Poincaré symmetries and representations in pseudo-Hermitian quantum field theory
arXiv:2307.16805 · doi:10.1103/PhysRevD.109.065012
Abstract
This paper explores quantum field theories with pseudo-Hermitian Hamiltonians, where PT-symmetric Hamiltonians serve as a special case. In specific regimes, these pseudo-Hermitian Hamiltonians have real eigenspectra, orthogonal eigenstates, and unitary time evolution. So far, most pseudo-Hermitian quantum field theories have been constructed using analytic continuation or by adding non-Hermitian terms to otherwise Hermitian Hamiltonians. However, in this paper, we take a different approach. We construct pseudo-Hermitian scalar and fermionic quantum field theories from first principles by extending the Poincaré algebra to include non-Hermitian generators. This allows us to develop consistent pseudo-Hermitian quantum field theories, with Lagrangian densities that transform appropriately under the proper Poincaré group. By doing so, we establish a more solid theoretical foundation for the emerging field of non-Hermitian quantum field theory.
arXiv comment49 pages, revtex format; discussion of fermions and the C operator extended; to match published version
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