Related papers: Exact Solution of the Schwinger Model with Compact…
The complete exact solution of the Schwinger model with compact gauge group U(1), in the Hamiltonian approach, is presented . The compactification is imposed by demanding that the only surviving true electromagnetic degree of freedom has…
The Schwinger model, defined in the space interval $-L \le x \le L$, with (anti)periodic boundary conditions, is canonically quantized in the light-cone gauge $A_-=0$ by means of equal-time (anti)commutation relations. The transformation…
A free spinor field on a noncommutative sphere is described starting from a canonical realization of the enveloping algebra U(u(2|1)). The gauge extension of the model - the Schwinger model on a noncommutative sphere is defined and the…
We describe the scalar and spinor fields on noncommutative sphere starting from canonical realizations of the enveloping algebra ${\cal A}={\cal U}{u(2))}$. The gauge extension of a free spinor model, the Schwinger model on a noncommutative…
Gauge theories embedded into higher-dimensional spaces with certain topologies acquire inductance terms, which reflect the energy cost of topological charges accumulated in the extra dimensions. We compute topological susceptibility in the…
In this paper we extend our previously discovered exact solution for an SU(2) gauge theory coupled to a massless, non-interacting scalar field, to the general group SU(N+1). Using the first-order formalism of Bogomolny, an exact,…
We use a prescription to gauge the su(2) Skyrme model with a U(1) field, characterised by a conserved Baryonic current. This model reverts to the usual Skyrme model in the limit of the gauge coupling constant vanishing. We show that there…
Stationary 1D Schr\"odinger equations with polynomial potentials are reduced to explicit countable closed systems of exact quantization conditions, which are selfconsistent constraints upon the zeros of zeta-regularized spectral…
The lattice regularized pure gauge compact U(1) theory is an ideal laboratory to explore how confinement is realized as its phase diagram has a confined and a deconfined phase that depends on the value of the coupling constant, i.e. on…
The solution of the axial U(1) problem, the role of the topology of the gauge group in forcing the breaking of axial symmetry in any irreducible representation of the observable algebra and the theta vacua structure are revisited in the…
We compute the fixed point action of a properly defined renormalization group transformation for the Schwinger model through an expansion in the gauge field. It is local, with couplings exponentially suppressed with the distance. We check…
I shall recall a number of solutions to the Schwinger model in different gauges, having different boundary conditions and using different quantization surfaces. I shall discuss various properties of these solutions emphasizing the degrees…
In the continuum, the single flavor massless Schwinger model has an exact global axial $U(1)$ symmetry in the sector of perturbative gauge fields. This symmetry is explicitly broken by gauge fields with nonzero topological charge inducing a…
The stationary 1D Schr\"odinger equation with a polynomial potential $V(q)$ of degree N is reduced to a system of exact quantization conditions of Bohr-Sommerfeld form. They arise from bilinear (Wronskian) functional relations pairing…
Evaluation of a product integral with values in the Lie group SU(1,1) yields the explicit solution to the impedance form of the Schr\"odinger equation. Explicit formulas for the transmission coefficient and $S$-matrix of the classical…
We analyze non-perturbatively the one-dimensional Schr\"odinger equation describing the emission of electrons from a model metal surface by a classical oscillating electric field. Placing the metal in the half-space $x\leqslant 0$, the…
We investigate the continuum limit of a compact formulation of the lattice U(1) gauge theory in 4 dimensions using a nonperturbative gauge-fixed regularization. We find clear evidence of a continuous phase transition in the pure gauge…
An interacting spin-fermion model is exactly solved on an open chain. In a certain representation, it is the nearest-neighbor Hubbard model in the limit of infinite $U$ (local interaction). Exact solution of its complete energy…
Using the exact path integral solution of the Schwinger model -- a model where instantons are present -- the Dyson-Schwinger equation is shown to hold by explicit computation. It turns out that the Dyson-Schwinger equation separately holds…
A new noncommutative model invariant with respect to U(1) gauge group is proposed. The model is free of nonintegrable infrared singularities. Its commutative classical limit describes a free scalar field. Generalization to U(N) models is…