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.

All of these define the relative numbers of particles in a system as decreasing exponential functions of energy ( at the particle level ) over kT, with k representing the Boltzmann constant and T representing the temperature observed at the macroscopic level.

Due to the smallness of Planck's constant it is practically impossible to realize experiments that directly reveal the wave nature of any system bigger than a few atoms but, in general, quantum mechanics considers all matter as possessing both particle and wave behaviors.

Thus, u < sub > ρ </ sub > and u < sub > θ </ sub > form a local Cartesian coordinate system attached to the particle, and tied to the path traveled by the particle.

Selective catalytic reduction ( SCR ) system in Mercedes, Euro 4 with EGR system and particle filters of MAN.

Particles can spread out by diffusion, but will not spontaneously re-order themselves ( absent changes to the system, assuming no creation of new chemical bonds, and absent external forces acting on the particle ).

Fermionic or bosonic behavior of a composite particle ( or system ) is only seen at large ( compared to size of the system ) distances.

At proximity, where spatial structure begins to be important, a composite particle ( or system ) behaves according to its constituent makeup.

The EPD used silicon solid state detectors and a time-of-flight detector system to measure changes in the energetic particle population at Jupiter as a function of position and time.

Hyperbolas arise in practice in many ways: as the curve representing the function in the Cartesian plane, as the appearance of a circle viewed from within it, as the path followed by the shadow of the tip of a sundial, as the shape of an open orbit ( as distinct from a closed and hence elliptical orbit ), such as the orbit of a spacecraft during a gravity assisted swing-by of a planet or more generally any spacecraft exceeding the escape velocity of the nearest planet, as the path of a single-apparition comet ( one travelling too fast to ever return to the solar system ), as the scattering trajectory of a subatomic particle ( acted on by repulsive instead of attractive forces but the principle is the same ), and so on.

The motion due to any one particle will vary due to the motion of all the other particles in the system.

For non-interacting particles, i. e. particles which do not interact mutually and move independently, the potential of the system is the sum of the separate potential energy for each particle, that is

where the sum is taken over all particles and their corresponding potentials ; the result is that the Hamiltonian of the system is the sum of the separate Hamiltonians for each particle.

Let ε ( n ) denote the energy of a particle in state n. As the particles do not interact, the total energy of the system is the sum of the single-particle energies.

Consider a state of the system, described by the single particle states ..., n < sub > N </ sub >.

For a single particle, this quantity is the rest mass ; for a system of bound or unbound particles, this quantity is the invariant mass.

Other units commonly used are Gaussian units ( based on the cgs system ), Lorentz – Heaviside units ( used mainly in particle physics ) and Planck units ( used in theoretical physics ).

The simplest form of the particle in a box model considers a one-dimensional system.

Usually, a system will not be in an eigenstate of the observable ( particle ) we are interested in.

An important guide for making these choices is the correspondence principle, which states that the predictions of quantum mechanics reduce to those of classical mechanics when a system moves to higher energies or — equivalently — larger quantum numbers, i. e. whereas a single particle exhibits a degree of randomness, in systems incorporating millions of particles averaging takes over and, at the high energy limit, the statistical probability of random behaviour approaches zero.

Large and small distance scales, as well as strong and weak coupling strengths, are quantities that have always marked very distinct limits of behavior of a physical system in both classical field theory and quantum particle physics.