含外规范场和动力学费米子自能的狄拉克算符及费米子凝聚

将非阿贝尔规范理论中狄拉克算符行列式的计算从传统的只能含有硬费米子质量项的情况推广到可以含有动量相关的费米子自能的情况，并且行列式与费米子凝聚的计算都被推广到使之能够含有任意的外规范场. 关键词： 费米子自能 外规范场 狄拉克算符的行列式 费米子凝聚     

Group-theoretic description of external gauge fields

For an arbitrary external gauge field we construct an infinite group which contains all the information about the given field and describes some of its properties. We construct a field representation of the group . We show that covariant derivatives become translation generators in such a representation of the group . This allows us to interpret transformations from the group as motions in an external gauge field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 31–35, December, 1988.     

Hot gauge theories in external electromagnetic fields

A general treatment of finite temperature and external electromagnetic field effects for gauge theories is presented. The results are illustrated explicitly for the SU(2) model of Georgi and Glashow for which we obtain the finite temperature one-loop effective action in the presence of an external magnetic field. We discuss briefly the possible use of the results obtained.     

Dirac bound states of anharmonic oscillator in external fields

We explore the effect of the external magnetic and Aharonov–Bohm (AB) flux fields on the energy levels of Dirac particle subjects to mixed scalar and vector anharmonic oscillator field in the two-dimensional (2D) space. We calculate the exact energy eigenvalues and the corresponding un-normalized two-spinor-components wave functions in terms of the chemical potential parameter, magnetic field strength, AB flux field and magnetic quantum number by using the Nikiforov–Uvarov (NU) method.     

On the adiabatic limit for Dirac particles in external fields

An adiabatic switching formalism is proposed to bypass the difficulties in defining the spontaneous pair creation in static electromagnetic fields.On leave from I.F.I.N. Bucharest, Rumania     

Simulating Dirac fermions with Abelian and non-Abelian gauge fields in optical lattices

In this work we present an optical lattice setup to realize a full Dirac Hamiltonian in 2+1 dimensions. We show how all possible external potentials coupled to the Dirac field can arise from perturbations of the existing couplings of the honeycomb lattice pattern. This greatly simplifies the proposed implementations, requiring only spatial modulations of the intensity of the laser beams to induce complex non-Abelian potentials. We finally suggest several experiments to observe the properties of the quantum field theory in the setup.     

Particle picture in external fields,quantum holonomy,and gauge anomaly

We formulate a path integral of chiral gauge theories by means of the canonical quantization of fermions in time-dependent background gauge fields. The expression of the path integral is composed of two parts. One is due to the nontrivial holonomy of the fermionic Fock vacua and the other is the conventional form which is used in the perturbation theory. The nontrivial holonomy part is expected to be a nonlocal counter term. We show a possibility of the perturbative calculation     

Polarization of vacuum of quantum fields in the Aaronov-Bohm external field. II

A spinor field interacting with the Aaronov-Bohm external field is examined. Analytical expressions for the vacuum average components of the energy-momentum tensor are derived. Dependences of the components of energymomentum tensor of the spinor field in the vacuum state on the distance and field strength are investigated. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 3–8, April, 2006.     

QCD Dirac spectrum and components of the gauge field

We analyze the relation between the Dirac spectrum and the gauge field in SU(3) lattice QCD. We focus on how a certain component of the gauge field is related to the Dirac spectrum. First, we consider momentum components of the gauge field. It turns out that the broad momentum region is relevant for the low-lying Dirac spectrum and topological charges. The connection with chiral random matrix theory is also discussed. Second, we consider an SU(2) subgroup component of the SU(3) gauge field. The SU(2) subgroup component behaves like the SU(2) gauge field in the low-lying Dirac spectrum.     

Double-beta decay in gauge theories

Neutrinoless double-beta decay is a very important process both from the particle and nuclear physics point of view. From the elementary particle point of view, it pops up in almost every model, giving rise among others to the following mechanisms: (a) the traditional contributions like the light neutrino mass mechanism as well as the j _L –j _R leptonic interference (λ and η terms), (b) the exotic R-parity-violating supersymmetric (SUSY) contributions. Thus, its observation will severely constrain the existing models and will signal that the neutrinos are massive Majorana particles. From the nuclear physics point of view, it is challenging, because (1) the nuclei, which can undergo double-beta decay, have complicated nuclear structure; (2) the energetically allowed transitions are suppressed (exhaust a small part of all the strength); (3) since in some mechanisms the intermediate particles are very heavy one must cope with the short distance behavior of the transition operators (thus novel effects, like the double-beta decay of pions in flight between nucleons, have to be considered; in SUSY models, this mechanism is more important than the standard two-nucleon mechanism; and (4) the intermediate momenta involved are quite high (about 100 MeV/c). Thus one has to take into account possible momentum-dependent terms of the nucleon current, like modification of the axial current due to PCAC, weak magnetism terms, etc. We find that, for the mass mechanism, such modifications of the nucleon current for light neutrinos reduce the nuclear matrix elements by about 25%, almost regardless of the nuclear model. In the case of heavy neutrino, the effect is much larger and model-dependent. Taking the above effects into account, the needed nuclear matrix elements have been obtained for all the experimentally interesting nuclei A=76, 82, 96, 100, 116, 128, 130, 136, and 150. Then, using the best presently available experimental limits on the half-life of the 0νββ decay, we have extracted new limits on the various lepton-violating parameters. In particular, we find 〈m _ν〉 < 0.3 eV/c ², and, for reasonable choices of the parameters of SUSY models in the allowed SUSY parameter space, we get a stringent limit on the R-parity-violating parameter λ′₁₁₁<4.0×10^?4.     

Cosmic dark matter and Dirac gauge function

It is suggested that the dark matter of the universe is due to the presence of a scalar field described by the gauge function introduced by Dirac in his modification of the Weyl geometry. The behavior of such dark matter is investigated.     

Naturally light Dirac neutrinos in gauge theories

Motivated by recent experimental results, we discuss the possibility of generating small Dirac neutrino masses in a natural way. We give a mechanism based on symmetry arguments which works in the SU(2) × U(1) and SU(5) models, but fails in left-right symmetric theories. We conclude that in these models Dirac masses can only be made small by a fine tuning.     

Polarization of vacuum of quantum fields in the external Aharonov-Bohm field. Part I

A charged scalar field interacting with an external Aharonov-Bohm field is considered. Analytical expressions for vacuum average components of the energy-momentum tensor are derived. Their dependence on the distance and field magnitude is investigated. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 26–34, February, 2006.     

How to fix the gauge in internal and external gauge theories

A recently presented method, that permits one to calculate gauge-fixing conditions from a given gauge-breaking term, is applied to internal as well as external Yang-Mills theories. As to the internal case, the known gauge-fixing conditions can easily be reproduced in a unified way. For the external case, i.e., the Poincaré gauge theory of gravitation, new gauge-fixing conditions are obtained, in particular the full nonlinear generalization of the Coulomb and axial gauge. They prove to be simultaneously valid for theories with or without torsion.