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Physics · 术语表

什么是 Four-vectors？

Definition 6.1 University Physics — Year 3 · 第 6 章 — Covariant Electromagnetism

A four-vector is a quadruple $a^\mu = (a^0, \vect a)$ , $\mu = 0, 1, 2, 3$ , whose components mix under a boost exactly as $(ct, \vect r)$ do:

a'^0 = \gamma(a^0 - \beta a^1) , \qquad a'^1 = \gamma(a^1 - \beta a^0) , \qquad a'^{2,3} = a^{2,3}

for a boost at $\beta c$ along $x$ . Any two four-vectors give the invariant scalar product $a\cdot b = a^0b^0 - \vect a\cdot\vect b$ , the same number in every frame — the pattern behind $c^2t^2 - x^2$ and $E^2 - p^2c^2$ . Position $(ct, \vect r)$ and four-momentum $(E/c, \vect p)$ are the two we have; electromagnetism now supplies three more: current, potential, and wave-vector.

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