The Nambu---Jona-Lasinio model is reviewed in its flavor SU(2) and SU(3) versions applied to quarks. dynamical generation of quark masses demonstrated as a feature chiral symmetry breaking. One finds that the associated meson spectra, well static properties, can be described. Current-algebra results, which arise consequence considerations, automatically hold for this are explicitly do so. These include Goldberger-Treiman Gell-Mann-Oakes-Renner relations. Effects finite temperature, chemical...

The hadronization process for quarks combining into two mesons, q\bar q\to MM' at temperature T is described within the SU(3) Nambu- Jona-Lasinio model with finite current quark masses. Invariant matrix elements, cross-sections and transition rates are calculated to leading order in a 1/N_c expansion. Four independent classes, u\bar d, s, u s\bar s\to hadrons analysed, yield found be dominated by pion production. Threshold behaviour determined exothermic or endothermic nature of processes...

The proper-time Schwinger formalism is implemented in a derivation of the gap equation and total energy system interacting fermions described by Nambu--Jona-Lasinio model that minimally coupled to constant electromagnetic field. Inclusion Lagrange multiplier term vary scalar density enables calculation curves as function plays role an order parameter. A consistent gauge- Lorentz-invariant regularization divergent quantities occur this theory calculating relation. Specializing electric...

We reexamine the recent instanton motivated studies of Alford, Rajagopal, and Wilczek, Berges Rajagopal in framework standard SU(2) Nambu--Jona-Lasinio (NJL) model. The chiral phase diagram is calculated temperature-density plane, pressure evaluated as function quark density. Obtaining simple approximate relations describing T-\ensuremath{\mu} $T\ensuremath{-}{p}_{F}$ transition lines, we find that results based model NJL are identical. diquark line also given.

$\mathcal{P}\mathcal{T}$-symmetric quantum mechanics began with a study of the Hamiltonian $H={p}^{2}+{x}^{2}(ix{)}^{ϵ}$. A surprising feature this non-Hermitian is that its eigenvalues are discrete, real, and positive when $ϵ\ensuremath{\ge}0$. This paper examines corresponding quantum-field-theoretic $H=\frac{1}{2}(\ensuremath{\nabla}\ensuremath{\phi}{)}^{2}+\frac{1}{2}{\ensuremath{\phi}}^{2}(i\ensuremath{\phi}{)}^{ϵ}$ in $D$-dimensional spacetime, where $\ensuremath{\phi}$ pseudoscalar...

This Letter examines the effectiveness of Dyson-Schwinger (DS) equations as a calculational tool in quantum field theory. The DS are an infinite sequence coupled that satisfied exactly by connected Green's functions G_{n} These link lower to higher and, if they truncated, resulting finite system is underdetermined. simplest way solve underdetermined set all function(s) zero and then determined for first few functions. G_{1} or G_{2} so obtained can be compared with exact results solvable...

This paper examines chains of $N$ coupled harmonic oscillators. In isolation, the $j$th oscillator ($1\leq j\leq N$) has natural frequency $\omega_j$ and is described by Hamiltonian $\frac{1}{2}p_j^2+\frac{1}{2}\omega_j^2x_j^2$. The oscillators are adjacently with coupling constants that purely imaginary; to $(j+1)$st bilinear form $i\gamma x_jx_{j+1}$ ($\gamma$ real). complex Hamiltonians for these systems exhibit {\it partial} $\mathcal{PT}$ symmetry; is, they invariant under $i\to-i$...

The Hamiltonian for a PT-symmetric chain of coupled oscillators is constructed. It shown that if the loss-gain parameter $\gamma$ uniform all oscillators, then as number increases, region unbroken PT-symmetry disappears entirely. However, localized in sense it decreases more distant unbroken-PT-symmetric persists even approaches infinity. In continuum limit oscillator system described by pair wave equations, and impurity leads to pseudo-bound state. also planar configuration can have...

The Dyson-Schwinger (DS) equations for a quantum field theory in $D$-dimensional space-time are an infinite sequence of coupled integro-differential that satisfied exactly by the Green's functions theory. This is underdetermined because if DS truncated to finite sequence, there always more than equations. An approach this problem close system setting highest function(s) zero. One can examine accuracy procedure $D=0$ special case just polynomial whose roots functions. For closed one calculate...

