Anticommutation relations for fermionic fields derived from basic properties of the inner product

Wen-ge Wang
Phys. Rev. A 94, 012112 – Published 20 July 2016

Abstract

For fermionic fields with nonzero mass, it is shown that the spinor factor of the anticommutation relation between creation and annihilation operators can be justified in a natural way, based on basic properties of Lorentz-invariant inner product in Hilbert space. Furthermore, from the physical point that predictions for measurement results should take real and definite values, we examine the basic requirements for inner product and propose to make certain relaxation to them. Under the relaxed requirements, there exists an alternative way of introducing the anticommutation relation, independent of the mass. In a theory with the latter type of anticommutation relation, the ultraviolet divergence may become less serious than that met in ordinary theories.

  • Received 20 April 2016

DOI:https://doi.org/10.1103/PhysRevA.94.012112

©2016 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Atomic, Molecular & Optical

Authors & Affiliations

Wen-ge Wang

  • Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China

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Issue

Vol. 94, Iss. 1 — July 2016

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