Connes has applied his work in areas of mathematics and theoretical physics, including number theory, differential geometry and particle physics.

The standard model of particle physics was developed that so far has successfully explained the properties of the nucleus in terms of these sub-atomic particles and the forces that govern their interactions.

In particle physics, antimatter is material composed of antiparticles, which have the same mass as particles of ordinary matter but have opposite charge and quantum spin.

After 1965 Sakharov returned to fundamental science and began working on particle physics and cosmology.

) In the field of particle physics, " shmoo " refers to a high energy survey instrument, as utilized at the Los Alamos National Laboratory to capture subatomic cosmic ray particles emitted from the Cygnus X-3 constellation.

Because of its low density and atomic mass, beryllium is relatively transparent to X-rays and other forms of ionizing radiation ; therefore, it is the most common window material for X-ray equipment and in particle physics experiments.

After about 10 < sup >− 11 </ sup > seconds, the picture becomes less speculative, since particle energies drop to values that can be attained in particle physics experiments.

Dark energy in its simplest formulation takes the form of the cosmological constant term in Einstein's field equations of general relativity, but its composition and mechanism are unknown and, more generally, the details of its equation of state and relationship with the Standard Model of particle physics continue to be investigated both observationally and theoretically.

Precise modern models of the Big Bang appeal to various exotic physical phenomena that have not been observed in terrestrial laboratory experiments or incorporated into the Standard Model of particle physics.

The particle physics community as a whole did not view their existence as likely in 2006 ,< ref name = PDGPentaquarks2006 > W .- M. Yao et al.

Within the prevailing Standard Model of particle physics, the number of baryons may change in multiples of three due to the action of sphalerons, although this is rare and has not been observed under experiment.

Some grand unified theories of particle physics also predict that a single proton can decay, changing the baryon number by one ; however, this has not yet been observed under experiment.

Areas relevant to cosmology include particle physics experiments and theory, including astrophysics, general relativity, and plasma physics.

One is that there is no compelling reason, using current particle physics, to expect the universe to be flat, homogeneous and isotropic ( see the cosmological principle ).

Moreover, grand unified theories of particle physics suggest that there should be magnetic monopoles in the universe, which have not been found.

The physical model behind cosmic inflation is extremely simple, however it has not yet been confirmed by particle physics, and there are difficult problems reconciling inflation and quantum field theory.

The theory of baryogenesis was worked out by Andrei Sakharov in 1967, and requires a violation of the particle physics symmetry, called CP-symmetry, between matter and antimatter.

Both the problems of baryogenesis and cosmic inflation are very closely related to particle physics, and their resolution might come from high energy theory and experiment, rather than through observations of the universe.

Dark matter has never been detected in the laboratory, and the particle physics nature of dark matter remains completely unknown.

While the detailed particle physics mechanism responsible for inflation is not known, the basic picture makes a number of predictions that have been confirmed by observation.

Theoretical condensed matter physics shares important concepts and techniques with theoretical particle and nuclear physics.

In the Schrödinger equation for this system of one negative and one positive particle, the atomic orbitals are the eigenstates of the Hamiltonian operator for the energy.

The higher value for alpha radiation is generally attributable to the high linear energy transfer ( LET ) coefficient, which is about one ionization of a chemical bond for every angstrom of travel by the alpha particle.

The same rule applies if one were to address a particle by its constituent components.

Sometimes, however, one of these negative-energy particles could be lifted out of this Dirac sea to become a positive-energy particle.

This opens the way for virtual pair production or annihilation in which a one particle quantum state may fluctuate into a two particle state and back.

It also opens the way for neutral particle mixing through processes such as the one pictured here, which is a complicated example of mass renormalization.

If denotes the quantum state of a particle ( n ) with momentum p, spin J whose component in the z-direction is σ, then one has

It is the same angular momentum one would obtain if there were just one particle of mass M moving at velocity V located at the center of mass.

( For one particle, J = L + S.

A baryon is a composite subatomic particle made up of three quarks ( as distinct from mesons, which comprise one quark and one antiquark ).

Conservation laws ensure that the measured spin of one particle must be the opposite of the measured spin of the other, so that if the spin of one particle is measured, the spin of the other particle is now instantaneously known.

The moment one observer measures the spin of one particle, he knows the spin of the other.

In the CNO cycle, four protons fuse, using carbon, nitrogen and oxygen isotopes as a catalyst, to produce one alpha particle, two positrons and two electron neutrinos.

:: * chain transfer ( the case in which one active particle enters an elementary reaction with the inactive particle which as a result becomes another active particle along with forming of another inactive particle from the initial active one );

The new particles predicted by models of grand unification cannot be observed directly at particle colliders because their masses are expected to be of the order of the so-called GUT scale, which is predicted to be just a few orders of magnitude below the Planck scale and thus far beyond the reach of currently foreseen collision experiments.

Some beyond-the-Standard Model grand unified theories ( GUTs ) explicitly break the baryon number symmetry, allowing protons to decay via the Higgs particle, magnetic monopoles or new X bosons.

This in turn led to the grand synthesis of theoretical physics which unified theories of particle and condensed matter physics through quantum field theory.

Modern interest in the concept stems from particle theories, notably the grand unified and superstring theories, which predict their existence.

Further advances in theoretical particle physics, particularly developments in grand unified theories and quantum gravity, have led to more compelling arguments that monopoles do exist.

At the colossal energy scale of 10 < sup > 15 </ sup > GeV ( far beyond the reach of our current particle accelerators ), they all become approximately the same size ( Grotz and Klapdor 1990, p. 254 ), a major motivation for speculations about grand unified theory.

In particle physics, E < sub > 6 </ sub > plays a role in some grand unified theories.

In particle physics, the Georgi – Glashow model is a particular grand unification theory ( GUT ) proposed by Howard Georgi and Sheldon Glashow in 1974.

The Boltzmann factor is normally used when discussing systems described by the canonical ensemble-for the grand canonical ensemble, it is more appropriate to use the Gibbs ' factor which takes into account particle transfer between the system and the environment.

Adding the ground state to the equation for the particle number corresponds to adding the equivalent ground state term to the grand potential:

The physical system represented by a grand canonical ensemble is in equilibrium with an external reservoir with respect to both particle and energy exchange.

* SO ( 10 ) ( physics ), a term used in particle physics, one of the grand unified theories is based on the SO ( 10 ) Lie group

By providing a better physical understanding of the renormalization procedure invented in the 1940s, the renormalization group sparked what has been called the " grand synthesis " of theoretical physics, uniting the quantum field theoretical techniques used in particle physics and condensed matter physics into a single theoretical framework.