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In statistical physics, the kinetic theory of gases applies Newton's laws of motion to large numbers (typically on the order of the Avogadro number) of particles. Kinetic theory can explain, for example, the pressure that a gas exerts upon the container holding it as the aggregate of many impacts of atoms, each imparting a tiny amount of momentum.
However, perturbation theory (and with it the concept of a "force-mediating particle") fails in other situations. These include low-energy quantum chromodynamics, bound states , and solitons . The interactions between all the particles described by the Standard Model are summarized by the diagrams on the right of this section.
For example, when rotating a stationary (zero momentum) spin-5 particle about its center, is a rotation in 3D space (an element of ()), while () is an operator whose domain and range are each the space of possible quantum states of this particle, in this example the projective space associated with an 11-dimensional complex Hilbert space .
the mass–energy equivalence formula which gives the energy in terms of the momentum and the rest mass of a particle. The equation for the mass shell is also often written in terms of the four-momentum ; in Einstein notation with metric signature (+,−,−,−) and units where the speed of light c = 1 {\displaystyle c=1} , as p μ p μ ≡ p ...
J. J. Sakurai was born in Tokyo in 1933 and moved to the United States when he was a high school student. He studied physics at Harvard and Cornell, where he proposed his theory of weak interactions.
In 1998–99 Merab Gogberashvili published on arXiv (and subsequently in peer-reviewed journals) a number of articles where he showed that if the Universe is considered as a thin shell (a mathematical synonym for "brane") expanding in 5-dimensional space then it is possible to obtain one scale for particle theory corresponding to the 5 ...
In quantum mechanics, the Landau–Yang theorem is a selection rule for particles that decay into two on-shell photons. The theorem states that a massive particle with spin 1 cannot decay into two photons. [original 1] [original 2]
This rule does not hold for bosons. In quantum field theory, a state or a wavefunction is described by field operators operating on some basic state called the vacuum . In order for the operators to project out the symmetric or antisymmetric component of the creating wavefunction, they must have the appropriate commutation law.