of translation, rotation, and time progression (these kinds of symmetry imply the conservation of momentum, angular momentum, and massenergy respectively). However, the symmetry of the "Action" or the field equation does not guarantee the same for its solution. For example, the Schrodinger Equation (mentioned in topic 12) have rotational symmetry for the hydrogen atom, and yet only the wave function corresponding to zero angular momentum possesses a spherical configuration. (See Figure 1207.)
The modern theory of elementary particles depends heavily on the concept of gauge invariance, which was used to describe some global changes that do not have any effect on observation. For example, if the electric voltage throughout the circuit is raised uniformly by the same amount, there would not be any observable effect. But locally at a specific space and time, when a disturbance happens to a fermion field for example, something will react to restore the original "appearance". That something turns out to be the gauge bosons mentioned earlier in Figure 1503. For example, in the electromagnetic interaction a local disturbance can be considered as a two dimensional rotation of the quantum field (which is usually a complex function) in an "internal space". The photon (the gauge boson) is the response to restore the "appearance", which signifies mathematically the invariance of the "Action" with this internal rotation. Theoretical physicists are fond of putting similar objects together called a group. For the case of electromagnetic interaction, there is only one kind of objects  the two dimensional internal rotation. The different rotational displacements form a group, this particular group is called U(1). The symbol U indicates that the transformation (the internal rotation) is unitary, which preserves the normalization (probability). This U(1) group has the property that the internal rotation operations are commutative  mathematicians call such kind of group an Abelian group. Similar gauge invariances exist for the strong and weak interactions, the "internal rotation" depends on more than one parameter in these cases. Group of objects can be formed from these generalized "rotational displacements". However, these elements are no longer commutative. Such groups are called nonAbelian. The gauge theory for the U(1) is called Quantum Electrodynamics (QED).
The nonAbelian group called SU(2) is applicable to the case of weak interaction. The internal rotation is generalized to three parameters corresponding to three different gauge bosons  W^{+}, W^{}, and Z^{0}. The participating particles are the lefthanded pair of leptons. In the WeinbergSalam model, the lefthanded leptons can undergo both electromagnetic and weak interactions while the righthanded electron can only participate in electronmagnetic interaction. Thus the model unifies these two interactions. This asymmetry in chirality is related to the phenomenon of parity violation in weak interaction, and has been verified conclusively in the 1950s. The electroweak unification occurs at energy above 10^{2} Gev. A complication arises with regards to the mass of gauge bosons for which, the original YangMills theory^{ } failed to account for. In the modern version, the mass is generated with a process called the Higgs mechanism, which proposes that some scalar fields called the Higgs fields exist in the vacuum. In the mathematical formalism these Higgs fields are added to the "Action" for the electroweak interaction. At the transition temperature (happened early in the Big Bang), these Higgs fields move to more stable states in lower energy level. Once this happens, all the particles (both bosons and fermions) would acquire mass by interacting with the Higgs condensates. There is now a convincing consensus of experimental results supporting this electroweak theory.
When the internal rotation is generalized to
SU(3), The gauge
theory can be applied to the case of strong interaction. There are eight
parameters for this group corresponding to eight gauge bosons called gluons. The
participating particles are the quarks with 3 different colour charges  red
(r), green (g), and blue (b). Three quarks with different colour charges combine
to form a baryon. Each quark can carry different colour charges at different
time, provided the colour combination is "white". Unlike the case of the U(1)
group where the gauge boson (the photon) does not carry charge, the gluons do
themselves carry the colour charges. Such difference produces phenomenon such as
asymptotic freedom and quark confinement. The gauge theory for the SU(3) group
is called Quantum Chromodynamics (QCD). The formulism for QCD and electroweak
interaction together is known as the
Standard Model,
which describes all the phenomena associated with leptons and quarks.
