Schwinger Model Research Articles

EXACT RENORMALIZATION OF MASSLESS QED2

We perform the exact renormalization of two-dimensional massless gauge theories. Using these exact results we discuss the cluster property and confinement in both the anomalous and chiral Schwinger models.

Hamiltonian and BRST formulations of a gauge-invariant chiral Schwinger model with the Faddeevian regularization

The Hamiltonian and BRST formulations of a gauge-invariant chiral Schwinger model with the Faddeevian regularization due to Mukhopadhyay and Mitra in one-space one-time dimensions (obtained by the inclusion of an appropriate Wess–Zumino term in the action of the originally gauge-noninvariant model due to Mitra) are investigated under some specific gauge choices in the usual instant form of dynamics (on the hyperplanes x0= constant). The physical contents of the original gauge-noninvariant theory are recovered from that of this gauge-invariant theory under a special choice of gauge, and the quantum equivalence of the two quantized theories is established.PACS Nos.: 03.65+, 03.70+, 11.10lm, 11.10Ef, and 11.30Rd

The general correlation function in the Schwinger model on a torus

In the framework of the Euclidean path integral approach we derive the exact formula for the general N-point chiral densities correlator in the Schwinger model on a torus

Uniting Gross–Neveu and massive Schwinger models

We show that it is possible to obtain the Gross–Neveu model in 1+1 dimensions from gauge fields only. This is reminiscent of the fact that in 1+1 dimensions the gauge field tensor is essentially a pseudo-scalar. We also show that it is possible in this context to combine the Gross–Neveu model with the massive Schwinger model in the limit where the fermion mass is larger than the electric charge.

The front-form Hamiltonian and BRST formulations of the Jackiw–Rajaraman chiral Schwinger model

The Hamiltonian and BRST formulations of the Jackiw–Rajaraman chiral Schwinger model are investigated in the light-front frame. PACS No.: 11.15-q

Density matrix renormalization group approach to the massive Schwinger model

The massive Schwinger model is studied, using a density matrix renormalisation group approach to the staggered lattice Hamiltonian version of the model. Lattice sizes up to 256 sites are calculated, and the estimates in the continuum limit are almost two orders of magnitude more accurate than previous calculations. Coleman's picture of `half-asymptotic' particles at background field theta = pi is confirmed. The predicted phase transition at finite fermion mass (m/g) is accurately located, and demonstrated to belong in the 2D Ising universality class.

Unexpected results in the chiral limit with staggered fermions

A cluster algorithm is constructed and applied to study the chiral limit of the strongly coupled lattice Schwinger model involving staggered fermions. The algorithm is based on a novel loop representation of the model. Finite size scaling of the chiral susceptibility based on data from lattices of size up to 64×64 indicates the absence of long range correlations at strong couplings. Assuming that there is no phase transition at a weaker coupling, the results imply that all mesons acquire a mass at non-zero lattice spacings. Although this does not violate any known physics, it is surprising since typically one expects a single pion to remain massless at non-zero lattice spacings in the staggered fermion formulation.

Density matrix renormalisation group approach to the massive Schwinger model

The massive Schwinger model is studied, using a density matrix renormalisation group approach to the staggered lattice Hamiltonian version of the model. Lattice sizes up to 256 sites are calculated, and the estimates in the continuum limit are at least an order of magnitude more accurate than previous calculations. The position of the phase transition at background field θ = π is accurately located, and the results suggest it belongs in the Ising universality class.

THE HAMILTON–JACOBI TREATMENT OF FRONT-FORM SCHWINGER MODEL

The Hamilton–Jacobi formalism was applied to quantize the front-form Schwinger model. The importance of the surface term is discussed in detail. The BRST–anti-BRST symmetry was analyzed within Hamilton–Jacobi formalism.

General axial gauge for the light-front Schwinger model

Abstract The canonical light-front (LF) quantization of the massive Schwinger model and its perturbation theory are presented. The closed fermion loops contribution is calculated via the Pauli-Villars regularization and the massless limit is safely taken. The Dyson-Schwinger equations for exact propagators are solved for the gauge and the fermion fields, showing their dependence on the axial gauge fixing parameter α. The four-fermion Green function is found and for coinciding pairs of end-points it becomes explicitly a gauge invariant expression.

