Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories

TY - JOUR

T1 - Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories

AU - Alexandre, Jean

AU - Ellis, John

AU - Millington, Peter

AU - Seynaeve, Dries

N1 - 20 pages, revtex format

PY - 2018/8/1

Y1 - 2018/8/1

N2 - We demonstrate the extension to PT-symmetric field theories of the Goldstone theorem, confirming that the spontaneous appearance of a field vacuum expectation value via minimisation of the effective potential in a non-Hermitian model is accompanied by a massless scalar boson. Laying a basis for our analysis, we first show how the conventional quantisation of the path-integral formulation of quantum field theory can be extended consistently to a non-Hermitian model by considering PT conjugation instead of Hermitian conjugation. The extension of the Goldstone theorem to a PT-symmetric field theory is made possible by the existence of a conserved current that does not, however, correspond to a symmetry of the non-Hermitian Lagrangian. In addition to extending the proof of the Goldstone theorem to a PT-symmetric theory, we exhibit a specific example in which we verify the existence of a massless boson at the tree and one-loop levels.

AB - We demonstrate the extension to PT-symmetric field theories of the Goldstone theorem, confirming that the spontaneous appearance of a field vacuum expectation value via minimisation of the effective potential in a non-Hermitian model is accompanied by a massless scalar boson. Laying a basis for our analysis, we first show how the conventional quantisation of the path-integral formulation of quantum field theory can be extended consistently to a non-Hermitian model by considering PT conjugation instead of Hermitian conjugation. The extension of the Goldstone theorem to a PT-symmetric field theory is made possible by the existence of a conserved current that does not, however, correspond to a symmetry of the non-Hermitian Lagrangian. In addition to extending the proof of the Goldstone theorem to a PT-symmetric theory, we exhibit a specific example in which we verify the existence of a massless boson at the tree and one-loop levels.

KW - hep-th

KW - hep-ph

KW - quant-ph

U2 - 10.1103/PhysRevD.98.045001

DO - 10.1103/PhysRevD.98.045001

M3 - Article

SN - 1550-7998

VL - 98

JO - Physical Review D (Particles, Fields, Gravitation and Cosmology)

JF - Physical Review D (Particles, Fields, Gravitation and Cosmology)

M1 - 045001

ER -