Although the Standard Model has been very successful in accounting for all experimental phenomena, it is not expected to be the ultimate theory because of its great complexity and the many questions it leaves unanswered. These objections seem to suggest that there may be deeper symmetries underlying the standard model, leading perhaps to the unification of the strong and electroweak interactions into a single "Grand Unified theory", or GUT. Such scheme is indeed possible if the internal rotation group is further generalized to SU(5) with 24 parameters. All the elementary particles are assigned into
two 5multiplets and two 10multiplets. Figure 1510 shows one of the 5 multiplets with the 24 gauge bosons assignment arranged into a matrix. Of these, 12 are familiar (the photon, W^{+}, W^{}, Z^{0} and 8 gluons). The remaining 12 are new bosons denoted by X; these carry new forces which can transform quarks into leptons and vice versa. The mass of the X bosons have been calculated under the Higgs mechanism, and turns out to be about 10^{15} Gev. These superheavy particles lie many orders of magnitude beyond the energy ranges of any conceivable accelerator. However, they would be present in great abundance in the first 10^{35} sec after the Big Bang.  
Figure 1510 SU(5) Symmetry 
Figure 1511 Grand Unified Theory 
At energies well above 10^{15} Gev, all gauge bosons (including the Xs) can be produced freely and all interactions have the same strength and quarks can transform into leptons as easily as they change colours; and the grand SU(5) symmetry is manifest. At an energy of about 10^{15} Gev, the SU(5) symmetry breaks down to separate SU(3) and SU(2)XU(1) symmetries and the grand unified interaction separates into the strong and electroweak interactions. At about 10^{2} Gev, the SU(2)XU(1) symmetry becomes broken, reflecting the separation of electroweak interaction into the distinct weak and electromagnetic interactions. This picture of the unification of interactions also incorporates the variation in the strengths of charges, depending on the distance from which they are acted upon as shown in Figure 1511. The most dramatic consequence of grand unification is that the proton is no longer stable, it has a small probability for decay into a neutral pion and a positron (with a half life of about 10^{31} years). No such decay has been detected so far.
Supersymmetry differs from all other symmetries in that it relates two
classes of elementary particles which are so fundamentally different  the
fermions and the bosons. According to supersymmetry, every "ordinary" particle
has a companion particle  differing in spin by half a unit, but with otherwise
identical properties. Furthermore, the strengths of the interactions of the
superpartners are identical to those of the corresponding ordinary particle.
is a good approximation. Supersymmetry also addresses a host of other mysteries in modern physics such as the tremendous concentration of energy in the universe (the cosmological constant problem), the origin of cosmic inflation, matter/antimatter asymmetry, the nature of cold dark matter, and the special forms of the Higgs interactions.
If supersymmetry were an exact, unbroken symmetry, the superpartners would have the same mass of the ordinary particles. However, no such particles have ever been observed, and supersymmetry, therefore, if it is a true symmetry of particle physics, must be broken. If the breaking of supersymmetry is in such a way that the explanation for the hierarchy problem is still valid, then the mass of the superpartners would be in the order of 10^{3} Gev  just at the mass range accessible to the new generation of accelerators.
According to the theory of superstrings, the fundamental constituents of the material world are not pointlike elementary particles, but tiny onedimensional strings having a length of about 10^{33} cm (the Planck length). Like the string of a violin, they can vibrate in many different ways (different modes), which correspond to the different elementary particles observed in nature. It is a quantum theory that incorporates gravity naturally. In its larger framework of Mtheory, the strengths of all the four fundamental forces merge together at very small distance (~10^{33} cm.) as shown in Figure 1513.
There are two classes of strings, those with ends (open strings), and those without (closed strings  a loop) as shown in Figure 1514. The particles associated with the open strings are the spin1 gauge bosons and fermions. Their movement is restricted on the surface of a membrane by some boundary conditions. Graviton with spin2 is an example of closed string, which can travel freely in all spatial dimensions. These are the ingredients for the theory of manyfold universe.  
