P T -symmetric quantum field theory in D dimensions

TY - JOUR

T1 - P T -symmetric quantum field theory in D dimensions

AU - Bender, Carl M.

AU - Hassanpour, Nima

AU - Klevansky, S. P.

AU - Sarkar, Sarben

PY - 2018/12/15

Y1 - 2018/12/15

N2 - PT-symmetric quantum mechanics began with a study of the Hamiltonian H=p2+x2(ix)μ. A surprising feature of this non-Hermitian Hamiltonian is that its eigenvalues are discrete, real, and positive when μ≥0. This paper examines the corresponding quantum-field-theoretic Hamiltonian H=12( φ)2+12φ2(iφ)μ in D-dimensional spacetime, where φ is a pseudoscalar field. It is shown how to calculate the Green's functions as series in powers of μ directly from the Euclidean partition function. Exact finite expressions for the vacuum energy density, all of the connected n-point Green's functions, and the renormalized mass to order μ are derived for 0≤D<2. For D≥2 the one-point Green's function and the renormalized mass are divergent, but perturbative renormalization can be performed. The remarkable spectral properties of PT-symmetric quantum mechanics appear to persist in PT-symmetric quantum field theory.

AB - PT-symmetric quantum mechanics began with a study of the Hamiltonian H=p2+x2(ix)μ. A surprising feature of this non-Hermitian Hamiltonian is that its eigenvalues are discrete, real, and positive when μ≥0. This paper examines the corresponding quantum-field-theoretic Hamiltonian H=12( φ)2+12φ2(iφ)μ in D-dimensional spacetime, where φ is a pseudoscalar field. It is shown how to calculate the Green's functions as series in powers of μ directly from the Euclidean partition function. Exact finite expressions for the vacuum energy density, all of the connected n-point Green's functions, and the renormalized mass to order μ are derived for 0≤D<2. For D≥2 the one-point Green's function and the renormalized mass are divergent, but perturbative renormalization can be performed. The remarkable spectral properties of PT-symmetric quantum mechanics appear to persist in PT-symmetric quantum field theory.

UR - http://www.scopus.com/inward/record.url?scp=85059395696&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.98.125003

DO - 10.1103/PhysRevD.98.125003

M3 - Article

AN - SCOPUS:85059395696

SN - 2470-0010

VL - 98

SP - 1

EP - 9

JO - Physical Review D

JF - Physical Review D

IS - 12

M1 - 125003

ER -