non-Hermitian Quantum Field Theories Research Articles

Non-Hermitian gauge field theories and BPS limits

We present an overview of some key results obtained in a recent series devoted to non-Hermitian quantum field theories for which we systematically modify the underlying symmetries. Particular attention is placed on the interplay between the continuous symmetry group that we alter from global to local, from Abelian to non-Abelian, from rank one to generic rank N, and the discrete anti-linear modified CPT-symmetries. The presence of the latter guarantees the reality of the mass spectrum in a certain parameter regime. We investigate the extension of Goldstone’s theorem and the Higgs mechanism, which we demonstrate to work in the conventional fashion in the CPT-symmetric regime, but which needs to be modified technically at the standard exceptional points of the mass spectrum and entirely fails at what we refer to as zero exceptional points as well as in the broken CPT-symmetric regime. In the full non-Hermitian non-Abelian gauge theory we identify the t’Hooft-Polyakov monopoles by means of a fourfold Bogomol’nyi-Prasad-Sommerfield (BPS) limit. We investigate this limit further for other types of non-Hermitian field theories in 1+1 dimensions that possess complex super-exponential and inverse hyperbolic kink/anti-kink solutions and for 3+1 dimensional Skyrme models for which we find new types of complex solutions, that all have real energies due to the presence of different types of CPT-symmetries.

PT -symmetric non-Hermitian quantum field theories with supersymmetry

We formulate supersymmetric non-Hermitian quantum field theories with PT symmetry, starting with free chiral boson/fermion models and then including trilinear superpotential interactions. We consider models with both Dirac and Majorana fermions, analyzing them in terms of superfields and at the component level. We also discuss the relation between the equations of motion, the (non-)invariance of the Lagrangian and the (non-)conservation of the supercurrents in the two models. We exhibit a similarity transformation that maps the free-field supersymmetric PT-symmetric Dirac model to a supersymmetric Hermitian theory, but there is, in general, no corresponding similarity transformation for the Majorana model. In this model, we find generically a mass splitting between bosons and fermions, even though its construction is explicitly supersymmetric, offering a novel non-Hermitian mechanism for soft supersymmetry breaking.

Pseudo-Hermitian approach to Goldstone’s theorem in non-Abelian non-Hermitian quantum field theories

We generalise previous studies on the extension of Goldstone's theorem from Hermitian to non-Hermitian quantum field theories with Abelian symmetries to theories possessing a glocal non-Abelian symmetry. We present a detailed analysis for a non-Hermitian field theory with two complex two component scalar fields possessing a SU(2)-symmetry and indicate how our finding extend to the general case. In the PT-symmetric regime and at the standard exceptional point the Goldstone theorem is shown to apply, although different identification procedures need to be employed. At the zero exceptional points the Goldstone boson can not be identified. Comparing our approach, based on the pseudo-Hermiticity of the model, to an alternative approach that utilises surface terms to achieve compatibility for the non-Hermitian system, we find that the explicit forms of the Goldstone boson fields are different.

Goldstone bosons in different PT-regimes of non-Hermitian scalar quantum field theories

We study the interplay between spontaneously breaking global continuous and discrete antilinear symmetries in a newly proposed general class of non-Hermitian quantum field theories containing a mixture of complex and real scalar fields. We analyse the model for different types of global symmetry preserving and breaking vacua. In addition, the models are symmetric under various types of discrete antilinear symmetries composed out of nonstandard simultaneous charge conjugations, time-reversals and parity transformations; CPT. While the global symmetry governs the existence of massless Goldstone bosons, the discrete one controls the precise expression of the Goldstone bosons in terms of the original fields in the model and its physical regimes. We show that even when the CPT-symmetries are broken on the level of the action expanded around different types of vacua, the mass spectra might still be real when the symmetry is preserved at the tree approximation and the breaking only occurs at higher order. We discuss the parameter space of some of the models in the proposed class and identify physical regimes in which massless Goldstone bosons emerge when the vacuum spontaneously breaks the global symmetry or equivalently when the corresponding Noether currents are conserved. The physical regions are bounded by exceptional points in different ways. There exist special points in parameter space for which massless bosons may occur already before breaking the global symmetry. However, when the global symmetry is broken at these points they can no longer be distinguished from genuine Goldstone bosons.

REPRESENTATION DEPENDENCE OF SUPERFICIAL DEGREE OF DIVERGENCES IN QUANTUM FIELD THEORY

In this work, we investigate a very important but unstressed result in the work of C. M. Bender, J.-H. Chen, and K. A. Milton, J. Phys. A39, 1657 (2006). These authors have calculated the vacuum energy of the iϕ3 scalar field theory and its Hermitian equivalent theory up to g4 order of calculations. While all the Feynman diagrams of the iϕ3 theory are finite in 0+1 space–time dimensions, some of the corresponding Feynman diagrams in the equivalent Hermitian theory are divergent. In this work, we show that the divergences in the Hermitian theory originate from superrenormalizable, renormalizable and nonrenormalizable terms in the interaction Hamiltonian even though the calculations are carried out in the 0+1 space–time dimensions. Relying on this interesting result, we raise a question: Is the superficial degree of divergence of a theory is representation dependent? To answer this question, we introduce and study a class of non-Hermitian quantum field theories characterized by a field derivative interaction Hamiltonian. We showed that the class is physically acceptable by finding the corresponding class of metric operators in a closed form. We realized that the obtained equivalent Hermitian and the introduced non-Hermitian representations have coupling constants of different mass dimensions which may be considered as a clue for the possibility of considering nonrenormalizability of a field theory as a nongenuine problem. Besides, the metric operator is supposed to disappear from path integral calculations which means that physical amplitudes can be fully obtained in the simpler non-Hermitian representation.

PT-symmetric kinks

Some kinks for non-Hermitian quantum field theories in $1+1$ dimensions are constructed. A class of models where the soliton energies are stable and real are found. Although these kinks are not Hermitian, they are symmetric under $PT$ transformations.

Properties of non-hermitian quantum field theories

Dans cet article, je traite des systemes quantiques dont l'hamiltonien est non-hermitien mais dont les niveaux d'energie sont tous reels et positifs. De telles theories doivent etre symetriques sous CPT, mais pas sous P et T separement. Recemment, des systemes quantiques avec de telles proprietes ont ete etudies en detail. Dans cet article, j'etends ces resultats aux theories des champs quantiques. Parmi les systemes dont je parle, se trouvent les theories -Φ 4 et iΦ 3 . Toutes ces theories ont des proprietes inattendues et remarquables. Je decris les fonctions de Green qui apparaissent dans ces theories et je presente de nouveaux resultats concernant les etats lies, la renormalisation et les calculs non-perturbatifs.

Bound states of non-Hermitian quantum field theories

The spectrum of the Hermitian Hamiltonian 12p2+12m2x2+gx4 (g>0), which describes the quantum anharmonic oscillator, is real and positive. The non-Hermitian quantum-mechanical Hamiltonian H=12p2+12m2x2−gx4, where the coupling constant g is real and positive, is PT-symmetric. As a consequence, the spectrum of H is known to be real and positive as well. Here, it is shown that there is a significant difference between these two theories: when g is sufficiently small, the latter Hamiltonian exhibits a two-particle bound state while the former does not. The bound state persists in the corresponding non-Hermitian PT-symmetric −gφ4 quantum field theory for all dimensions 0⩽D<3 but is not present in the conventional Hermitian gφ4 field theory.

Bound states of non-Hermitian quantum field theories

Bound states of non-Hermitian quantum field theories