TY - JOUR

T1 - Scattering in pseudo-Hermitian quantum field theory and causality violation

AU - Novikov, Oleg O.

PY - 2019/3/15

Y1 - 2019/3/15

N2 - The non-Hermitian but PT-symmetric quantum field theories are known to have a pseudo-Hermitian interpretation. However, the corresponding intertwining operator happens to be nonlocal that raises the question to what extent this nonlocality affects observable quantities. We consider the case when the intrinsic parity of the interaction terms is determined by degree of coupling constant. We show that the perturbative S matrix of the equivalent Hermitian description can be easily obtained from the perturbative S matrix of the non-Hermitian model. Namely, the first order vanishes whereas the second order is given by the real part of the second order T matrix of the non-Hermitian model. We compute directly the 2-point and 4-point correlation functions in the equivalent Hermitian model for the iφ3 model and find the results consistent with this relation. The 1-loop correction to the mass happens to be real reflecting the disappearance of 2-body decays. However, the 2 to 2 scattering amplitude obtained using LSZ formula has poles taken in principal value which implies the violation of the causality.

AB - The non-Hermitian but PT-symmetric quantum field theories are known to have a pseudo-Hermitian interpretation. However, the corresponding intertwining operator happens to be nonlocal that raises the question to what extent this nonlocality affects observable quantities. We consider the case when the intrinsic parity of the interaction terms is determined by degree of coupling constant. We show that the perturbative S matrix of the equivalent Hermitian description can be easily obtained from the perturbative S matrix of the non-Hermitian model. Namely, the first order vanishes whereas the second order is given by the real part of the second order T matrix of the non-Hermitian model. We compute directly the 2-point and 4-point correlation functions in the equivalent Hermitian model for the iφ3 model and find the results consistent with this relation. The 1-loop correction to the mass happens to be real reflecting the disappearance of 2-body decays. However, the 2 to 2 scattering amplitude obtained using LSZ formula has poles taken in principal value which implies the violation of the causality.

KW - HAMILTONIANS

KW - MECHANICS

KW - SYMMETRY

UR - http://www.scopus.com/inward/record.url?scp=85064046602&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.99.065008

DO - 10.1103/PhysRevD.99.065008

M3 - Article

VL - 99

JO - Physical review D

JF - Physical review D

SN - 2470-0010

IS - 6

M1 - 065008

ER -