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E. V. Prokhvatilov

Publications and source records attributed to E. V. Prokhvatilov.

At least 19 recordsLinked to original sources
arXiv2020

Deconfinement temperature in AdS/QCD from the spectrum of scalar glueballs

We scrutinize various holographic estimations of the deconfinement temperature within the bottom-up AdS/QCD models. A special emphasis is put on the recent idea of isospectral potentials in the holographic approach. It is demonstrated that different models from an isospectral family (i.e., the models leading to identical predictions for the spectrum of hadrons with fixed quantum numbers) result in different predictions for the deconfinement temperature. This difference is found to be quite small in the scalar glueball channel but very large in the vector meson channel which is often used for fixing parameters of holographic models. The observed stability in the former case clearly favors the choice of the glueball channel for thermodynamic predictions in AdS/QCD models, with the scalar glueball trajectory being taken from lattice simulations and used as a basic input in improved versions of the Soft Wall holographic model.

hep-ph↗
arXiv2019

New solutions for graphene with scalar potentials by means of generalized intertwining

The intertwining relations between superpartner Hamiltonians are the main ingredients of well known Supersymmetrical Quantum Mechanics (SUSY QM). In the present paper, the generalized form of intertwining is used for investigation of a massless (zero energy) two-dimensional Dirac equation with scalar external potential. This equation is related to the description of graphene and some other materials in the field of external electrostatic potential. The use of modified intertwining relations allows to find analytically solutions for the wave functions in the field of some external scalar potentials which depend on both space coordinates. A few examples of this construction are given explicitly.

cond-mat.mes-hall↗
arXiv2015

Pauli-Villars Regularization and Light Front Hamiltonian in (2+1)-dimensional Yang-Mills Theory

The renormalization problem of (2+1)-dimensional Yang-Mills theory quantized on the light front is considered. Extra fields analogous to those used in Pauli-Villars regularization are introduced to restore perturbative equivalence between such quantized theory and conventional formulation in Lorentz coordinates. These fields also provide necessary ultraviolet regularization to the theory. Obtained results allow to construct renormalized Hamiltonian of the theory on the light front.

hep-th↗
arXiv2015

Pauli-Villars Regularization in nonperturbative Hamiltonian approach on the Light Front

The advantage of Pauli-Villars regularization in quantum field theory quantized on the light front is explained. Simple examples of scalar $λφ^4$ field theory and Yukawa-type model are used. We give also an example of nonperturbative calculation in the theory with Pauli-Villars fields, using for that a model of anharmonic oscillator modified by inclusion of ghost variables playing the role similar to Pauli-Villars fields.

hep-th↗
arXiv2014

Renormalized Light Front Hamiltonian in the Pauli-Villars Regularization

We address the problem of nonperturbative calculations on the light front in quantum field theory regularized by Pauli-Villars method. As a preliminary step we construct light front Hamiltonians in (2+1)-dimensional $λϕ^4$ model, for the cases without and with spontaneous symmetry breaking. The renormalization of these Hamiltonians in Pauli-Villars regularization is carried out via comparison of all-order perturbation theory, generated by these Hamiltonians, and the corresponding covariant perturbation theory in Lorentz coordinates.

hep-th↗
arXiv2007

Formulating Light Cone QCD on the Lattice

We present the near light cone Hamiltonian $H$ in lattice QCD depending on the parameter $η$, which gives the distance to the light cone. Since the vacuum has zero momentum we can derive an effective Hamiltonian $H_{eff}$ from $H$ which is only quadratic in the momenta and therefore solvable by standard methods. An approximate ground state wave functional is determined variationally in the limit $η\to 0$.

hep-lat↗
arXiv2007

Hamiltonian Lattice QCD near the Light Cone

We give a status report of our work on light cone Hamiltonian lattice QCD. We have derived an effective Hamiltonian $H_{eff}$ which is only quadratic in the momenta and therefore can be simulated by standard methods. For this Hamiltonian we determine variationally an approximate ground state wave functional in the light cone limit.

hep-lat↗
arXiv2006

Quantum Fields on the Light Front, Formulation in Coordinates close to the Light Front, Lattice Approximation

We review the fundamental ideas of quantizing a theory on a Light Front including the Hamiltonian approach to the problem of bound states on the Light Front and the limiting transition from formulating a theory in Lorentzian coordinates (where the quantization occurs on spacelike hyperplanes) to the theory on the Light Front, which demonstrates the equivalence of these variants of the theory. We describe attempts to find such a form of the limiting transition for gauge theories on the Wilson lattice.

hep-th↗
arXiv2005

Quantization of Field Theory on the Light Front

Canonical formulation of quantum field theory on the Light Front (LF) is reviewed. The problem of constructing the LF Hamiltonian which gives the theory equivalent to original Lorentz and gauge invariant one is considered. We describe possible ways of solving this problem: (a) the limiting transition from the equal-time Hamiltonian in a fast moving Lorentz frame to LF Hamiltonian, (b) the direct comparison of LF perturbation theory in coupling constant and usual Lorentz-covariant Feynman perturbation theory. The results of the application of method (b) to QED-1+1 and QCD-3+1 are given. Gauge invariant regularization of LF Hamiltonian via introducing a lattice in transverse coordinates and imposing periodic boundary conditions in LF coordinate x^- for gauge fields on the interval |x^-| smaller than L is also considered.

