Spinor analysis of Yang-Mills theory in the Minkowski space

Self-duality equations for Yang-Mills fields and the Dirac equation with an external (anti-) selfdual gauge field are studied in the Minkowski space by spinorial methods. For the Dirac equations, all (four) possible combinations of the fermion chirality and duality of the external fields are considered.     

Green functions of scalar particles in stochastic fields

A variational method of evaluating functional integrals is proposed. This method is used to investigate the asymptotic behavior of the scalar-particle Green functions in stochastic fields. The equations for the Green functions in Euclidean space in stochastic fields are written. The solutions of these equations are represented in the form of a functional integral and then they are averaged over Gaussian stochastic fields. The variational method formulated above is used to evaluate the asymptotic behavior of these Green functions. The following equations are considered in this paper: a stochastic contribution to the mass of a scalar particle, a gauge stochastic field, and a weak stochastic contribution to the flat metric of Euclidean space.     

Yang-Mills fields permitted by abelian complete sets of first-order symmetry operators of the Dirac equation

Nonequivalent complete sets of first-order symmetry operators of the Dirac free equation determine the Yang-Mills field, permitting complete variable separation in the Dirac equations with an external Yang-Mills field. Typical representatives of the classes of permissible fields are considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 30–34, October, 1989.     

Källen's theorem and the unphysical nature of abelian external fields in Yang-Mills theory

Yang-Mills theory is considered in an abelian external field with a covariant background gauge-fixing condition. The failure mechanism of Källen's inequality for the charge renormalization constant is studied, and indicates that a uniform external electric field should decay predominantly into negative norm gluon ghost states. Explicit calculation verifies this conjecture. This result is interpreted as evidence of the unphysical nature of abelian field configurations in Yang-Mills quantum theory.     

Green functions in a super self-dual Yang-Mills background

In euclidean supersymmetric theories of chiral superfields and vector superfields coupled to a super-self-dual Yang-Mills background, we define Green functions for the Laplace-type differential operators which are obtained from the quadratic part of the action. These Green functions are expressed in terms of the Green function on the space of right chiral superfields, and an explicit expression for the right chiral Green function in the fundamental representation of an SU(n) gauge group is presented using the supersymmetric version of the ADHM formalism. The superfield kernels associated with the Laplace-type operators are used to obtain the one-loop quantum corrections to the super-self-dual Yang-Mills action, and also to provide a superfield version of the super-index theorems for the components of chiral superfields in a self-dual background.     

Functional Methods for Arbitrary Densities in Curved Spacetime

This paper gives an introduction to the technique of functional differentiation and integration in curved spacetime, applied to examples from quantum field theory. Special attention is drawn on the choice of functional integral measure. Referring to a suggestion by Toms, fields are choosen as arbitrary scalar, spinorial or vectorial densities. The technique developed by Toms for a pure quadratic Lagrangian are extended to the calculation of the generating functional with external sources. Included are two examples of interacting theories, a self-interacting scalar field and a Yang-Mills theory. For these theories the complete set of Feynman graphs depending on the weight of variables is derived.     

The scattering of certain Yang-Mills fields

The Yang-Mills fields considered by us in an earlier paper are asymptotically non-interacting. Also any free field is an incoming field for some Yang-Mills field.     

Monopole vacuum in non-Abelian theories

It is shown that, in the theory of interacting Yang-Mills fields and a Higgs field, there is a topological degeneracy of Bogomol'nyi-Prasad-Sommerfield (BPS) monopoles and that there arises, in this case, a chromoelectric monopole characterized by a new topological variable that describes transitions between topological states of the monopole in Minkowski space (in just the same way as an instanton describes such transitions in Euclidean space). The limit of an infinitely large mass of the Higgs field at a finite density of the Bogomol'nyi-Prasad-Sommerfield monopole is considered as a model of the stable vacuum in pure Yang-Mills theory. It is shown that, in QCD, such a monopole vacuum may lead to a growing potential, a topological confinement, and an additional mass of the η₀ meson. The relationship between the result obtained here for the generating functional of perturbation theory and the Faddeev-Popov integral is discussed.     

Magnetization distribution in a helicoidal structure containing a point defect

The helicoid that forms in an external magnetic field in the presence of a point defect is modeled in the framework of the Landau theory of second-order phase transitions. A general solution to the nonlinear problem retaining all terms in the Helmholtz free-energy functional is obtained by means of Green functions. The magnetization distribution in the plane perpendicular to the helicoid axis and to the external field is calculated.     

Particle Creation in the Effective Action Method

The effect of particle creation by nonstationary external fields is considered as a radiation effect in the expectation-value spacetime. The energy of created massless particles is calculated as the vacuum contribution in the energy-momentum tensor of the expectation value of the metric. The calculation is carried out for an arbitrary quantum field coupled to all external fields entering the general second-order equation. The result is obtained as a functional of the external fields. The paper gives a systematic derivation of this result on the basis of the nonlocal effective action. Although the derivation is quite involved and touches on many aspects of the theory, the result itself is remarkably simple. It brings the quantum problem of particle creation to the level of complexity of the classical radiation problem. For external fields like the electromagnetic or gravitational field there appears a quantity, the radiation moment, that governs both the classical radiation of waves and the quantum particle production. The vacuum radiation of an electrically charged source is considered as an example. The research is aimed at the problem of backreaction of the vacuum radiation.     