The dissipative phenomena of a quark plasma are studied within the two flavor Nambu--Jona-Lasinio model at and above chiral phase transition. In medium, qq, qq\ifmmode\bar\else\textasciimacron\fi{}, q\ifmmode\bar\else\textasciimacron\fi{}q\ifmmode\bar\else\textasciimacron\fi{} cross sections calculated to order 1/${\mathit{N}}_{\mathit{c}}$ correspond \ensuremath{\pi} \ensuremath{\sigma} meson exchanges in s t channels. angle-integrated qq\ifmmode\bar\else\textasciimacron\fi{} section...

The 1/${\mathit{N}}_{\mathit{c}}$ expansion is developed for the Nambu--Jona-Lasinio model, a commonly used low-energy model of QCD. next to leading order in this that represents pion and sigma meson exchange gap equation evaluated perturbatively. These contributions are seen be differing sign, feature due their opposite parities. Physically one can interpret as giving rise screening (\ensuremath{\pi}) or antiscreening (\ensuremath{\sigma}) bare four-point interaction. As consequence higher...

Abstract A comparative study of entropy dynamics as an indicator physical behavior in open two-state system with balanced gain and loss is presented. To begin with, we illustrate the phase portrait this non-Hermitian model on Bloch sphere, elucidating changes one moves across transition boundary, well emergent feature unidirectional state evolution spontaneously broken <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi class="MJX-tex-calligraphic"...

An elementary field-theoretic mechanism is proposed that allows one Lagrangian to describe a family of particles having different masses but otherwise similar physical properties. The relies on the observation Dyson-Schwinger equations derived from can have many equally valid solutions. Nonunique solutions arise when functional integral for Green's functions quantum field theory converges in pairs Stokes' wedges complex-field space, and are physically viable if $\mathcal{P}\mathcal{T}$ symmetric.

Relativistic PT-symmetric fermionic interacting systems are studied in 1+1 and 3+1 dimensions. The objective is to include non-Hermitian interaction terms that give {\it real} spectra. Such could describe new physics. simplest Lagrangian density $L=L_0+L_{int}=\bar\psi(i\not\partial-m)\psi-g\bar\psi\gamma^5\psi$. associated relativistic Dirac equation PT invariant dimensions the Hamiltonian commutes with PT. However, dispersion relation $p^2=m^2-g^2$ shows symmetry broken chiral limit...

PT-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers more than 15 international conferences entirely devoted to this topic. Originally, PTQM was studied at highly mathematical level the techniques complex variables, asymptotics, differential equations perturbation theory were used understand subtleties associated with analytic continuation eigenvalue problems. However, as...

This paper presents a non-Hermitian $\mathcal{PT}$-symmetric extension of the Nambu--Jona-Lasinio (NJL) model quantum chromodynamics in $3+1$ and $1+1$ dimensions. In dimensions, SU(2)-symmetric NJL Hamiltonian...

In a previous paper it was shown how to calculate the ground-state energy density $E$ and $p$-point Green's functions $G_p(x_1,x_2,...,x_p)$ for $PT$-symmetric quantum field theory defined by Hamiltonian $H=\frac{1}{2}(\nabla\phi)^2+\frac{1}{2}\phi^2(i\phi)^\varepsilon$ in $D$-dimensional Euclidean spacetime, where $\phi$ is pseudoscalar field. this earlier were expressed as perturbation series powers of $\varepsilon$ calculated first order $\varepsilon$. (The parameter measure nonlinearity...

A recent paper by Jones-Smith and Mathur, Phys. Rev. 82, 042101 (2010) extends $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics from bosonic systems (systems for which ${\mathcal{T}}^{2}=\mathbf{1}$) to fermionic ${\mathcal{T}}^{2}=\ensuremath{-}\mathbf{1}$). The current shows how the formalism developed Mathur can be used construct matrix representations operator algebras of form ${\ensuremath{\eta}}^{2}=0$, ${\overline{\ensuremath{\eta}}}^{2}=0$,...