A.6 Clifford algebras and spinors

对照

The Clifford algebra associated to an inner product $(\cdot ,\cdot )$ satisfies the relation

$$uv+vu=2(u,v)$$

With the choice of signature for the Minkowski inner product above, the Clifford algebra is isomorphic to a real matrix algebra

$$\mathrm{Cliff}(3,1)=M(4,\mathbf{R})$$

Under this isomorphism, basis element of Minkowski space correspond to $\gamma$ matrices, which satisfy

$${\gamma }_0^2=-1,{\gamma }_1^2={\gamma }_2^2={\gamma }_3^2=1$$

Explicit choices of these matrices are described in sections 41.2, 47.2 and 47.3.

The Dirac equation is taken to be

$$(/\partial -m)\psi (x)=0$$

see section 47.1.

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上一节：A.5 Special relativity

附录：约定与记号

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正文：英文 · 原著转录

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原书 PDF · 印刷页 536

来源版本：2025-10-20

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