Four-vectors

Four-momentum

In special relativity, four-momentum (also called momentum-energy or momenergy ) is the generalization of the classical three-dimensional momentum to four-dimensional spacetime. Momentum is a vector in three dimensions; similarly four-momentum is a four-vector in spacetime. The contravariant four-momentum of a particle with relativistic energy E and three-momentum p = (px, py, pz) = γmv, where v is the particle's three-velocity and γ the Lorentz factor, is The quantity mv of above is 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. The above definition applies under the coordinate convention that x0 = ct. Some authors use the convention x0 = t, which yields a modified definition with p0 = E/c2. It is also possible to define covariant four-momentum pμ where the sign of the energy (or the sign of the three-momentum, depending on the chosen metric signature) is reversed. (Wikipedia).

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Four-vector | Action (physics) | Four-acceleration | Pauli–Lubanski pseudovector | Hamilton–Jacobi equation | Charged particle | Momentum | Electric charge | Hamilton's principle | Electron | Four-velocity | Four-gradient | Minkowski space | Muon | Energy | Lagrangian mechanics | Positron | Four-force | Fundamental theorem of calculus | Vector potential | Metric tensor (general relativity) | Scalar potential | Metric signature | Electromagnetic four-potential | Lorentz force | Speed of light