Double field formulation of Yang-Mills theory

Based on our previous work on the differential geometry for the closed string double field theory, we construct a Yang-Mills action which is covariant under O(D,D) T-duality rotation and invariant under three-types of gauge transformations: non-Abelian Yang-Mills, diffeomorphism and one-form gauge symmetries. In double field formulation, in a manifestly covariant manner our action couples a single O(D,D) vector potential to the closed string double field theory. In terms of undoubled component fields, it couples a usual Yang-Mills gauge field to an additional one-form field and also to the closed string background fields which consist of a dilaton, graviton and a two-form gauge field. Our resulting action resembles a twisted Yang-Mills action.     

Super-symmetry and non-Abelian gauges

We show that the conventional Yang-Mills Lagrangian with the Yang-Mills field interacting with Majorana fermions belonging to the adjoint representation of an internal symmetry group like SU(n) is super-gauge invariant.     

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.     

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.     

N = 4 Yang-Mills theory in terms of N = 3 and N = 2 light-cone superfields

The N = 4 Yang-Mills theory is truncated to an N = 3 Yang-Mills theory and to an N = 2 Yang-Mills theory coupled to an N = 2 Wess-Zumino field. The whole procedure is performed in the light-cone gauge. It is then shown that these theories are unique even if we only insist on N = 3 or N = 2 supersymmetry respectively. Finally we show in detail how the introduction of the fermionic Wess-Zumino field renders the one-loop self-energy finite.     

The parallel propagator as basic variable for Yang-Mills theory

The parallel propagator (associated with a Yang-Mills connection) taken along all null geodesics from a field point to null infinity is introduced as a basic variable in Yang-Mills theory. It is shown that the Yang-Mills connection can be reconstructed from this parallel propagator.The Yang-Mills equations are expressed as an equation for the parallel propagator. This equation can be given as a sum of two parts. The first of these, when set equal to zero on its own, satisfies the Huygens property and is soluble. When the second part is included, the Huygens property is destroyed. This leads to an approximation scheme which at first order is soluble yet already captures much of the non-linearity of Yang-Mills theory.     

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.     

Application of Lie Algebroid Structures to Unification of Einstein and Yang-Mills Field Equations

Yang-Mills field equations describe new forces in the context of Lie groups and principle bundles. It is of interest to know if the new forces and gravitation can be described in the context of algebroids. This work was intended as an attempt to answer last question. The basic idea is to construct Einstein field equation in an algebroid bundle associated to space-time manifold. This equation contains Einstein and Yang-Mills field equations simultaneously. Also this equation yields a new equation that can have interesting experimental results.     

Gravitational Gauge Theory Developed Based on the Stephenson-Kilmister-Yang Equation

A Yang-Mills formulation of Einstein gravity with spin-affine connection as the dynamical variable of gravitational field is suggested based on the Stephenson-Kilmister-Yang (SKY) equation. A physically interesting property of the present formalism is that the Einstein field equation appears as a first-integral solution to the Yang-Mills type gravitational gauge field equation. The gravitational current density, the law of conservation and the gravitational gauge field strength in vierbein formulation are discussed. The present scheme could provide us with new insight into a possible way to include both Yang-Mills field and gravitational gauge field into one framework of generalized vierbein fields.     

Quantization of the massive Yang-Mills field in arbitrary gauges

A general gauge formulation of the massive Yang-Mills theory is presented with emphasis on the fact that the massive Yang-Mills field is, like the massless counterpart, also a non-Abelian gauge field.     

There are no Magnetically Charged Particle-like Solutions of the Einstein Yang-Mills Equations for Models with an Abelian Residual Group

We prove that there are no magnetically charged particle-like solutions for any model with an Abelian residual group in Einstein Yang-Mills, but for the non-Abelian models the possibility remains open. An analysis of the Lie algebraic structure of the Yang-Mills fields is essential to our results. In one key step of our analysis we use invariant polynomials to determine which orbits of the gauge group contain the possible asymptotic Yang-Mills field configurations. Together with a new horizontal/vertical space decomposition of the Yang-Mills fields this enables us to overcome some obstacles and complete a dynamical system existence theorem for asymptotic solutions with nonzero total magnetic charge. We then prove that these solutions cannot be extended globally for Abelian models and begin an investigation of the details for non-Abelian models.     

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.     

Gauge fixing and renormalization in topological quantum field theory

We show how Witten's topological Yang-Mills and gravitational quantum field theories may be obtained by a straightforward BRST gauge fixing procedure. We investigate some aspects of the renormalization of the topological Yang-Mills theory. It is found that the beta function for the Yang-Mills coupling constant is not zero.     

Infrared divergences and a non-local gauge for superspace Yang-Mills theory

The usual superspace approach to supersymmetric gauge theories suffers from problems with infrared divergences which greatly complicate multiloop calculations. We eliminate these divergences by introducing a non-local gauge-fixing term. In the background field method this term leads to unusual quantum-background interactions. Functional methods are presented for dealing with these interactions. As an example we compute the two-loop Yang-Mills β-function using the background field method in superspace. We also show how a non-local gauge can be used in ordinary, non-supersymmetric Yang-Mills theory.     

The Continual Approach in the Yang-Mills Theory in the External Non-Abelian Field

The theory of Yang-Mills field in interaction with matter fields is considered in the presence of external gauge field. A closed expression for the generating functional of the Green functions is obtained, and a detailed analysis of the Green functions of the scalar, spinor, ghost and Yang-Mills fields is performed. The path-integral solution for all these Green functions is obtained, which includes the functional averaging over the classical trajectories in the space of commuting and anticommuting variables, the latter being anociated with the particle spin and isospin. For illustration an arbitrary Abelian-like external field is considered, as well as non-Abelian-like constant external field.     

规范场与主纤维丛上的联络

本文较详细地给出物理上的规范场与数学上的主纤维丛上的联络论之间的对应关系,从而以联络论的观点统一地处理杨振宁所说的规范场的“微分方法”与“积分”方法,并指出存在有更广泛的规范场的可能性。此外,讨论了引力场如何作为规范场及比较了一些已知的引力场方程。     

Cosmological models with Yang-Mills fields

Cosmological models with an SU(2) Yang-Mills field are studied. For a specific model with a minimally coupled Yang-Mills Lagrangian, which includes an arbitrary function of the second-order term and a fourth-order term, a corresponding reconstruction program is proposed. It is shown that the model with minimal coupling has no de Sitter solutions, for any nontrivial function of the second-order term. To get de Sitter solutions, a gravitational model with nonminimally coupled Yang-Mills fields is then investigated. It is shown that the model with non-minimal coupling has in fact a de Sitter solution, even in absence of the cosmological constant term.     

A model regularizing gauge fields in the strong coupling region

We propose a model using an effective lagrangian for bilocal gauge extended fields, looking somehow as an average over all open strings with fixed end points. The locality of the action is retrieved as a range parameter, which acts as a regulator, shrinks, and the Yang-Mills theory is recovered in this limit. The system is invariant by rotation and translation, generalizes lattice gauge theories and allows regularized strong coupling expansions for Yang-Mills field theory.