PT symmetry and renormalisation in quantum field theory

Carl M Bender, Alexander Felski, Sarben Sarkar, Sandra Klevansky

Research output: Contribution to journalConference paperpeer-review


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.
Original languageEnglish
JournalJournal of Physics: Conference Series
Publication statusAccepted/In press - 15 Jun 2021


  • PT symmetry, renormalisation


Dive into the research topics of 'PT symmetry and renormalisation in quantum field theory'. Together they form a unique fingerprint.

Cite this