Massive Gross-Neveu Model Research Articles

Momentum projection of a soliton in the massive Gross-Neveu model

Abstract We study a solitonic state in the SU ( N c ) Gross-Neveu model using the Peierls-Yoccoz projection. It is found by an order estimation that the Fock term and the det B term, are the leading order corrections in 1 N c of the spurious zero-point energy of translational motion. We calculate these terms numerically in the scalar approximation. It is shown numerically that the corrected energy estimated by replacing the inertial mass by the soliton energy agrees reasonably well with that estimated by the Fock term and the det B term when the coupling constant is large.

The massive Gross-Neveu model at finite temperature and density

We have studied the thermodynamics of the massive Gross-Neveu model with explicitly broken symmetry for finite temperature and fermion densities. The main purpose of the study is to serve as analytical orientation for the more complex problem of chiral transition in 4—dimensional QCD with quarks. For any non-vanishing fermion mass we find, at finite densities, lines of first order phase transitions. For small mass values traces of would-be second order transitions and a tricritical point are recognizable.

Bound State Spectrum of SU(N) Massive Gross-Neveu Model

Applying the inifinite momentum frame technique, we solve the charge zero sector of the SU(N) massive Gross-Neveu model. For positive charge conjugation state (C = 1), the boson spectrum at large N limit is equivalent to the result obtained from light cone approach with mean field approximations. The bound state energy behaves similar to that of semiclassical calculation and the leading term appears at 1/N2 order. Also, there is a negative charge conjugation state (C = -1). This spectrum is found to be identical to that of the U(1) massive Thirring model for any value of N. Further, we find a phase transition at some critical coupling for N = 0 case, which may correspond to that of the random bond Ising model.

Constructing the three-dimensional Gross-Neveu model with a large number of flavor components.

We construct the ultraviolet limit of the massive Gross-Neveu model in three dimensions and with a large number of flavor components N.Received 4 February 1991DOI:https://doi.org/10.1103/PhysRevLett.66.3233©1991 American Physical Society

Renormalization of the linear σ expansion. The gross-neveu model

A recently proposed expansion interpolating between different actions S = S0+S1(σ) was previously defined and extensively studied with a finite ultraviolet cut-off. Here we study the renormalizability of this σ-expansion in the case of an exactly soluble theory, the Gross-Neveu model at N → ∞. We determine the necessary renormalization conditions to all orders in σ, taking into account the renormalization group equation. A crucial role is played by the asymptotic behaviour of the bare mass parameter in the massive Gross-Neveu model.

Bethe-Salpeter kernel and short distance expansion in the massive Gross-Neveu model

The Bethe-Salpeter kernel is defined (non-perturbatively) for the weakly coupled massive Gross-Neveu model. Its large momentum properties are established. They are used to justify “subtracted” Bethe-Salpeter equations initially proposed (forϕ44) by K. Symanzik, and in turn to give non-perturbative proofs of the Wilson short distance expansion at first order and of 2-particle asymptotic completeness and related results.

Large momentum properties and Wilson short distance expansion in non-perturbative field theory

Large momentum properties and Wilson-Zimmerman short-distance expansion are established via phase-space analysis for the weakly coupled massive Gross-Neveu model in dimension 2. Methods are applicable more generally.

Massive Gross-Neveu model in the leading order of the 1/N expansion. Allowance for the temperature and the chemical potential

The massive Gross-Neveu model is treated self-consistently in the leading order of the 1/N expansion. The properties of the model when the temperature and the chemical potential are included are studied. It is shown that there exists a critical value of the chemical potential at which the effective mass of the fermion abruptly changes its value.

Asymptotic completeness and multiparticle structure in field theories

The ideas developed in Part I (ref. (1)) are applied to the recently constructed massive Gross-Neveu model. We define in this case an irreducible kernel satisfying a regularized Bethe-Salpeter equation which is convenient to derive asymptotic completeness in the 2-particle region. As in Part I, the method aIlows direct graphical definition of general irreducible kernels and is well suited to the analysis of asymptotic completeness and related results in more general energy regions. A large part of the paper is devoted to a new self-contained construction (via phase space expansion) of the Gross-Neveu model. The presentation is somewhat simpler than previous ones, is more complete on some points and is best suited to our purposes.

A renormalizable field theory: The massive Gross-Neveu model in two dimensions

The Euclidean massive Gross-Neveu model in two dimensions is just renormalizable and asymptotically free. Thanks to the Pauli principle, bare perturbation theory with an ultra-violet cut-off (and the correct ansatz for the bare mass) is convergent in a disk, whose radius corresponds by asymptotic freedom to a small finite renormalized coupling constant. Therefore, the theory can be fully constructed in a perturbative way. It satisfies the O.S. axioms and is the Borel sum of the renormalized perturbation expansion of the model

Semi-Classical Quantization of the Massive Gross-Neveu Model by the Inverse Scattering Method

Semi-Classical Quantization of the Massive Gross-Neveu Model by the Inverse Scattering Method

Semi-Classical Quantization of the Massive Gross-Neveu Model by the Inverse Scattering Method

Semi-Classical Quantization of the Massive Gross-Neveu Model by the Inverse Scattering Method

Quantization of the localized solutions in two-dimensional field theories of massive fermions

Using the semiclassical functional method developed by Dashen, Hasslacher, and Neveu, the classical localized solutions for the bound states of massive fermions in two-dimensional field theories are quantized. The mass spectra of the bound states are then obtained. For the massive Gross-Neveu model, the mass spectrum agrees with what has been found by Dashen et al. for the massless Gross-Neveu model where fermions acquire mass through dynamical symmetry breaking. For a theory of massive fermions with scalar as well as pseudoscalar Fermi interactions, the mass spectrum is found to be very similar to that for the doublet in the sine-Gordon equation. In fact, under certain conditions they become identical.