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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 .
Similar is the situation in the case of charged-particle optics. Let us recall that in relativistic quantum mechanics too one has a similar problem of understanding the relativistic wave equations as the nonrelativistic approximation plus the relativistic correction terms in the quasi-relativistic regime.
The following notations are used very often in special relativity: Lorentz factor = where = and v is the relative velocity between two inertial frames.. For two frames at rest, γ = 1, and increases with relative velocity between the two inertial frames.
Relativistic quantum mechanics (RQM) is quantum mechanics applied with special relativity. Although the earlier formulations, like the Schrödinger picture and Heisenberg picture were originally formulated in a non-relativistic background, a few of them (e.g. the Dirac or path-integral formalism) also work with special relativity.
In physics, specifically relativistic quantum mechanics (RQM) and its applications to particle physics, relativistic wave equations predict the behavior of particles at high energies and velocities comparable to the speed of light. In the context of quantum field theory (QFT), the equations determine the dynamics of quantum fields.
In theoretical physics, Pauli–Villars regularization (P–V) is a procedure that isolates divergent terms from finite parts in loop calculations in field theory in order to renormalize the theory.
The development of non-relativistic quantum mechanics in the early twentieth century preserved the Newtonian concept of time in the Schrödinger equation. The ability of non-relativistic quantum mechanics and special relativity to successfully describe observations motivated efforts to extend quantum concepts to the relativistic domain.
These two types of relativistic particles are remarked as massless and massive, respectively. In experiments, massive particles are relativistic when their kinetic energy is comparable to or greater than the energy = corresponding to their rest mass. In other words, a massive particle is relativistic when its total mass-energy is at least twice ...