## 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 renormalisation. We also consider the effects of

renormalisation on field theories that are non-Hermitian but $\PT$-symmetric

from the start.

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 renormalisation. We also consider the effects of

renormalisation on field theories that are non-Hermitian but $\PT$-symmetric

from the start.

Original language | English |
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Journal | Journal of Physics: Conference Series |

Publication status | Accepted/In press - 15 Jun 2021 |

## Keywords

- PT symmetry, renormalisation

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