arXiv subjects

A. A. Abrikosov Jr

Publications and source records attributed to A. A. Abrikosov Jr.

9 recordsLinked to original sources

arXiv2005

Modified Spectral Boundary conditions in the Bag Model

We propose a reduced form of Atiah-Patodi-Singer spectral boundary conditions for odd ($d$) dimensional spatial bag evolving in even ($d+1$) dimensional space-time. The modified boundary conditions are manifestly chirally invariant and do not depend on time. This allows to apply Hamiltonian approach to confined massless fermions and study chirality effects in spatially closed volume. The modified boundary conditions are equally suitable for chiral fermions in Minkowski and Euclidean metric space-times.

hep-th↗

arXiv2004

Spectral Boundary Conditions in the Bag Model

We propose a reduced form of spectral boundary conditions for holding fermions in the bag in a chiral invariant way. Our boundary conditions do not depend on time and allow Hamiltonian treatment of the system. They are suited for studies of chiral phenomena both in Minkowski and Euclidean spaces.

hep-th↗

arXiv2004

Geometric Dequantization

Dequantization is a set of rules which turn quantum mechanics (QM) into classical mechanics (CM). It is not the WKB limit of QM. In this paper we show that, by extending time to a 3-dimensional "supertime", we can dequantize the system in the sense of turning the Feynman path integral version of QM into the functional counterpart of the Koopman-von Neumann operatorial approach to CM. Somehow this procedure is the inverse of geometric quantization and we present it in three different polarizations: the Schroedinger, the momentum and the coherent states ones.

quant-ph↗

arXiv2003

Time and Geometric Quantization

In this paper we briefly review the functional version of the Koopman-von Neumann operatorial approach to classical mechanics. We then show that its quantization can be achieved by freezing to zero two Grassmannian partners of time. This method of quantization presents many similarities with the one known as Geometric Quantization.

quant-ph↗

arXiv2002

Dirac operator on the Riemann sphere

We solve for spectrum, obtain explicitly and study group properties of eigenfunctions of Dirac operator on the Riemann sphere $S^2$. The eigenvalues $λ$ are nonzero integers. The eigenfunctions are two-component spinors that belong to representations of SU(2)-group with half-integer angular momenta $l = |λ| - \half$. They form on the sphere a complete orthonormal functional set alternative to conventional spherical spinors. The difference and relationship between the spherical spinors in question and the standard ones are explained.

hep-th↗

arXiv2000

Instantons in non-Cartesian coordinates

The explicit multi-instanton solutions by 'tHooft and Jackiw, Nohl & Rebbi are generalized to curvilinear coordinates. The idea is that a gauge transformation can notably simplify the expressions obtained after the change of variables. The gauge transform generates a compensating addition to the gauge potential of pseudoparticles. Singularities of the compensating field are irrelevant for physics but may affect gauge dependent quantities.

hep-th↗

arXiv1999

Multiinstantons in curvilinear coordinates

The 'tHooft's 5N-parametric multiinstanton solution is generalized to curvilinear coordinates. Expressions can be simplified by a gauge transformation that makes $η$-symbols constant in the vierbein formalism. This generates the compensating addition to the gauge potential of pseudoparticles. Typical examples (4-spherical, 2+2- and 3+1-cylindrical coordinates) are studied and explicit formulae presented for reference. Singularities of the compensating field are discussed. They are irrelevant for physics but affect gauge dependent quantities.

hep-th↗

arXiv1994

The Problem of Ground State in Thermo-Field Dynamics

Analytic continuation of quantum statistical physics from imaginary to real time is analyzed. Adiabatic vanishing of interactions at real time infinities gives origin to singularities at complex times. This undermines the hypothesis of decoupling of interactions at $t \rightarrow \infty$. Hence an interacting thermal vacuum is a necessary component of the exact real-time formalism. Consequences for Thermo-field dynamics are discussed.

hep-th↗

arXiv1993

White Noise and Heating of Open Quantum Field Fermi Systems

I study the time evolution of the density matrices of quantum Fermi systems interacting with classic external Fermi fields. This interaction either changes the temperature of the system or it affects the density of particles. For relativistic Dirac fermions, variations of temperature lead to creation (annihilation) of particle - antiparticle pairs. The change of the density (or of the chemical potential) indicates the existence of the incoming (outgoing) flux of fermions from (to) the bath. These changes are independent for the different modes and in order to model the thermalization one should adjust the spectrum of the noise. The linear time dependences of the densities of particles are characteristic for all the processes.

hep-th↗