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Fuad M. Saradzhev

Publications and source records attributed to Fuad M. Saradzhev.

14 recordsLinked to original sources
arXiv2025

Rest energy effects for non-relativistic Fermi fields in external potentials

The generalized Levy-Leblond equation (GLL) is used to study the bound state problem for a non-relativistic Fermi field in external potentials. A condition when the rest energy term can be removed from the GLL equation is determined. For external potentials which do not obey the condition, the bound state spectrum is affected non-trivially by the rest energy of the Fermi field. This is demonstrated for a spherical finite-depth well potential. The existence, number, and energies of bound states depend on the value of the rest energy.

hep-th↗
arXiv2023

Non-relativistic Fermi particle in one-dimensional pseudoscalar $δ$-function potential

It is shown that a non-relativistic Fermi particle with a non-zero rest energy moving in a pseudoscalar $δ$-function potential in one dimension can be confined for both signs of the coupling constant. The binding energies depend on the value of the particle's rest energy, and in the limit of vanishing rest energy only one of the bound states survives. The coefficients of reflection and transmission are determined, and the conditions for complete reflection and transmission are discussed.

hep-th↗
arXiv2012

Spin operator and spin states in Galilean covariant Fermi field theories

Spin degrees of freedom of the Galilean covariant Dirac field in (4+1) dimensions and its nonrelativistic counterpart in (3+1) dimensions are examined. Two standard choices of spin operator, the Galilean covariant and Dirac spin operators, are considered. It is shown that the Dirac spin of the Galilean covariant Dirac field in (4+1) dimensions is not conserved, and the role of non-Galilean boosts in its nonconservation is stressed out. After reduction to (3+1) dimensions the Dirac field turns into a nonrelativistic Fermi field with a conserved Dirac spin. A generalized form of the Levy-Leblond equations for the Fermi field is given. One-particle spin states are constructed. A particle-antiparticle system is discussed.

math-ph↗
arXiv2007

A magnetization equation for non-equilibrium spin systems

A magnetization equation for a system of spins evolving non-adiabatically and out of equilibrium is derived without specifying the internal interactions. For relaxation processes, this equation provides a general form of magnetization damping. A special case of the spin-spin exchange interaction is considered.

cond-mat.other↗
arXiv2005

On spontaneous symmetry breaking in hot QCD

We prove that nontrivial vacuum states which can arise in hot QCD are associated with the tachyonic regime of hadronic matter fluctuations. This allows us to improve the condition for such states to appear.

hep-th↗
arXiv2005

Non-Markovian source term for particle production by a self-interacting scalar field in the large-N approximation

The particle production in the self-interacting N-component complex scalar field theory is studied at large N. A non-Markovian source term that includes all higher order back-reaction and collision effects is derived. The kinetic amplitudes accounting for the change in the particle number density caused by collisions are obtained. It is shown that the production of particles is symmetric in the momentum space. The problem of renormalization is briefly discussed.

hep-th↗
arXiv2002

Kinetic equation for tachyons

The tachyonic regime of the quantum fluctuations of a self-interacting scalar field around its vacuum mean value is studied within a kinetic approach. We derive a quantum kinetic equation which determines the time evolution of the momentum distribution function of produced tachyonic modes and includes memory effects. The back-reaction of the quantum fluctuations on the vaccum mean field is taken into account, while their interaction is neglected. We show that the tachyonic modes do not correspond to real particles and contribute to the decay of the metastable vacuum state.

hep-th↗
arXiv2001

Bound state problem for a Dirac particle in an external static charge distribution in (1+1)-dimensions

We study the self-interaction effects for the Dirac particle moving in an external field created by static charges in (1+1)-dimensions. Assuming that the total electric charge of the system vanishes, we show that the asymptotically linearly rising part of the external potential responsible for nonexistence of bound states in the external field problem without self-interaction is cancelled by the self-potential of the zero mode of the Dirac particle charge density. We derive the Dirac equation which includes the self-potential of the non-zero modes and is nonlinear. We solve the spectrum problem in the case of two external positive charges of the same value and prove that the Dirac particle and external charges are confined in a stable system.

hep-th↗
arXiv1999

Self-field QED(1+1) with massless matter fields: Two-body problem

We consider two-body problem in the self-field (1+1)-dimensional quantum electrodynamics on the circle. We present two formulations of the problem which correspond to two different types of variational principles and prove that both formulations lead to the same spectrum of the two-body Hamiltonian with massless matter fields. We give the exact and complete solution of the relativistic two-body equation in the massless case.

hep-th↗
arXiv1998

Berry phase connection and anomaly in two dimensions

For the generalized chiral Schwinger model defined on the circle, a direct calculation of the zero curvature part of the vacuum Berry phase connection is given. Although this part does not contribute to the curvature, it is shown to attach several features to the total connection and to produce a physical background of linearly rising electric fields.

hep-th↗
arXiv1998

Light-front two-dimensional QED: Self-field approach

The self-field approach to quantum electrodynamics (QED) is used to study the bound state problem in light-front two-dimensional QED with massive matter fields. A composite matter field describing bound states is introduced and the relativistic bound state equation for the composite field including a self-potential is obtained. The Hamiltonian form of the bound state equation in terms of the invariant mass squared operator is given. The eigenvalue problem of this operator is solved for a fixed value of the self-potential, the corresponding eigenfunctions and the mass spectrum are found. In the case of massless matter fields, there are no self-field terms in the bound state equation, and the invariant mass spectrum can be evaluated explicitly. Possible ways of deriving more complete information about the bound state spectrum are briefly discussed.

hep-th↗
arXiv1997

Generalised chiral QED2 : Anomaly and Exotic Statistics

We study the influence of the anomaly on the physical quantum picture of the generalized chiral Schwinger model defined on the circle. We show that the anomaly i) results in the background linearly rising electric field and ii) makes the spectrum of the physical Hamiltonian nonrelativistic without a massive boson. The physical matter fields acquire exotic statistics . We construct explicitly the algebra of the Poincare generators and show that it differs from the Poincare one. We exhibit the role of the vacuum Berry phase in the failure of the Poincare algebra to close. We prove that, in spite of the background electric field, such phenomenon as the total screening of external charges characteristic for the standard Schwinger model takes place in the generalized chiral Schwinger model, too.

hep-th↗
arXiv1996

Poincare Algebra in Chiral QCD_2

For the chiral QCD_2 on a cylinder, we give a construction of a quantum theory consistent with anomaly. We construct the algebra of the Poincare generators and show that it differs from the Poincare one.

hep-th↗