Relative time dependence as gauge freedom and bilocal models of hadrons

We introduce the shift of relative time variable as a gauge transformation of bilocal field operator. The corresponding gauge invariant free bilocal Lagrangian theory is formulated. The subsidiary condition which eliminates the relative time appears as a gauge invariance condition for bilocal field operator. As an example we quantize the bilocal field describing covariant three dimensional oscillator model of hadrons.     

Proof for Gauge Independence of the Energy-Momentum Tensor in Quantum Electrodynamics

Proof is given for gauge independence of the (Belinfante's) symmetric energy-momentum tensor in QED. Under the covariant LSZ-formalism it is shown that expectation values, supplemented with physical state conditions, of the energy-momentum tensor are gauge independent to all orders of the purturbation theory (the loop expansion). A study is also made, in terms of the gauge invariant operators of electron (known as the Dirac's or Steinmann's electron) and photon, in expectation of gauge invariant result without any restriction. It is, however, shown that singling out gauge invariant quantities is merely synonymous to fixing a gauge, then there needs again a use of the asymptotic condition to obtain gauge independent results.     

P-vortices and the Gribov problem

We study the possible connection between centre vortices and P-vortices in SU(2) gauge theory. After briefly recalling some essential properties of centre vortices we point out that there is no known a priori connection between the gauge dependent P-vortices and the gauge invariant centre vortices. We then show by Monte Carlo simulations that the `centre projected physics' strongly depends on the gauge copy from which the maximal centre gauge fixing is started. This reveals the presence of Gribov problems, and casts some doubts on the physical meaning of P-vortices, and should be further investigated.     

Gauge invariant formulation of non-Abelian chiral gauge theories in two dimensions

We study the gauge invariant version of a chiral non-Abelian gauge theory. A local bosonic effective action is obtained and the covariant conservation of the gauge current is verified. A Hamiltonian analysis of the model and of its constraints is performed. We show that the constraints are first class and that no anomalous term appears in the commutators of the gauge group generators. The current algebra of the model is obtained and the gauge fixing is analyzed.     

Lattice Chern-Simons gravity via the Ponzano-Regge model

We propose a lattice version of Chem-Simons gravity and show that the partition function coincides with the Ponzano-Regge model and the action leads to the Chem-Simons gravity in the continuum limit. The action is explicitly constructed by the lattice dreibein and spin connection and is shown to be invariant under lattice local Lorentz transformations and gauge diffeomorphisms. The action includes the constraint which can be interpreted as a gauge fixing condition of the lattice gauge diffeomorphism.     

BRST and Anti-BRST Symmetries in Perturbative Quantum Gravity

In perturbative quantum gravity, the sum of the classical Lagrangian density, a gauge fixing term and a ghost term is invariant under two sets of supersymmetric transformations called the BRST and the anti-BRST transformations. In this paper we will analyse the BRST and the anti-BRST symmetries of perturbative quantum gravity in curved spacetime, in linear as well as non-linear gauges. We will show that even though the sum of ghost term and the gauge fixing term can always be expressed as a total BRST or a total anti-BRST variation, we can express it as a combination of both of them only in certain special gauges. We will also analyse the violation of nilpotency of the BRST and the anti-BRST transformations by introduction of a bare mass term, in the massive Curci-Ferrari gauge.     

A generalised manifestly gauge invariant exact renormalisation group for SU(N) Yang–Mills

We take the manifestly gauge invariant exact renormalisation group previously used to compute the one-loop β function in SU(N) Yang–Mills without gauge fixing, and generalise it so that it can be renormalised straightforwardly at any loop order. The diagrammatic computational method is developed to cope with general group theory structures, and new methods are introduced to increase its power, so that much more can be done simply by manipulating diagrams. The new methods allow the standard two-loop β function coefficient for SU(N) Yang–Mills to be computed, for the first time without fixing the gauge or specifying the details of the regularisation scheme.     

