Analytic properties of the Green's functions with respect to the coupling constant in an exactly solvable model of field theory

It is found in an exactly solvable model of field theory that Green's functions for boson fields are analytic in the coupling constant, except for a cut along the real semiaxis. In the case of fermion fields, Green's functions are analytic in the coupling constant near zero.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 28–30, November, 1978.     

Gauge Covariant Fermion Propagator in the Presence of Arbitrary External Gauge Field and Its Schwinger--Dyson Equation

Gauge covariance for Green＇s functions of a gauge theory through a fermion propagator in the presence of arbitrary external gauge field is proven and a formalism of gauge and Lorentz covariant Schwinger-Dyson equation for the fermion propagator with external gauge field is built up within ladder approximation.     

原子核费密多体系统平均场近似的推广

本文应用先前得到的序参量——统计格林函数耦合方程组,对于原子核多费密子体系,系统地导出了它的平均场近似,Hartree-Fock近似和无规相位近似。并求出了相应近似下系统热力学势的明显表达式。本文的讨论也适用于处于平衡或非平衡定常态的其他多体系统。 关键词：     

Topological Invariants in Terms of Green's Function for the Interacting Kitaev Chain

A one-dimensional closed interacting Kitaev chain and the dimerized version are studied. The topological invariants in terms of Green's function are calculated by the density matrix renormalization group method and the exact diagonalization method. For the interacting Kitaev chain, we point out that the calculation of the topological invariant in the charge density wave phase must consider the dimerized configuration of the ground states. The variation of the topological invariant is attributed to the poles of eigenvalues of the zero-frequency Green functions. For the interacting dimerized Kitaev chain, we show that the topological invariant defined by Green's functions can distinguish more topological nonequivalent phases than the fermion parity.     

Nature of correlations in the atomic limit of the boson fermion model

Using the equation of motion technique for Green's functions we derive the exact solution of the boson fermion model in the atomic limit. Both (fermion and boson) subsystems are characterised by the effective three level excitation spectra. We compute the spectral weights of these states and analyse them in detail with respect to all possible parameters. Although in the atomic limit there is no true phase transition, we notice that upon decreasing temperature some pairing correlations start to appear. Their intensity is found to be proportional to the depleted amount of the fermion nonbonding state. We notice that pairing correlations behave in a fashion observed for the optimally doped and underdoped high T_c superconductors. We try to identify which parameter of the boson fermion model can possibly correspond to the actual doping level. This study clarifies the origin of pairing correlations within the boson fermion model and may elucidate how to apply it for interpretation of experimental data. Received 31 January 2003 / Received in final form 18 March 2003 Published online 23 May 2003 RID="a" ID="a"e-mail: doman@kft.umcs.lublin.pl     

Axial anomaly at finite temperature and finite density

TheU(1) axial anomaly in a hot fermion medium is investigated by using the real time Green's function method. After calculating the lowest order triangle diagrams, we find that finite temperature as well as finite fermion density does not affect the axial anomaly. The higher order corrections for the axial anomaly are discussed.     

The Effect of Nonmagnetic Doping on the d-Wave Heavy Fermion Superconductivity

In the present article, the use of slave-boson mean-field theory of the extended Anderson lattice model has been generalized to the Nambu space. The Green's functions of heavy fermion superconductors (HFS) have been obtained. The high sensitivity of the d-wave pairing HFS to the nonmagnetic impurities has been studied. The obtained results are in good agreement with the recent experiments on HFS.     

Renormalization problem in the quantum electrodynamics of non-point particles

The main postulates of the quantum electrodynamics of bilocal fields are formulated, the theory containing three universal constants c, h, and k. The fermion-photon form factor is determined, and the new theory is used to calculate radiative corrections in first-order perturbation theory for the fine-structure constant, fermion mass and magnetic moment, Coulomb potential, and fermion and photon Green's functions. The value = 1/137.0345 is obtained for the fine-structure constant.Kharkov Physico-Technical Institute of the Ukrainian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 76–89, June, 1994.     

Discrete phase space II. Relativistic lattice wave equations and divergence-free green's functions

Therelativistic lattice Klein-Gordon equation, Dirac equation, electromagnetic equations, and gauge field equations are presented as partialdifference equations. Various lattice Green's functions are constructed (except for non-abelian gauge fields). It is proved that many of the lattice Green's functions are non-singular or divergence-free. Moreover, it is conjectured that all lattice Green's functions are non-singular.     

Investigation of Green's functions in an external electromagnetic field by the eigenfunction method

This paper contains a study of Green's functions in a quantum electrodynamics (QED) with an external electromagnetic field that disrupts vacuum stability. Representations are found for the Green's functions of a scalar QED in the eigenfunction basis of Klein-Gordon equations for a uniform constant electromagnetic field in combination with the field of a plane wave.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 70–74, June, 1989.     

Green's function of a generalized Dirac equation for constant fields

Schwinger's method is used to find the Green's function for a Dirac equation in which the presence of anomalous moments of the fermion is taken into account phenomenologically and constant and homogeneous electromagnetic fields are assumed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 70–75, November, 1980.     

