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
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