Infinite class of PT-symmetric theories from one timelike liouville Lagrangian

TY - JOUR

T1 - Infinite class of PT-symmetric theories from one timelike liouville Lagrangian

AU - Bender, Carl M.

AU - Hook, Daniel W.

AU - Mavromatos, Nick E.

AU - Sarkar, Sarben

PY - 2014/12/3

Y1 - 2014/12/3

N2 - Logarithmic timelike Liouville quantum field theory has a generalized PT invariance, where T is the time-reversal operator and P stands for an S-duality reflection of the Liouville field φ. In Euclidean space, the Lagrangian of such a theory L=12(∇φ)2-igφexp(iaφ) is analyzed using the techniques of PT-symmetric quantum theory. It is shown that L defines an infinite number of unitarily inequivalent sectors of the theory labeled by the integer n. In one-dimensional space (quantum mechanics), the energy spectrum is calculated in the semiclassical limit and the mth energy level in the nth sector is given by Em,n∼(m+1/2)2a2/(16n2).

AB - Logarithmic timelike Liouville quantum field theory has a generalized PT invariance, where T is the time-reversal operator and P stands for an S-duality reflection of the Liouville field φ. In Euclidean space, the Lagrangian of such a theory L=12(∇φ)2-igφexp(iaφ) is analyzed using the techniques of PT-symmetric quantum theory. It is shown that L defines an infinite number of unitarily inequivalent sectors of the theory labeled by the integer n. In one-dimensional space (quantum mechanics), the energy spectrum is calculated in the semiclassical limit and the mth energy level in the nth sector is given by Em,n∼(m+1/2)2a2/(16n2).

UR - http://www.scopus.com/inward/record.url?scp=84918575289&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.113.231605

DO - 10.1103/PhysRevLett.113.231605

M3 - Article

AN - SCOPUS:84918575289

SN - 0031-9007

VL - 113

JO - Physical Review Letters

JF - Physical Review Letters

IS - 23

ER -