<i>PT</i> symmetry and renormalisation in quantum field theory
Carl M. Bender, Alexander Felski, Sarkar, Sarben; id_orcid 0000-0003-1369-7794, Sandra Pamela Klevansky
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<br/>formulation of quantum field theory; there is no requirement to calculate<br/>explicitly the $\PT$ norm that occurs in Hamiltonian quantum theory. We discuss<br/>examples where $\PT$-symmetric field theories emerge from Hermitian field<br/>theories due to effects of renormalisation. We also consider the effects of<br/>renormalisation on field theories that are non-Hermitian but $\PT$-symmetric<br/>from the start.<br/>