On the Higgs feature of gravity

The gauge gravitation theory, based on the equivalence principle besides the gauge principle, is formulated in the fibre bundle terms. The correlation between gauge geometry on spinor bundles describing Dirac fermion fields and space-time geometry on a tangent bundle is investigated. We show that field functions of fermion fields in presence of different gravitational fields are always written with respect to different reference frames. Therefore, the conventional quantization procedure is applicable to fermion fields only if gravitational field is fixed. Quantum gravitational fields violate the above mentioned correlation between two geometries.     

Finite-mode regularization of the fermion functional integral

We present a regularization of the fermion functional integral in the presence of a gauge field, obtained by projecting the fermion fields on a finite subspace of the fermion wave functions. We find the basis that ensures manifest gauge covariance. We are able, in this way, to develop a non-perturbative method of calculation and test it by calculating the triangle anomalies in different models. All the calculations are carried out on a finite-size momentum space lattice. Finally we briefly discuss the zero-mode problem.     

Thermal and thermoelectric response from Keldysh formalism with application to gapped Dirac fermions

Based on the Keldysh Green's functions theory, we present a general formula of the thermal and thermoelectric transport. In the clean limit, our formula recovers the previous results obtained from the semiclassical transport theory.In our approach, we propose an appropriate energy current operator and electric current operator, and the unphysical divergence from the direct application of the Kubo formula is eliminated. As an application, we study the thermal and the thermoelectric Hall conductivities of a gapped Dirac fermion model in the presence of impurity scattering.     

Exact Monte Carlo for few-fermion systems

We have reconsidered the fundamental difficulties of fermion Monte Carlo as applied to few-body systems. We conclude that necessary ingredients of successful algorithms include the following: There must be equal populations of random walkers that carry positive and negative weights. The positions of positive walkers should be selected from a distribution that uses Green's functions to couple all walkers. The positions of negative walkers should be generated from those of positive walkers by means of odd permutations. The correct importance functions that take into account the global interactions of the populations are different for positive and negative walkers. Use of such importance functions breaks the symmetry that otherwise would exist between configurations (of the entire population) and configurations derived by interchanging positive and negative walkers. Based upon these observations, we have constructed a stable and accurate algorithm that solves a fully-polarized, three-dimensional, three-body model problem.     

费密子与Dirac双子系统的耦合问题

除了库仑耦合和Kazama-杨振宁耦合——кqβ∑·r/2Mr³外,本文同时讨论了费密子Dirac双子应当存在的另一耦合iкzz_de²γ·r/2Mr³。结果表明,对所有角动量态,费密子径向波函数具有物理上合理的原点渐近行为。定性地分析了束缚态的必要条件。发现,对于双子情形,当额外磁矩к→0时,存在费密子束缚态是可能的;但对于磁单极情形,当к→0时,必不存在费密子束缚态。 关键词：     

Method for breaking chains of equations for green's functions

This article presents a new method for closing infinite systems of equations for Green's functions. Its basis is a procedure for simultaneously splitting two higher-order Green's functions. There is a particular relationship between the three Green's functions that result. These Green's functions are self-consistent. Known Green's functions are used to reconstruct the corresponding correlation functions. An example is provided by the problem of magnetization for a spin system in the Heisenberg model with first-and secondorder approximations in the spin-spin interaction. The first-order approximation corresponds to the molecular-field approximation. The second-order computation corresponds to obtaining general relations determining the magnetization of a system. V. I. Lenin Moscow State Pedagogical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 42–47, August, 1996.     

Form factors and correlation functions of an interacting spinless fermion model

Introducing the fermionic R-operator and solutions of the inverse scattering problem for local fermion operators, we derive a multiple integral representation for zero-temperature correlation functions of a one-dimensional interacting spinless fermion model. Correlation functions particularly considered are the one-particle Green's function and the density–density correlation function both for any interaction strength and for arbitrary particle densities. In particular for the free fermion model, our formulae reproduce the known exact results. Form factors of local fermion operators are also calculated for a finite system.     

Quantum States of a Neutral Massive Fermion with an Anomalous Magnetic Moment in an External Electric Field

The quantum dynamics of a nonrelativistic neutral massive fermion with an anomalous magnetic moment (AMM) is examined in the external electric field of an infinitely long thin homogeneously charged thread in the plane with a normal directed along the thread. The Hamiltonian of the Dirac–Pauli equation for a neutral fermion with AMM is essentially singular in the considered external field and requires a supplementary extension of the definition in order for it to be treated as a self-adjoint quantum-mechanical operator. All one-parameter self-adjoint extensions of the Hamiltonian of the Dirac–Pauli equation in the considered external field are found in the nonrelativistic approximation. The corresponding Hilbert space of squareintegrable functions, including a singularity point of the Hamiltonian, is specified for each self-adjoint extension of the Hamiltonian. The wave functions of free and bound states, as well as discrete energy levels, are determined by the self-adjoint extension method and their correspondence with similar quantities obtained by the physical regularization procedure is discussed. It is shown that energy levels of bound states are simple poles of the scattering amplitude, which should be extended in definition by introducing the self-adjoint extension parameter into it. Expressions for the scattering amplitude and cross-section, depending on the orientation of the initial-state spin of fermion, are obtained.