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.     

The construction of gauge-links in arbitrary hard processes

Transverse momentum dependent parton distribution and fragmentation functions are described by hadronic matrix elements of bilocal products of field operators off the light-cone. These bilocal products contain gauge-links, as required by gauge-invariance. The gauge-links are path-ordered exponentials connecting the field operators along a certain integration path. This integration path is process-dependent, depending specifically on the short-distance partonic subprocess. In this paper we present the technical details needed in the calculation of the gauge-links, and a calculational scheme is provided to obtain the gauge invariant distribution and fragmentation correlators corresponding to a given partonic subprocess. PACS 12.38.-t; 13.85.Ni; 13.88.+e     

一种新的可能的复合场的量子场论

本文引进了双粒子的双重定域场算符和Bethe-Salpeter的算子方程来描述复合场的运动和变化,进一步扩展了H-N-Z的束缚态场论。     

Bilocal recursion structure of two-dimensional integrable equations

A bilocal approach to the construction of the general Bäcklund transformations and integrable equations connected with thw two-dimensional spectral problems is considered. The bilocal adjoint representation of the spectral problem plays a principal role in such a construction and, in particular, in the calculation of the bilocal “recursion” operator.     

Theory of nonlinear optical response of gauge invariant currents to linear and nonlinear couplings

When a gauge field interacts with a quantum condensed matter system, at first order of the gauge field it couples to the current operator of the electrons. Higher orders of the gauge field couple to electrons through other operators such as the stress tensor, etc. On the other hand, when one performs a measurement on a quantum system, not only the current operator, but also stress tensor operator of the electrons, etc. are hidden in the measurement, as they contribute to the gauge invariant current. We formulate a general problem of nonlinear optical response of the gauge invariant currents in presence of nonlinear couplings. We show that the new couplings along with new responses arising from field current have a very simple structure which can be formulated as time ordered multi-particle correlation functions. We also obtain their Lehman representation and thereby show that one need not use non-equilibrium formulations to deal with them. These new correlation functions suggest that in nonlinear optical response many new processes are possible. The experimental detection of the new terms in the current operator, and application corresponding multi-photon processes needs further theoretical and experimental investigations.     

Gauge invariance and the dirac equation

The gauge invariance of the Dirac equation is reviewed and gauge-invariant operators are defined. The Hamiltonian is shown to be gauge dependent, and an energy operator is defined which is gauge invariant. Gauge-invariant operators corresponding to observables are shown to satisfy generalized Ehrenfest theorems. The time rate of change of the expectation value of the energy operator is equal to the expectation value of the power operator. The virial theorem is proved for a relativistic electron in a time-varying electromagnetic field. The conventional approach to probability amplitudes, using the eigenstates of the unperturbed Hamiltonian, is shown in general to be gauge dependent. A gaugeinvariant procedure for probability amplitudes is given, in which eigenstates of the energy operator are used. The two methods are compared by applying them to an electron in a zero electromagnetic field in an arbitrary gauge. Presented at the Dirac Symposium, Loyola University, New Orleans, May 1981.     

The matrix element of the transverse component of the bilocal vector current and its parton interpretation

In this paper we study the matrix element of the transverse component of the bilocal vector current in the context of deep inelastic scattering. The BJL limit of high energy amplitudes together with light-front current algebra imply the same parton interpretation for its matrix element as that of the plus component. On the other hand, the transverse component depends explicitly on the gluon field operator in QCD, appears as “twist three” and hence its matrix element has no manifest parton interpretation. In this paper we perform calculations in light-front time-ordering perturbative QCD for a dressed quark target to order α_s and demonstrate that the matrix element of the transverse component of the bilocal vector current has the same parton interpretation as that of the plus component.     

String representation of field correlators in the Dual Abelian Higgs Model

By making use of the path integral duality transformation, we derive the string representation for the partition function of an extended Dual Abelian Higgs Model containing gauge fields of external currents of electrically charged particles. By the same method, we obtain the corresponding representations for the generating functionals of gauge field and monopole current correlators. In the case of bilocal correlators, the obtained results are found to be in agreement with the dual Meissner scenario of confinement and the Stochastic Model of the QCD vacuum. Received: 28 September 1998 / Revised version: 18 November 1998 / Published online: 11 March 1999     

Gauge identities in dual field theory

In the dual and fermion proposed by Neveu, Schwarz and Ramond, we find gauge identities involving vertex parts and also off-shell supergauge identities. When their models are translated into the secondary quantized field theory, we no longer can impose the gauge identities as operator ones, since they would lead to a contradiction of the second-quantization rules. We therefore require weak forms of the gauge identities just in an analogous way to the Lorentz condition in quantum electrodynamics. It is then shown that the weak forms of the identities are consistent with the second-quantization rules and also with field equations.     

