Fermion and meson mass generation in non-Hermitian Nambu--Jona-Lasinio models

• URL: http://arxiv.org/abs/2102.01491v1
• Date: Tue, 2 Feb 2021 13:56:11 GMT
• Title: Fermion and meson mass generation in non-Hermitian Nambu--Jona-Lasinio models
• Authors: Alexander Felski and S. P. Klevansky
• Abstract summary: We investigate the effects of non-Hermiticity on interacting fermionic systems. We do this by including non-Hermitian bilinear terms into the 3+1 dimensional Nambu--Jona-Lasinio (NJL) model.
• Score: 77.34726150561087
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate the effects of non-Hermiticity on interacting fermionic systems. We do this by including non-Hermitian bilinear terms into the 3+1 dimensional Nambu--Jona-Lasinio (NJL) model. Two possible bilinear modifications give rise to $\mathcal{PT}$ symmetric theories; this happens when the standard NJL model is extended either by a pseudovector background field $ig \bar\psi\gamma_5 B_\mu \gamma^\mu \psi$ or by an antisymmetric-tensor background field $g \bar\psi F_{\mu\nu}\gamma^\mu \gamma^\nu \psi$. The three remaining bilinears are {\it anti}-$\mathcal{PT}$-symmetric in nature, $ig \bar\psi B_\mu \gamma^\mu \psi, ig\bar\psi \gamma_5 \psi$ and $ig\bar\psi {1}\psi$, so that the Hamiltonian then has no overall symmetry. The pseudovector $ig \bar\psi\gamma_5 B_\mu \gamma^\mu \psi$ and the vector $ig \bar\psi B_\mu \gamma^\mu \psi$ combinations, are, in addition, chirally symmetric. Thus, within this framework we are able to examine the effects that the various combinations of non-Hermiticity, $\mathcal{PT}$ symmetry, chiral symmetry and the two-body interactions of the NJL model have on the existence and dynamical generation of a real effective fermion mass (a feature which is absent in the corresponding modified massless free Dirac models) as well as on the masses of the composite particles, the pseudoscalar and scalar mesonic modes ($\pi$ and $\sigma$ mesons). Our findings demonstrate that $\mathcal{PT}$ symmetry is not necessary for real fermion mass solutions to exist, rather the two-body interactions of the NJL model supersede the non-Hermitian bilinear effects. The effects of chiral symmetry are evident most clearly in the meson modes, the pseudoscalar of which will always be Goldstone in nature if the system is chirally symmetric. Second solutions of the mesonic equations are also discussed.

Related papers

• Small Circle Expansion for Adjoint QCD$_2$ with Periodic Boundary Conditions [0.0]
  Supersymmetry is found at the adjoint mass-squared $g2 hvee/ (2pi)$, where $hvee$ is the dual Coxeter number of $G$. We generalize our results to other gauge groupsG$, for which supersymmetry is found at the adjoint mass-squared $g2 hvee/ (2pi)$, where $hvee$ is the dual Coxeter number of $G$.
  arXiv  Detail & Related papers  (2024-06-24T19:07:42Z)
• Rigorous derivation of the Efimov effect in a simple model [68.8204255655161]
  We consider a system of three identical bosons in $mathbbR3$ with two-body zero-range interactions and a three-body hard-core repulsion of a given radius $a>0$.
  arXiv  Detail & Related papers  (2023-06-21T10:11:28Z)
• Towards Antisymmetric Neural Ansatz Separation [48.80300074254758]
  We study separations between two fundamental models of antisymmetric functions, that is, functions $f$ of the form $f(x_sigma(1), ldots, x_sigma(N)) These arise in the context of quantum chemistry, and are the basic modeling tool for wavefunctions of Fermionic systems.
  arXiv  Detail & Related papers  (2022-08-05T16:35:24Z)
• Some Remarks on the Regularized Hamiltonian for Three Bosons with Contact Interactions [77.34726150561087]
  We discuss some properties of a model Hamiltonian for a system of three bosons interacting via zero-range forces in three dimensions. In particular, starting from a suitable quadratic form $Q$, the self-adjoint and bounded from below Hamiltonian $mathcal H$ can be constructed. We show that the threshold value $gamma_c$ is optimal, in the sense that the quadratic form $Q$ is unbounded from below if $gammagamma_c$.
  arXiv  Detail & Related papers  (2022-07-01T10:01:14Z)
• Construction of a new three boson non-hermitian Hamiltonian associated to deformed Higgs algebra: real eigenvalues and Partial PT-symmetry [0.0]
  Fusion of Jordan-Schwinger realization of complexified $mathfraksu(2)$ with Dyson-Maleev representation. Non-hermitian Hamiltonian has real eigenvalues and eigensymmetry inducedity.
  arXiv  Detail & Related papers  (2021-11-07T06:40:47Z)
• Anti-$\mathcal{PT}$ Transformations And Complex Non-Hermitian $\mathcal{PT}$-Symmetric Superpartners [1.243080988483032]
  We propose a new formalism for constructing complex non-Hermitian $mathcalPT$-symmetric superpartners. The resulting potential is an unbroken super- and parity-time ($mathcalPT$)-symmetric shape-invariant potential. This framework allows for the unification of various areas of physics, including classical optics and quantum mechanics.
  arXiv  Detail & Related papers  (2021-08-29T12:34:47Z)
• Conformal bridge transformation and PT symmetry [0.0]
  The conformal bridge transformation (CBT) is reviewed in the light of the $mathcalPT$ symmetry. In this work we review the applications of this transformation for one- and two-dimensional systems, as well as for systems on a cosmic background, and for a conformally extended charged particle in the field of Dirac monopole.
  arXiv  Detail & Related papers  (2021-04-16T20:01:19Z)
• $\PT$ Symmetry and Renormalisation in Quantum Field Theory [62.997667081978825]
  Quantum systems governed by non-Hermitian Hamiltonians with $PT$ symmetry are special in having real energy eigenvalues bounded below and unitary time evolution. We show how $PT$ symmetry may allow interpretations that evade ghosts and instabilities present in an interpretation of the theory within a Hermitian framework.
  arXiv  Detail & Related papers  (2021-03-27T09:46:36Z)
• Non-Hermitian extension of the Nambu--Jona-Lasinio model in 3+1 and 1+1 dimensions [68.8204255655161]
  We present a non-Hermitian PT-symmetric extension of the Nambu--Jona-Lasinio model of quantum chromodynamics in 3+1 and 1+1 dimensions. We find that in both cases, in 3+1 and in 1+1 dimensions, the inclusion of a non-Hermitian bilinear term can contribute to the generated mass.
  arXiv  Detail & Related papers  (2020-04-08T14:29:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.