Extended Connection in Yang-Mills Theory

The three fundamental geometric components of Yang-Mills theory –gauge field, gauge fixing and ghost field– are unified in a new object: an extended connection in a properly chosen principal fiber bundle. To do this, it is necessary to generalize the notion of gauge fixing by using a gauge fixing connection instead of a section. From the equations for the extended connection’s curvature, we derive the relevant BRST transformations without imposing the usual horizontality conditions. We show that the gauge field’s standard BRST transformation is only valid in a local trivialization and we obtain the corresponding global generalization. By using the Faddeev-Popov method, we apply the generalized gauge fixing to the path integral quantization of Yang-Mills theory. We show that the proposed gauge fixing can be used even in the presence of a Gribov’s obstruction.     

NONLOCAL CURRENTS AS NOETHER CURRENTS DUE TO A NONLOCALLY TRANSFORMED GLOBAL SYMMETRY

In this paper we first present the gauge invariant conserved Noether current for the Yang-Mi11s theory, which is nonlocal is some sense. Then we introduce for the two dimensional chiral model, plain and supersymmetric, the nonlocal one-complex parameter-dependent symmetric generators, which shift the Lagrangian density by a total divergence. Both the equations of motion and the energy momentum density are tnvaunt. The associated ically Into infinite Noether current may be expanded analyt-series of nonlocal currents.     

一种自对偶理论的规范不变形式及其量子化

对于一种新提出的自对偶场与规范场耦合的拉氏理论,本文给出相应的单上闭链,即Wess-Zumino项,构造了这种理论的规范不变的形式。利用正则量子化方法并通过选取适当的规范固定条件,证明了这规范不变的形式等价于原来的规范非不变的形式。此外,利用Batalin-Fradkin-Vilkovisky量子化方法,进一步指出这种等价性与规范固定条件的选择是无关的。 关键词：     

Non-Abelianizable First Class Constraints

We study the necessary and sufficient conditions on Abelianizable first class constraints. The necessary condition is derived from topological considerations on the structure of the gauge group. The sufficient condition is obtained by applying the implicit function theorem in calculus and studying the local structure of gauge orbits. Since the sufficient condition is necessary for the existence of proper gauge fixing conditions, we conclude that in the case of a finite set of non-Abelianizable first class constraints, the Faddeev-Popov determinant is vanishing for any choice of subsidiary constraints. This result is explicitly examined for the SO(3) gauge invariant model.Acknowledgement The financial support of Isfahan University of Technology (IUT) is acknowledged.     

The configuration space of low-dimensional Yang-Mills theories

We discuss the construction of the physical configuration space for Yang-Mills quantum mechanics and Yang-Mills theory on a cylinder. We explicitly eliminate the redundant degrees of freedom by either fixing a gauge or introducing gauge invariant variables. Both methods are shown to be equivalent if the Gribov problem is treated properly and the necessary boundary identifications on the Gribov horizon are performed. In addition, we analyze the significance of non-generic configurations and clarify the relation between the Gribov problem and coordinate singularities.     

Loop variables and gauge invariant exact renormalization group equations for (open) string theory

An exact renormalization group equation is written down for the world sheet theory describing the bosonic open string in general backgrounds. Loop variable techniques are used to make the equation gauge invariant. This is worked out explicitly up to level 3. The equation is quadratic in the fields and can be viewed as a proposal for a string field theory equation. As in the earlier loop variable approach, the theory has one extra space dimension and mass is obtained by dimensional reduction. Being based on the sigma model RG, it is background independent. It is intriguing that in contrast to BRST string field theory, the gauge transformations are not modified by the interactions up to the level calculated. The interactions can be written in terms of gauge invariant field strengths for the massive higher spin fields and the non-zero mass is essential for this. This is reminiscent of Abelian Born–Infeld action (along with derivative corrections) for the massless vector field, which is also written in terms of the field strength.     

Gauge quantization for spin-32 fields

The free massless Rarita-Schwinger equation and a recently constructed interacting field theory known as supergravity are invariant under fermionic gauge transformations. Gauge field quantization techniques are applied in both cases. For the free field the Faddeev-Popov ansatz for the generating functional is justified by showing that it is equivalent to canonical quantization in a particular gauge. Propagators are obtained in several gauges and are shown to be ghost-free and causal. For supergravity the Faddeev-Popov ansatz is presented and the gauge fixing and determinant terms are discussed in detail in a Lorentz covariant gauge. The Slavnov-Taylor identity is obtained. It is argued that supergravity theory is free from the difficulty of acausal wave propagation of the type found by Velo and Zwanziger and that pole residues in tree approximation S-matrix elements are positive as required by unitarity.     

