Poincaré symmetries and representations in pseudo-Hermitian quantum field theory

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.

49 pages, revtex format; discussion of fermions and the C operator extended; to match published version

References in corpus (18)

• The physics of exceptional points
• Visualization of Branch Points in PT-Symmetric Waveguides
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Symmetries and conservation laws in non-Hermitian field theories
• Spontaneously Breaking Non-Abelian Gauge Symmetry in Non-Hermitian Field Theories
• Pseudo-Hermitian approach to Goldstone's theorem in non-Abelian non-Hermitian quantum field theories
• Semi-Lorentz invariance, unitarity, and critical exponents of symplectic fermion models
• $\mathcal{P}\mathcal{T}$-symmetric $-g{\phi }^4$ theory
• Critical behavior of the PT-symmetric $i{\varphi }^3$ quantum field theory
• Foldy-Wouthuysen transformation for non-Hermitian Hamiltonians
• 't Hooft-Polyakov monopoles in non-Hermitian quantum field theory
• Relativistic PT-symmetric fermionic theories in 1+1 and 3+1 dimensions
• On the consistency of a non-Hermitian Yukawa interaction
• Discrete spacetime symmetries, second quantization, and inner products in a non-Hermitian Dirac fermionic field theory
• IR/UV mixing from local similarity maps of scalar non-Hermitian field theories
• The phase diagram and vortex properties of PT-symmetric non-Hermitian two-component superfluid
• Non-perturbative calculations for the effective potential of the $PT$ symmetric and non-Hermitian $(-g{\varphi }^4)$ field theoretic model
• Linearly stable and unstable complex soliton solutions with real energies in the Bullough-Dodd model

Cited by in corpus (2)

• Second-order pseudo-Hermitian spin-$1/2$ bosons
• Bosonic Spin-1 SOPHY