Figure 1513 Superunifi

Figure 1514 String, Open & Closed 
When a point particle moves through spacetime, it follows a geodesic (a path of minimum length) and sweeps out a onedimensional curve which is referred to as its worldline. However, when a string propagates through spacetime, it sweeps out a twodimensional surface which, by analogy, is called its worldsheet, and moves along a surface of minimum area. (See Figure 1514.)
When supersymmetry is incorporated into the original string theory, it resolves the problem with tachyon (square of mass is negative), accommodates the ferminonic vibrational pattern, and merge general relativity with quantum mechanics. The Theory of Strings becomes the Theory of Superstrings.
The "heterotic" superstring theory is a theory of closed strings. In contrast to open strings with gauge charges at the endpoints, here the gauge charges are "smeared" over the entire heterotic string. Vibrations (waves) can travel around any closed string in two directions, but the unusual feature of the heterotic string is that the waves moving in each direction are completely different. The clockwise moving waves are the waves of the 10dimensional superstring, whereas the waves moving anticlockwise are those of the original 26dimensional bosonic string. To obtain a consistent 10 dimensional theory, 16 of the extra dimensions are interpreted as internal degrees of freedom, which are found to be related to local gauge symmetry.


Figure 1515 Compactification  
Figure 1516 CalabiYau Space 
A tendimensional space is required in order to eliminate ghosts (negative probability) in the formalism. To specify a point in this 10dimensional space requires the usual four (x, y, z, t), plus an additional six more coordinates. Suppose one of these extra coordinates is curled into a small circle, 
(see Figure 1515.) its value is now the angle in the circle. Because the radius of the circle is so small (~10^{33} cm), the value of the angle is completely unobservable. Consequently, the laws of physics should be invariant under shifts in the angle. This behaviour is reminiscent of the internal rotation mentioned earlier in the U(1) symmetry and they can be identified with each others. Therefore, distortion of this curledup dimension corresponds to the presence of spin1 gauge bosons. Actually the compactification is on a sixdimensional space, the theory of superstring severely restrict the geometrical form. It has been shown that a particular class of sixdimensional geometrical shapes called CalabiYau spaces can meet these conditions. Figure 1516 shows the ordinary space (in twodimension) with the curledup CalabiYau space at each point. It is drawn only on the intersecting grid lines for visual clarity.
It has been mentioned inTopic 12 that the transition from classical to quantum field is via the sum over all possible paths in evaluating the Action. In superstrings, there are two parameters along the worldsheet (in the integral defining the Action) and the sum is over all possible connected surfaces. In particular, it includes all the surfaces formed by stretching, pulling, twisting and otherwise deforming (without tearing) the classical worldsheet. So included in the sum are surfaces with very long, thin tentacles as shown in Figure 1518. These tentacles can be interpreted as very small closed strings that appear from out the vacuum and join on the the original string, or as closed strings which break off from the original and then disappear into the vacuum.
Interaction between two strings can be portrayed by a diagram similar to the Feynman diagram for the interaction of two point particles. In place of lines and points in the latter case, the paths of the strings become tubes. The two strings do not meet at a point, they interact by merging (from the incoming) and splitting (to the outgoing). Such a smearing of the interaction avoids the singularity at the point where the two particles meet and thus the theory of string is not plagued by infinities in point particle  
Figure 1519 Strings Interaction 
quantum field theories. Perturbation theory is used to expand the interaction into a sum of individual diagrams as shown in Figure 1519. The first one is the main part called treelevel diagram. The others with increasing number of holes are called loop diagrams, they are contributions from virtual particle pairs. If the interaction strength is small, the series would converge rapidly, otherwise calculation becomes increasingly difficult as the number of loops grows.
Figure 1520 Superstrings Theories
According to the differences in gauge symmetry, kinds of strings or branes, etc. there are five different versions of superstrings theories as shown in Figure 1520. They are related by the Sduality, which relates the strong coupling limit of one theory to the weak coupling limit of another theory; and the Tduality, which relates a theory which is compactified on a circle with radius R, to another theory compactified on a circle with radius 1/R. 
