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In special relativity, four-momentum 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 energy and three-momentum , where is the particles and the Lorentz factor, is : The quantity of above is ordinary non-relativistic momentum of the particle and its rest mass. The four-momentum is useful in relativistic calculations because it is a Lorentz 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 . Some authors use the convention , which yields a modified definition with . It is also possible to define covariant four-momentum where the sign of the energy is reversed. == Minkowski norm == Calculating the Minkowski norm of the four-momentum gives a Lorentz invariant quantity equal (up to factors of the speed of light ) to the square of the particle's proper mass: : where we use the convention that : is the metric tensor of special relativity. The fact that the norm is negative reflects that the momentum is a timelike for massive particles. The Minkowski norm is Lorentz invariant, meaning its value is not changed by Lorentz transformations/boosting into different frames of reference. More generally, for any two and , the quantity is invariant. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Four-momentum」の詳細全文を読む スポンサード リンク
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