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Using the method of the "exact discretization" of the Schr\"odinger equation, we propose a particular discretized version of the N=2 Supersymmetric Quantum Mechanics. After defining the corresponding shape invariance condition, we show that…
Recently it was shown how to regularize the Batalin-Vilkovisky (BV) field-antifield formalism of quantization of gauge theories with the non-local regularization (NLR) method. The objective of this work is to make an analysis of the…
We clarify the notion of Wilsonian renormalization group (RG) invariance in supersymmetric gauge theories, which states that the low-energy physics can be kept fixed when one changes the ultraviolet cutoff, provided appropriate changes are…
We investigate a proposal for the construction of models with chiral fermions on the lattice using staggered fermions. In this approach the gauge invariance is broken by the coupling of the staggered fermions to the gauge fields. We aim at…
An exact analytical solution for the Bohr Hamiltonian with an energy dependent Coulomb-like $\gamma$-unstable potential is presented. Due to the linear energy dependence of the potential's coupling constant, the corresponding spectrum in…
A new generalization of the vector Schwinger model is considered where gauge symmetry is broken at the quantum mechanical level. By proper extension of the phase space this broken symmetry has been restored. Also an equivalent first class…
Considering the recent advances, the weak correlation between the massive Kalb-Ramond and the Proca interacting models is investigated by means of a set of complementary quantum field techniques beyond the semi-classical approach. A…
A new type of gauge fixing of the Coulomb gauge domain wall fermion system that reduces the fluctuation of the effective running coupling and the effective mass of arbitrary momentum direction including the region outside the cylinder cut…
As a prerequisite to dynamical fermion simulations a detailed study of optimal parameters and scaling behavior is conducted for the quenched Schr\"odinger functional at fixed renormalized coupling. We compare standard hybrid overrelaxation…
Various prescriptions employed for regulating gauged Nambu--Jona-Lasinio type models such as the top-quark condensate model are discussed. The use of dimensional regularization maintains gauge invariance but destroys the quadratic…
We analyze the chiral Schwinger model on an infinite lattice using the continuum definition of the fermion determinant and a linear interpolation of the lattice gauge fields. For non-compact and Wilson formulation of the gauge field action…
There exist both continuum and lattice regularizations of gauge theories with fermions which preserve chiral U(1) invariance ("fermion number"). Such regularizations necessarily break gauge invariance but, in a covariant gauge, one recovers…
A covariant quantization scheme employing reducible representations of canonical commutation relations with positive-definite metric and Hermitian four-potentials is tested on the example of quantum electrodynamic fields produced by a…
Using the hamiltonian formalism, we investigate the smooth bosonization method in which bosonization and fermionization are carried out through a specific gauge-fixing of an enlarged gauge invariant theory. The generator of the local gauge…
We define Weyl fermions on a finite lattice in such a way that in the path integral the action is gauge invariant but the functional measure is not. Two variants of such a formulation are tested in perturbative calculation of the fermion…
Effective quantum field theoretical continuum models for graphene are investigated. The models include a complex scalar field and a vector gauge field. Different gauge theories are considered and their gap patterns for the scalar, vector,…
In this paper we analyze the ground state phase diagram of a class of fermionic Hamiltonians by looking at the fidelity of ground states corresponding to slightly different Hamiltonian parameters. The Hamiltonians under investigation can be…
The compatibility between the conformal symmetry and the closure of conformal algebras is discussed on the nonlinear sigma model. The present approach, above the basis of field redefinition employed in the Hamiltonian scheme, attempts the…
The method of the quantum kinetic equation is applied to the problem of renormalization of the conductivity of normal metals by gauge electron-electron interactions. It is shown that in the three-dimensional case the relativistic…
The unique off-shell fermionic gauge invariance of a vector-spinor field theory is found, and the invariant action is derived. The latter is Weyl invariant in any dimension in the massless limit, and it coincides with the singular point of…