In 1995, Edward Witten gave evidence for a new, profound kind of duality. He suggested that the five theories, although apparently different in their basic construction, are all just different ways of describing the same underlying physics. The five theories are just five different windows onto this single theoretical framework (in 11dimensions), which is now called the MTheory. Mtheory contains extended objects of a whole slew of different spatial dimensions called pbrane (an object with p space dimensions, up to nine). It seems the fundamental ingredients in the Mtheory are "branes" of a variety of dimensions. The objects in the five theories show up only as strings (or membranes curled up to look like strings), which are light enough to make contact with physics as we know it. The perturbative analyses are not refined enough to discover even the existence of the supermassive extended objects of other dimensions; strings dominated the analyses and the theories was given the name of "string theories".
Currently there is no testable predictions from superstrings. However, it can be shown that at energies below 10^{16} Gev, the heterotic string theory effectively leads to an ordinary grand unified theory. Meanwhile at this moment, superstrings is the only viable theory that can unify the four interactions (See Figure 1504), and have the potential to provide explanations for all the fundamental phenomena. It could take the place at the end of the long journey toward the ultimate theory as depicted in Figure 1505 and 1506.
Each manifold has an unique potential energy, contributed by fluxes, branes and the curvature of the curledup dimensions. This energy is called the vacuum energy, because it is the energy of the spacetime when the large four dimensions are completely devoid of matter or fields. The geometry of the small manifold will try to adjust to minimize this energy. As the
By combining the laws of quantum mechanics and general relativity, it is deduced that in a region the size of the Planck length (10^{33} cm.), the vacuum fluctuations are so huge that space as we know it "boils" and becomes a froth of quantum foam.
In such a scenario, the space appears completely smooth at
the scale of 10^{12} cm.; a certain roughness starts to show up at
the scale of 10^{30} cm.; and at the scale of the Planck length space becomes a froth of probabilistic quantum foam (as shown in Figure 1524) and the notion of a simple, continuous space becomes inconsistent. According to the latest idea in superstring theory, the space at such small scale cannot be described by the Cartesian coordinates, x, y and z; it should be replaced by "noncommutative geometry", where the coordinates are represented by nondiagonal matrix. This is essentially the expression of uncertainty principle in quantum mechanics. 

Figure 1524 Quantum Foam 
A theory to describe space with the size of the Planck length has been developed lately. It is called theory of loop quantum gravity, which postulates that the minimum linear size of space is of the order of the Planck length. Space with larger expanse are built upon this lowest size such that the area and volume are quantized as shown in Figure 1525. In the loop quantum
Description of a quantum of space can be simplified by representing the
volume with a dot or node, and the area (enclosing the volume) with a line
perpendicular to the face (see Figure 1526 a and b). The numbers for the node
or line (in Figure 1526 b) indicate the size of the volume or area. In this
case, the quantum of the volume has eight units of the cubic Planck length.
Figure 1526 c and d show the connection of two volumes and its representation
in nodes and lines. The network in Figure 1528 shows the connection of many
discrete volumes; it is called the "spin network". Particles, such as electrons,
correspond to certain types of nodes, which are represented by adding more
labels on the nodes. Field, such as the electromagnetic field, are represented
by additional labels on the lines of the graph.
Predictions and Tests:
Figure 1528 Test
Nevertheless, radiation from distant cosmic explosions called gammaray bursts might provide a way to test whether the theory of loop quantum gravity is correct. Gammaray bursts occur billions of lightyears away and emit a huge amount of gamma rays within a short span. According to loop quantum gravity, each photon occupies a region of lines at each instant as it moves 
through the spin network. The discrete nature of space causes higherenergy gamma rays to travel slightly faster than lower 
energy ones. The difference is tiny, but its effect steadily accumulating during the rays' billionyear voyage. If a burst's gamma rays arrive at Earth in slightly different times according to their energy, that would be evidence for loop quantum gravity (see Figure 1528). The GLAST satellite, which is scheduled to be launched in 2005, will have the required sensitivity for this experiment.
