$\PT$ Symmetry and Renormalisation in Quantum Field Theory

• URL: http://arxiv.org/abs/2103.14864v1
• Date: Sat, 27 Mar 2021 09:46:36 GMT
• Title: $\PT$ Symmetry and Renormalisation in Quantum Field Theory
• Authors: Carl M Bender, Alexander Felski, S P Klevansky and Sarben Sarkar
• Abstract summary: Quantum systems governed by non-Hermitian Hamiltonians with $PT$ symmetry are special in having real energy eigenvalues bounded below and unitary time evolution. We show how $PT$ symmetry may allow interpretations that evade ghosts and instabilities present in an interpretation of the theory within a Hermitian framework.
• Score: 62.997667081978825
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum systems governed by non-Hermitian Hamiltonians with $\PT$ symmetry are special in having real energy eigenvalues bounded below and unitary time evolution. We argue that $\PT$ symmetry may also be important and present at the level of Hermitian quantum field theories because of the process of renormalisation. In some quantum field theories renormalisation leads to $\PT$-symmetric effective Lagrangians. We show how $\PT$ symmetry may allow interpretations that evade ghosts and instabilities present in an interpretation of the theory within a Hermitian framework. From the study of examples $\PT$-symmetric interpretation is naturally built into a path integral formulation of quantum field theory; there is no requirement to calculate explicitly the $\PT$ norm that occurs in Hamiltonian quantum theory. We discuss examples where $\PT$-symmetric field theories emerge from Hermitian field theories due to effects of renormalization. We also consider the effects of renormalization on field theories that are non-Hermitian but $\PT$-symmetric from the start.

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