Stability and decay of the Dirac vacuum in external gauge fields

We consider various gauge fields coupled to the free Dirac equation according to symmetry principles. The gauge fields are treated as classical, unquantized fields. Sufficiently strong time-independent fields may give rise to spontaneous particle creation and to the decay of the symmetric Dirac vacuum into a new ground state with broken symmetry. The vacuum stability of the Dirac field is studied for the cases of external electromagnetic (U(1)), gravitational (Poincaré group including torsion) and Yang-Mills (SU(2)) potentials.     

Magnetic monopole in the general theory of relativity

Equations of motion are obtained for Yang-Mills and Higgs fields using the Georgi-Glashow SO(3)-model in a curved spherically symmetric space-time. Magnetic monopole and dion solutions and the space-time metric are found in the intrinsic gravitational field. A particlelike solution of the magnetic monopole and dion type is constructed in the external field of a static universe in the Bogomol'nyi-Prasad-Sommerfield limit.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 89–93, November, 1982.     

Geometrical description of field algebra

The algebraic presentation, of the curvature tensor suggested earlier in [1] yields a simple form of the energymomentum tensor, presupposed by the Sugawara model. This expression gives rise to the expression of the Yang-Mills fields in terms of tetrads. This provides for an interpretation of the Yang-Mills fields as classical counter-parts of inhomogeneous group generators. A generalized form for the Yang-Mills fields is obtained for which commutation relations of the field algebra follow naturally.     

Stable Yang-Mills fields for an over-critical point source

The classical Yang-Mills energy functional in the presence of an external particle is explored as a function of the coupling strength. In the over-critical coupling region besides the Coulomb field other new saddle points as well as new minima are found. Near the critical point approximate expressions for the new static and stable solutions of the Yang-Mills equations are derived.     

First order corrections to the wave function of a hydrogen atom in an external electromagnetic field: A sturmian expansion

The linear response of a hydrogen atom in an external electromagnetic field is considered. Expressions for the lowest order corrections to discrete and continuum wave functions are derived with the help of a sturmian expansion of the Coulomb Green function.     

Green functions in stochastic field theory

Functional representations are reviewed for the generating function of Green functions of stochastic problems stated either with the use of the Fokker-Planck equation or the master equation. Both cases are treated in a unified manner based on the operator approach similar to quantum mechanics. Solution of a second-order stochastic differential equation in the framework of stochastic field theory is constructed. Ambiguities in the mathematical formulation of stochastic field theory are discussed. The Schwinger-Keldysh representation is constructed for the Green functions of the stochastic field theory which yields a functional-integral representation with local action but without the explicit functional Jacobi determinant or ghost fields.     

Composite field condensation and the renormalization group

The renormalization group is applied to the generating functional of connected Green functions of composite fields. Conditions for composite field condensation are formulated for the β and γ functions in a new renormalization scheme. The vacuum expectation value of a composite field is given completely in terms of the renormalization group parameters. As an example the formalism is applied to the Gross-Neveu model.     

Equations for the Green functions in quantum electrodynamics

Using the Freese-Matthews-Salam equations for chronological products of field operators, equations are written for Green functions of many electrons and photons. It is shown that in order to find any single Green function an infinite recursive system of these equations has to be solved. After adding terms containing the external electric current and external electromagnetic potential to the Lagrangian, this system is reduced to one equation containing functional derivatives of higher orders. It is shown that all relations and equations become much simpler when the definition of the Green function is appropriately changed.On leave from the Physical Institute of the Czechoslovak Academy of Sciences, Prague, Czechoslovakia.     

Post-Hartree-Fock methods and dynamic correlation in atoms and molecules

The methods of calculation of the matrix of the exchange-correlation interaction are considered within the framework of one post-Hartree-Fock one-electron method of investigation of the properties of many-electron systems. Such post-Hartree-Fock methods are based on two-step variational self-consistent calculations of the spin orbitals and superposition coefficients of configurations in the multiconfiguration approximation. The post-Hartree-Fock method used involves an approach related to the extended Koopmans’ theorem, which, in turn, proves to be a high-energy approximation for quantum Green’s functions. Obvious application areas of the calculations of the exchange-correlation interaction within the framework of the method proposed are the multiparticle perturbation theory, the parameterization of the energy representation as a functional of the single-particle density matrix, and the theory of Green’s functions in the multiconfiguration approximation. A relativistic generalization of the method with the aim of calculating the radiative corrections for many-electron atoms and for problems of interaction with an external field in the nonstationary Floquet theory is possible.