^{1}Inertial systems of reference are either at rest or moving with
constant velocity relative to each other.
^{2}In general, the function of a field F is complex, which can be
decomposed into the form: F = F_{R} + iF_{I} similar to the
complex number c = a + ib. The real part F_{R} and the imaginary part F_{I}
correspond to particle with negative and positive charge respectively.
^{3}It is found that only fermions with lefthanded chirality
participates in weak interaction. The chirality in elementary particle is
related to the property of spin. A righthanded particle has its spin oriented
along the particle's direction of motion, while the spin of a lefthanded
particle points the other way. All neutrinos are lefthanded, and all
antineutrinos are righthanded (if the neutrino mass is
strictly zero). Other particles can exist in either state.
^{4}Parity is about the behaviour of the field upon the reversal of the
coordinate (x,y,z) to (x,y,z). Even or odd parity refers to the case when the
field remains unchanged or just change a sign. It has been long held that parity
is conserved for all physical processes. In other word, the overall parity (for
the participating particles) after an interaction should be the same as the
initial one. This simple rule is very useful for selecting permissible processes.
With some hints from experimental results, T.C. Lee and C.N. Yang
pointed out that conservation of parity may be violated in weak interaction. A
test was arranged by C. S. Wu to observe the beta decay of cobalt60 in a
magnetic field. It shows a preferred direction for the emitting electrons (the
lefthanded electrons) and thus validates the hypothesis of parity violation for
weak interaction  the mirror world behaves differently from the real world.
^{5}In the summer of 1953 C. N. Yang and Robert Mills (a graduate
student at that time) invented the SU(2) gauge theory that has become synonymous
with their names. They did not immediately publish their results because they
were aware of the difficult problems posed by the gaugefield masses and
renormalization. After studying these problems for some time and realizing that
they would not be solved in the short term, they sent their paper for
publication in the spring of 1954. The problems were eventually resolved twenty
years later in a modern version called the Standard Model.
^{6}The transition is similar to water frozen to ice, the Higgs fields
move away from a state with higher symmetry to a state without this symmetry but
in lower energy. This is called spontaneous symmetry breaking. It is related to
the fact that although the system has certain symmetry as portrayed in the "Action",
the field itself needs not to possess the same kind of symmetry. According to
GUT (Grand Unified
Theory), the transition occurred at about 10^{37} sec after the Big
Bang when temperature was 10^{29} ^{o}K corresponding to 10^{16}
Gev.
Abelian group Accelerators Asymptotic freedom Bare mass Baryon Beta decay CalabiYau space CERN, LHC Charge Carriers Colour charge Compactification Cosmic rays Einstein, Albert Electroweak interaction Elementary particles Fermi, Enrico Fermilab Tevatron Fermion generations Feynman diagram Field equation Fundamental interactions Gauge boson Gauge invariance General theory of relativity Geodesic Ghosts Gluon Grand Unified Theory (GUT) Graviton Gravity Green's function Hardon Heterotic superstring Hierarchy problem Higgs field Higgs mechanism Lee, T. D. and Yang, C. N. Loop quantum gravity Manifold Manyfold universe Maxwell, J. C. 
Meson Mtheory Newton, Isaac Neutrino NonAbelian group Parity violation Pbrane Perturbation method Quantum Chromodynamics (QCD) Quantum domain Quantum electrodynamics (QED) Quantum field theory Quark Quark confinement Renormalization Sduality Second quantization Sheldon Glashow, Abdus Salam, Steven Weinberg S matrix Special theory of relativity Spontaneous symmetry breaking Standard model Strong residual interaction SU(2) SU(3) SU(5) Supergravity Superpartners Superstrings Supersymmetry Tachyon Tduality Theory Of Everything (TOE) Topology U(1) Unifications, A Brief History of Physcis Vacuum polarization W bosons Worldsheet X bosons Yukawa, H. 
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