Exact analysis of Coulomb gauge vacuum degeneracies in (2 + 1) dimensions

The solutions of the two-dimensional euclidean σ-model provide an infinite number of pure gauge field configurations satisfying the Coulomb gauge condition, in (2 + 1) dimensions. For vacuum gauge fields associated with finite action instanton solutions of the σ-model, we find that the winding number n configuration leads to n negative eigenvalues for the ghost operator, up to a finite calculable degeneracy.     

On bilocal gauge field theory

The nonlocal gauge group of unitary integral operators U _n (∞) is considered. Gluons in the nonlocal version of QCD are described by the bilocal gauge fields (BGF). The Higgs effect for BGF are discussed. It is shown that the local SU(n) gauge theory can be treated as a local limit of spontaneously broken U _n(∞)/SU(n) BGF theory.     

Landau electron in a rotating environment: A general factorization of time evolution

For the Landau problem with a rotating magnetic field and a confining potential in the (changing) direction of the field, we derive a general factorization of the time evolution operator that includes the adiabatic factorization as a special case. The confining potential is assumed to be of a general form and it can correspond to nonlinear Heisenberg equations of motion. The rotation operator associated with the solid angle Berry phase is used to transform the problem to a rotating reference frame. In the rotating reference frame, we derive a natural factorization of the time evolution operator by recognizing the crucial role played by a gauge transformation. The major complexity of the problem arises from the coupling between motion in the direction of the magnetic field and motion perpendicular to the field. In the factorization, this complexity is consolidated into a single operator which approaches the identity operator when the potential confines the particle sufficiently close to a rotating plane perpendicular to the magnetic field. The structure of this operator is clarified by deriving an expression for its generating Hamiltonian. The adiabatic limit and non-adiabatic effects follow as consequences of the general factorization which are clarified using the magnetic translation concept.     

On the virtual γγ annihilation to hadrons

The virtual γγ annihilation moments are calculated in the first order of perturbative QCD. The power corrections to these moments are obtained also by means of a modified operator expansion including the bilocal operators.     

A simple derivation of the overlap Dirac operator

We derive the vector-like four-dimensional overlap Dirac operator starting from a five-dimensional Dirac action in the presence of a delta-function space–time defect. The effective operator is obtained by first integrating out all the fermionic modes in the fixed gauge background, and then identifying the contribution from the localized modes as the determinant of an operator in one dimension less. We define physically relevant degrees of freedom on the defect by introducing an auxiliary defect-bound fermion field and integrating out the original five-dimensional bulk fields.     

Spontaneous symmetry breaking of Slavnov symmetry A restriction on the gauge condition

It is shown that the condition of vanishing vacuum expectation value of the gauge operator, using a gauge-fixing term quadratic in this operator, does not necessarily follow from the Slavnov identity, due to a possible spontaneous breakdown of the Slavnov symmetry. For a consistent renormalization such a condition may have to be imposed order by order in perturbation theory, depending on the choice of the gauge. This restriction on non-singular gauges is particularly relevant for the discussion of the spontaneously broken realizations of the gauge symmetry.     

Hamiltonian formulation of QED in the superaxial gauge

We present a hamiltonian formulation of QED in a fully fixed axial gauge. The equal-time commutators for all field variables are computed and are shown to lead to the correct equations of motion. The constraints and gauge conditions hold as strong operator relations.     

不可易规范场的对偶荷

本文讨论了不可易SU(2)规范场的各种规范不变物理量——电荷、对偶荷(磁荷)、电磁场以及有质量矢粒子场的表达式与关系,特别是对偶荷(磁荷)与电荷算符同位旋方向的大范围拓扑性质的关系。     

Globally conformal invariant gauge field theory with rational correlation functions

Operator product expansions (OPE) for the product of a scalar field with its conjugate are presented as infinite sums of bilocal fields V_κ(x₁,x₂) of dimension (κ,κ). For a globally conformal invariant (GCI) theory we write down the OPE of V_κ into a series of twist (dimension minus rank) 2κ symmetric traceless tensor fields with coefficients computed from the (rational) 4-point function of the scalar field.

We argue that the theory of a GCI hermitian scalar field of dimension 4 in D=4 Minkowski space such that the 3-point functions of a pair of 's and a scalar field of dimension 2 or 4 vanish can be interpreted as the theory of local observables of a conformally invariant fixed point in a gauge theory with Lagrangian density .     

Generalized coulomb gauges for the free photon field

We point out that the classical notion of gauge transformations can be interpreted in two different ways in the quantum theory. Beside the transformation of the field operator appearing in the Gupta-Bleuler theory, the gauge transformations can be viewed as acting on the wave functions in a generalization of the Coulomb gauge.