hep-th↗
arXiv2005

Calculation of the Mass Spectrum of QED-2 in Light-Front Coordinates

With the aim of a further investigation of the nonperturbative Hamiltonian approach in gauge field theories, the mass spectrum of QED-2 is calculated numerically by using the corrected Hamiltonian that was constructed previously for this theory on the light front. The calculations are performed for a wide range of the ratio of the fermion mass to the fermion charge at all values of the parameter \hatθrelated to the vacuum angle θ. The results obtained in this way are compared with the results of known numerical calculations on a lattice in Lorentz coordinates. A method is proposed for extrapolating the values obtained within the infrared-regularized theory to the limit where the regularization is removed. The resulting spectrum agrees well with the known results in the case of θ=0; in the case of θ=π, there is agreement at small values of the fermion mass (below the phase-transition point).

hep-th↗
arXiv2004

Constructing the light-front QCD Hamiltonian

We propose the light-front Lagrangian and the corresponding Hamiltonian that produce a theory perturbatively equivalent to the conventional QCD in the Lorentz coordinates after the regularization is removed. The regularization used is nonstandard and breaks the gauge invariance. But after the regularization is removed, this invariance is restored by the introduction of a finite number of counterterms with coefficients dependent on the regularization parameters.

hep-th↗
arXiv2004

A nonperturbative calculation of the electron's magnetic moment

In principle, the complete spectrum and bound-state wave functions of a quantum field theory can be determined by finding the eigenvalues and eigensolutions of its light-cone Hamiltonian. One of the challenges in obtaining nonperturbative solutions for gauge theories such as QCD using light-cone Hamiltonian methods is to renormalize the theory while preserving Lorentz symmetries and gauge invariance. For example, the truncation of the light-cone Fock space leads to uncompensated ultraviolet divergences. We present two methods for consistently regularizing light-cone-quantized gauge theories in Feynman and light-cone gauges: (1) the introduction of a spectrum of Pauli-Villars fields which produces a finite theory while preserving Lorentz invariance; (2) the augmentation of the gauge-theory Lagrangian with higher derivatives. In the latter case, which is applicable to light-cone gauge (A^+ = 0), the A^- component of the gauge field is maintained as an independent degree of freedom rather than a constraint. Finite-mass Pauli-Villars regulators can also be used to compensate for neglected higher Fock states. As a test case, we apply these regularization procedures to an approximate nonperturbative computation of the anomalous magnetic moment of the electron in QED as a first attempt to meet Feynman's famous challenge.

hep-ph↗
arXiv2003

Ultraviolet finiteness of Chiral Perturbation Theory for two-dimensional Quantum Electrodynamics

We consider the perturbation theory in the fermion mass (chiral perturbation theory) for the two-dimensional quantum electrodynamics. With this aim, we rewrite the theory in the equivalent bosonic form in which the interaction is exponential and the fermion mass becomes the coupling constant. We reformulate the bosonic perturbation theory in the superpropagator language and analyze its ultraviolet behavior. We show that the boson Green's functions without vacuum loops remain finite in all orders of the perturbation theory in the fermion mass.

hep-th↗
arXiv2003

Gauge Invariant Regularization of Quantum Field Theory on the Light-Front

Gauge invariant regularization of quantum field theory in the framework of Light-Front (LF) Hamiltonian formalism via introducing a lattice in transverse coordinates and imposing boundary conditions in LF coordinate $x^-$ for gauge fields on the interval $|x^-|\le L$ is considered. The remaining ultraviolet divergences in the longitudinal momentum $p_-$ are removed by gauge invariant finite mode regularization. We find that LF canonical formalism for the introduced regularization does not contain usual most complicated second class constraints connecting zero and nonzero modes of gauge fields. The described scheme can be used either for the regularization of conventional gauge theory or for gauge invariant formulation of effective low-energy models on the LF. The lack of explicit Lorentz invariance in our approach leads to difficulty with defining the vacuum state. We discuss this difficulty, particulary, in the connection with the problem of taking the limit of continuous space.

hep-th↗
arXiv2003

The Light-Front Hamiltonian formalism for two-dimensional Quantum Electrodynamics equivalent to the Lorentz-covariant approach

A light-front Hamiltonian reproducing the results of two-dimensional quantum electrodynamics in the Lorentz coordinates is constructed using the bosonization procedure and an analysis of the bosonic perturbation theory in all orders in the fermion mass. The resulting Hamiltonian involves a supplementary counterterm in addition to the usual terms appearing in the naive light-front quantization. This term is proportional to a linear combination of zeroth fermion modes (which are multiplied by a factor compensating the charge and fermion number). The coefficient of the counterterm has no ultraviolet divergence, depends on the value of the fermion condensate in the θ-vacuum, and is linear in this value for a small fermion mass.

hep-th↗
arXiv2001

On the correspondence between Light-Front Hamiltonian approach and Lorentz-covariant formulation for Quantum Gauge Theory

The problem of the restoring of the equivalence between Light-Front (LF) Hamiltonian and conventional Lorentz-covariant formulations of gauge theory is solved for QED(1+1) and (perturbatively to all orders) for QCD(3+1). For QED(1+1) the LF Hamiltonian is constructed which reproduces the results of Lorentz-covariant theory. This is achieved by bosonization of the model and by analysing the resulting bosonic theory to all orders in the fermion mass. For QCD(3+1) we describe nonstandard regularization that allows to restore mentioned equivalence with finite number of counterterms in LF Hamiltonian.

hep-th↗