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In other words, the configuration of particle A in state 1 and particle B in state 2 is different from the case in which particle B is in state 1 and particle A is in state 2. This assumption leads to the proper (Boltzmann) statistics of particles in the energy states, but yields non-physical results for the entropy, as embodied in the Gibbs ...
Thus in non-relativistic QM one has for a many particle system ψ(r 1, r 2, r 3, ..., t, σ 1, σ 2, σ 3...). In relativistic mechanics , the spatial coordinates and coordinate time are not absolute; any two observers moving relative to each other can measure different locations and times of events .
The form of the relativistic Breit–Wigner distribution arises from the propagator of an unstable particle, [4] which has a denominator of the form p 2 − M 2 + i M Γ . (Here, p 2 is the square of the four-momentum carried by that particle in the tree Feynman diagram involved.)
Due to the non-interacting quality, each available single-particle level (with energy level ϵ) forms a separate thermodynamic system in contact with the reservoir. That is, the number of particles within the overall system that occupy a given single particle state form a sub-ensemble that is also grand canonical ensemble; hence, it may be ...
In physics, relativistic mechanics refers to mechanics compatible with special relativity (SR) and general relativity (GR). It provides a non- quantum mechanical description of a system of particles, or of a fluid , in cases where the velocities of moving objects are comparable to the speed of light c .
If particle-antiparticle creation is allowed, then once the thermal energy is a significant fraction of , particle-antiparticle creation will occur and begin to increase the number of particles while generating antiparticles (the number of particles is not conserved, but instead the conserved quantity is the difference between particle number ...
However the total energy of the particle E and its relativistic momentum p are frame-dependent; relative motion between two frames causes the observers in those frames to measure different values of the particle's energy and momentum; one frame measures E and p, while the other frame measures E ′ and p ′, where E ′ ≠ E and p ′ ≠ p ...
The general equation can then be written as [6] = + + (),. where the "force" term corresponds to the forces exerted on the particles by an external influence (not by the particles themselves), the "diff" term represents the diffusion of particles, and "coll" is the collision term – accounting for the forces acting between particles in collisions.