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The Feynman checkerboard, or relativistic chessboard model, was Richard Feynman's sum-over-paths formulation of the kernel for a free spin- 1 / 2 particle moving in one spatial dimension. It provides a representation of solutions of the Dirac equation in (1+1)-dimensional spacetime as discrete sums.
where the first term is already the non-relativistic magnetic moment interaction, and the second term the relativistic correction of order (v/c)², but this disagrees with experimental atomic spectra by a factor of 1 ⁄ 2. It was pointed out by L. Thomas that there is a second relativistic effect: An electric field component perpendicular to ...
Since m 0 does not change from frame to frame, the energy–momentum relation is used in relativistic mechanics and particle physics calculations, as energy and momentum are given in a particle's rest frame (that is, E ′ and p ′ as an observer moving with the particle would conclude to be) and measured in the lab frame (i.e. E and p as ...
The quantity mv of above is the ordinary non-relativistic momentum of the particle and m its rest mass. The four-momentum is useful in relativistic calculations because it is a Lorentz covariant vector. This means that it is easy to keep track of how it transforms under Lorentz transformations.
This condition implies that the speed of the particle is close to the speed of light. According to the Lorentz factor formula, this requires the particle to move at roughly 85% of the speed of light. Such relativistic particles are generated in particle accelerators, [a] as well as naturally occurring in cosmic radiation.
Looking at the above formula for invariant mass of a system, one sees that, when a single massive object is at rest (v = 0, p = 0), there is a non-zero mass remaining: m 0 = E/c 2. The corresponding energy, which is also the total energy when a single particle is at rest, is referred to as "rest energy".
The energy of an ultrarelativistic particle is almost completely due to its kinetic energy = (). The total energy can also be approximated as E = γ m c 2 ≈ p c {\displaystyle E=\gamma mc^{2}\approx pc} where p = γ m v {\displaystyle p=\gamma mv} is the Lorentz invariant momentum .
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 ...