PT symmetry and renormalisation in quantum field theory

TY - JOUR

T1 - PT symmetry and renormalisation in quantum field theory

AU - Bender, Carl M

AU - Felski, Alexander

AU - Sarkar, Sarben

AU - Klevansky, Sandra

PY - 2021/6/15

Y1 - 2021/6/15

N2 - 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 integralformulation of quantum field theory; there is no requirement to calculateexplicitly the $\PT$ norm that occurs in Hamiltonian quantum theory. We discussexamples where $\PT$-symmetric field theories emerge from Hermitian fieldtheories due to effects of renormalisation. We also consider the effects ofrenormalisation on field theories that are non-Hermitian but $\PT$-symmetricfrom the start.

AB - 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 integralformulation of quantum field theory; there is no requirement to calculateexplicitly the $\PT$ norm that occurs in Hamiltonian quantum theory. We discussexamples where $\PT$-symmetric field theories emerge from Hermitian fieldtheories due to effects of renormalisation. We also consider the effects ofrenormalisation on field theories that are non-Hermitian but $\PT$-symmetricfrom the start.

KW - PT symmetry, renormalisation

M3 - Conference paper

SN - 1742-6588

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

ER -