Читать книгу Foundations of Quantum Field Theory - Klaus D Rothe - Страница 41

Fields describing fermions which are their own anti-particles are said to be self-conjugate and have the Fourier representation

with the property (4.73). These fields are real,

and play the role of real scalar fields in the case of spin 1/2 fields.

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¹P.A.M. Dirac, The Principles of Quantum Mechanics, 4th edn. (Oxford University Press, Oxford 1958).

²Here and in what follows: in formulae which hold generally, without reference to a particular basis such as the Dirac representation, we omit the subscript D.

³The reason for introducing c will become clear in Chapter 7, Eq. (7.15).

⁴The minus sign is a consequence of our Dirac scalar product.

⁵We follow in general the notation of S. Weinberg, Phys. Rev. 133 (1964) B1318.

⁶Substituting (4.27) into (4.28) yields . Noting that with our definitions (4.24) for tμ and , we have , we recover the Klein–Gordon equation, as desired.

⁷H. Weyl, The Theory of Groups and Quantum Mechanics (Dover Publications, Inc. New York, 1931).

⁸See Chapter 5 for this terminology.

⁹Note that

where S is given by (4.40). This agrees with the usual V − A coupling of neutrinos in the weak interactions.