ON THE BOUNDARY CONDITION AND CANONICAL S-WAVE HAMILTIONIAN FOR THE DYON-FERMION SYSTEM——THE SURFACE LAGRANGIAN AND GAUGE INVARIANT CHARGE CURRENT

By means of the surface Lagrangian and gauge invariant charge current, we make a detailed discussion to the physical meaning of each quantity in the boundary condition of the dyon-fermion dynamics; It is shown that adding the surface Lagrangian to the system is equivalent to selecting suitable boundary condition; By gauge trans-forming the Lagrangian by a charge generator, We get a corresponding U(1) charge current density which is both gauge invariant and spherosymmetrical. Ause of the canonical method and a careful treatment of surface terms show that the S-wave Hamiltonian given by Yamagishi requires amendment by a surface energy term.     

Quantum Deformation of Lattice Gauge Theory

A quantum deformation of 3-dimensional lattice gauge theory is defined by applying the Reshetikhin-Turaev functor to a Heegaard diagram associated to a given cell complex. In the root-of-unity case, the construction is carried out with a modular Hopf algebra. In the topological (weak-coupling) limit, the gauge theory partition function gives a 3-fold invariant, coinciding in the simplicial case with the Turaev-Viro one. We discuss bounded manifolds as well as links in manifolds. By a dimensional reduction, we obtain a q-deformed gauge theory on Riemann surfaces and find a connection with the algebraic Alekseev-Grosse-Schomerus approach. Received: 29 April 1996 / Accepted: 24 September 1996     

Reducibility and Gribov Problem in Topological Quantum Field Theory

In spite of its simplicity and beauty, the Mathai–Quillen formulation of cohomological topological quantum field theory with gauge symmetry suffers two basic problems: i) the existence of reducible field configurations on which the action of the gauge group is not free and ii) the Gribov ambiguity associated with gauge fixing, i. e. the lack of global definition on the space of gauge orbits of gauge fixed functional integrals. In this paper, we show that such problems are in fact related and we propose a general completely geometrical recipe for their treatment. The space of field configurations is augmented in such a way to render the action of the gauge group free and localization is suitably modified. In this way, the standard Mathai–Quillen formalism can be rigorously applied. The resulting topological action contains the ordinary action as a subsector and can be shown to yield a local quantum field theory, which is argued to be renormalizable as well. The salient feature of our method is that the Gribov problem is inherent in localization, and thus can be dealt within a completely equivariant setting, whereas gauge fixing is free of Gribov ambiguities. For the stratum of irreducible gauge orbits, the case of main interest in applications, the Gribov problem is solvable. Conversely, for the strata of reducible gauge orbits, the Gribov problem cannot be solved in general and the obstruction may be described in the language of sheaf theory. The formalism is applied to the Donaldson–Witten model. Received: 22 July 1996 / Accepted: 21 October 1996     

Quantization of chiral gauge theories in two-dimensions

It is shown that both abelian and non abelian chiral gauge theories in two dimensions can be made gauge invariant at the quantum level by adding a scalar field. In the bosonized form of the theory, the scalar field appears in a gauged Wess-Zumino action. The current algebra of the extended abelian theory is shown to be free of anomalous terms.     

BRST-BV quantization of gauge theories with global symmetries

We consider the general gauge theory with a closed irreducible gauge algebra possessing the non-anomalous global (super)symmetry in the case when the gauge fixing procedure violates the global invariance of classical action. The theory is quantized in the framework of BRST-BV approach in the form of functional integral over all fields of the configuration space. It is shown that the global symmetry transformations are deformed in the process of quantization and the full quantum action is invariant under such deformed global transformations in the configuration space. The deformed global transformations are calculated in an explicit form in the one-loop approximation.