Weyl gauge, Schwinger terms and bosonization in light-front field theory

Abstract A systematic study of non-perturbative quantum structure of the massive light-front Schwinger model and QED(3+1) in the continuum formulation is outlined. The light-front Hamiltonian and field algebra are derived in the Weyl gauge using the Dirac-Bergmann constrained quantization. Unitary transformation to the light-cone gauge representation is performed and the gauge-invariant fermi field is constructed. The importance of the Schwinger term in the current-current commutation relations for the derivation of the fermionic vacuum structure and bosonization in two dimensions is indicated.

The UA(1) problem on the lattice with Ginsparg–Wilson fermions

We show how it is possible to give a precise and unambiguous implementation of the Witten–Veneziano formula for the η′ mass on the lattice, which looks like the formal continuum one, if the expression of the topological charge density operator, suggested by fermions obeying the Ginsparg–Wilson relation, is employed. By using recent numerical results from simulations with overlap fermions in 2 (abelian Schwinger model) and 4 (QCD) dimensions, one obtains values for the mass of the lightest pseudo-scalar flavour-singlet state that agree within errors with theoretical expectations and experimental data, respectively.

The chiral densities correlator in the Schwinger model on a torus

In the framework of the Euclidean path integral approach we derive the exact formula for the general N-point chiral densities correlator in the Schwinger model on a torus.

Topology and pion correlators — a study in the N f = 2 Schwinger model

I readdress the issue whether the topological charge of the gauge background has an influence on a hadronic observable. To this end pion correlators in the Schwinger model with 2 dynamical flavours are determined on subensembles with a fixed topological charge. It turns out that the answer depends on a specific function of the sea-quark mass and the box volume which is in close analogy to the Leutwyler-Smilga parameter in full QCD.

Speeding up the Hybrid-Monte-Carlo algorithm for dynamical fermions

We propose a modification of the Hybrid-Monte-Carlo algorithm that allows for a larger step-size of the integration scheme at constant acceptance rate. The key ingredient is the splitting of the pseudo-fermion action into two parts. We test our proposal at the example of the two-dimensional lattice Schwinger model and four-dimensional lattice QCD with two degenerate flavours of Wilson-fermions.

The U A(1) problem on the lattice

If the expression of the topological charge density operator, suggested by fermions obeying the Ginsparg-Wilson relation, is employed, it is possible to prove on the lattice the validity of the Witten—Veneziano formula for the η′ mass. Recent numerical results from simulations with overlap fermions in 2 (abelian Schwinger model) and 4 (QCD) dimensions give values for the mass of the lightest pseudo-scalar flavour-singlet state that agree with theoretical expectations and/or experimental data.

Schwinger model on a half-line

We study the Schwinger model on a half-line in this paper. In particular, we investigate the behavior of the chiral condensate near the edge of the line. The effect of the chosen boundary condition is emphasized. The extension to the finite temperature case is straightforward in our approach.

Energy-momentum tensor in Schwinger model with strong coupling limit

Energy-momentum tensor in Schwinger model with strong coupling limit

Statistics of Composite Systems and Anyons in the Fractional Quantum Hall Effect

The commutation relations of the composite fields are studied in the 3, 2 and 1 space dimensions. It is shown that the field of an atom consisting of a nucleus and an electron fields satisfies, in the space-like asymptotic limit, the canonical commutation relations within the sub-Fock-space of the atom. The field-particle duality in the bound state is discussed from the statistics point of view. Then, the commutation relations of the scalar object in the Schwinger(Thirring) model are mentioned briefly and are shown consistent with its interpretation as the Nambu-Goldstone boson. The composite anyon fields are shown to satisfy the proper anyonic commutation relations with the additive phase exponents. Then, quasiparticle picture of the anyons is clarified under the restriction of this additibity. The difference between field and particle aspects becomes more prominent in the 2 space dimension. It is argued that the hierarchy of the fractional quantum Hall effect is rather simply understood by utilizing the quasiparticle charactors of the anyons when the background-boson gauge is assumed. In contrast to it, the coposite fermion theories are critically reviewed

Speeding up the hybrid Monte Carlo algorithm for dynamical fermions

We propose a modification of the Hybrid-Monte-Carlo algorithm that allows for a larger step-size of the integration scheme at constant acceptance rate. The key ingredient is that the pseudo-fermion action is split into two parts. We test our proposal at the example of the two-dimensional lattice Schwinger model with two degenerate flavours of Wilson-fermions.