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  2. Energy–momentum relation - Wikipedia

    en.wikipedia.org/wiki/Energy–momentum_relation

    In physics, the energy–momentum relation, or relativistic dispersion relation, is the relativistic equation relating total energy (which is also called relativistic energy) to invariant mass (which is also called rest mass) and momentum. It is the extension of mass–energy equivalence for bodies or systems with non-zero momentum.

  3. List of relativistic equations - Wikipedia

    en.wikipedia.org/wiki/List_of_relativistic_equations

    This is the formula for the relativistic doppler shift where the difference in velocity between the emitter and observer is not on the x-axis. There are two special cases of this equation. The first is the case where the velocity between the emitter and observer is along the x-axis. In that case θ = 0, and cos θ = 1, which gives:

  4. Relativistic mechanics - Wikipedia

    en.wikipedia.org/wiki/Relativistic_mechanics

    The relativistic four-velocity, that is the four-vector representing velocity in relativity, is defined as follows: = = (,) In the above, is the proper time of the path through spacetime, called the world-line, followed by the object velocity the above represents, and

  5. Relativistic particle - Wikipedia

    en.wikipedia.org/wiki/Relativistic_particle

    In other words, a massive particle is relativistic when its total mass-energy is at least twice its rest mass. 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.

  6. Relativistic Euler equations - Wikipedia

    en.wikipedia.org/wiki/Relativistic_Euler_equations

    The equations of motion are contained in the continuity equation of the stress–energy tensor: =, where is the covariant derivative. [5] For a perfect fluid, = (+) +. Here is the total mass-energy density (including both rest mass and internal energy density) of the fluid, is the fluid pressure, is the four-velocity of the fluid, and is the metric tensor. [2]

  7. Relativistic Lagrangian mechanics - Wikipedia

    en.wikipedia.org/wiki/Relativistic_Lagrangian...

    The relativistic Lagrangian can be derived in relativistic mechanics to be of the form: = (˙) (, ˙,). Although, unlike non-relativistic mechanics, the relativistic Lagrangian is not expressed as difference of kinetic energy with potential energy, the relativistic Hamiltonian corresponds to total energy in a similar manner but without including rest energy.

  8. Relativistic dynamics - Wikipedia

    en.wikipedia.org/wiki/Relativistic_dynamics

    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.

  9. Mathematical formulation of the Standard Model - Wikipedia

    en.wikipedia.org/wiki/Mathematical_formulation...

    The electric charge Q, third component of weak isospin T 3 (also called T z, I 3 or I z) and weak hypercharge Y W are related by = +, (or by the alternative convention Q = T 3 + Y W). The first convention, used in this article, is equivalent to the earlier Gell-Mann–Nishijima formula. It makes the hypercharge be twice the average charge of a ...

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