Is space-time symmetry a suitable generalization of parity-time symmetry?

PAOLO AMORE; FRANCISCO M. FERNÁNDEZ; JAVIER GARCIA

ANNALS OF PHYSICS (NEW YORK)

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: New York; Año: 2014 vol. 350 p. 533 - 548

0003-4916

We discuss space-time symmetric Hamiltonian operators of theform H = H0 + igH ′ , where H0 is Hermitian and g real. H0 isinvariant under the unitary operations of a point group G whileH ′ is invariant under transformation by elements of a subgroup G′of G. If G exhibits irreducible representations of dimension greaterthan unity, then it is possible that H has complex eigenvalues forsufficiently small nonzero values of g. In the particular case that His parity-time symmetric then it appears to exhibit real eigenvaluesfor all 0 < g < gc , where gc is the exceptional point closest to theorigin. Point-group symmetry and perturbation theory enable oneto predict whether H may exhibit real or complex eigenvalues forg > 0. We illustrate the main theoretical results and conclusions ofthis paper by means of two- and three-dimensional Hamiltoniansexhibiting a variety of different point-group symmetries.