General Class Of Gauges Research Articles

The pole of the fermion propagator in a general class of gauges

We study the behavior of the pole of the fermion propagator, in QED in n dimensions, in a general class of gauges which interpolate between the covariant, the axial and the Coulomb gauges. We use Nielsen identities, following from the BRST invariance of the theory, to determine the gauge variation of the fermion two point function in this general class of gauges. This allows us to show directly and in a simple manner, to all orders in perturbation theory, that in the absence of infrared divergences and mass shell singularities, the fermion pole mass is gauge independent.

General linear gauges and amplitudes in open string field theory

A general class of gauges for open string field theory, for which the gauge fixing condition is given by linear equations with respect to string field, is investigated in detail. This class of gauges includes almost all known ones like Siegel gauge and its various extensions such as a-gauges proposed by the present authors as well as Schnabl gauge and linear b-gauges. A general form of propagators is determined and their common features are analyzed. A consistent procedure for calculating the amplitudes is given. Gauge independence of the on-shell physical amplitudes is explicitly shown.

Reduced Hamiltonian for intersecting shells

The gauge usually adopted for extracting the reduced Hamiltonian of a thin spherical shell of matter in general relativity, becomes singular when dealing with two or more intersecting shells. We introduce here a more general class of gauges which is apt for dealing with intersecting shells. As an application we give the Hamiltonian treatment of two intersecting shells, both massive and massless. Such a formulation is applied to the computation of the semiclassical tunneling probability of two shells. The probability for the emission of two shells is simply the product of the separate probabilities thus showing no correlation in the emission probabilities in this model.

Binary black-hole dynamics at the third-and-a-half post-Newtonian order in the ADM formalism

We specialize the radiation-reaction part of the Arnowitt-Deser-Misner (ADM) Hamiltonian for many non-spinning point-like bodies, calculated by Jaranowski and Schaefer [1], to third-and-a-half post-Newtonian approximation to general relativity, to binary systems. This Hamiltonian is used for the computation of the instantaneous gravitational energy loss of a binary to 1PN reactive order. We also derive the equations of motion, which include PN reactive terms via Hamiltonian and Euler-Lagrangian approaches. The results are consistent with the expressions for reactive acceleration provided by Iyer-Will formalism in Ref. [2] in a general class of gauges.

BFV-BRST quantization of two-dimensional supergravity.

Two-dimensional supergravity theory is quantized as an anomalous gauge theory. In the Batalin-Fradkin (BF) formalism, the anomaly-canceling super-Liouville fields are introduced to identify the original second-class constrained system with a gauge-fixed version of a first-class system. The BFV-BRST quantization applies to formulate the theory in the most general class of gauges. A local effective action constructed in the configuration space contains two super-Liouville actions; one is a noncovariant but local functional written only in terms of two-dimensional supergravity fields, and the other contains the super-Liouville fields canceling the super-Weyl anomaly. Auxiliary fields for the Liouville and the gravity supermultiplets are introduced to make the BRST algebra close off-shell. Inclusion of them turns out to be essentially important especially in the super-light-cone gauge fixing, where the supercurvature equations (${\mathrm{\ensuremath{\partial}}}_{\mathrm{\ensuremath{-}}}^{3}$${\mathit{g}}_{++}$=${\mathrm{\ensuremath{\partial}}}_{\mathrm{\ensuremath{-}}}^{2}$${\mathrm{\ensuremath{\chi}}}_{++}$=0) are obtained as a result of BRST invariance of the theory. Our approach reveals the origin of the OSp(1,2) current algebra symmetry in a transparent manner. \textcopyright{} 1996 The American Physical Society.

Gauge equivalence in two-dimensional gravity.

Two-dimensional quantum gravity is identified as a second-class system which we convert into a first-class system via the Batalin-Fradkin (BF) procedure. Using the extended phase space method, we then formulate the theory in most general class of gauges. The conformal gauge action suggested by David, Distler and Kawai is derived from a first principle. We find a local, light-cone gauge action whose Becchi-Rouet-Stora-Tyutin invariance implies Polyakov's curvature equation $\partial_{-}R=\partial_{-}^{3}g_{++}=0$, revealing the origin of the $SL(2,R)$ Kac-Moody symmetry. The BF degree of freedom turns out be dynamically active as the Liouville mode in the conformal gauge, while in the light-cone gauge the conformal degree of freedom plays that r{\^o}le. The inclusion of the cosmological constant term in both gauges and the harmonic gauge-fixing are also considered.

CANONICAL TREATMENT OF TWO-DIMENSIONAL GRAVITY AS AN ANOMALOUS GAUGE THEORY

The extended phase space method of Batalin, Fradkin and Vilkovisky is applied to formulate two-dimensional gravity in a general class of gauges. A BRST formulation of the light-cone gauge is presented to reveal the relationship between the BRST symmetry and the origin of SL (2, ℝ) current algebra. From the same principle we derive the conformal gauge action suggested by David, Distler and Kawai.

Path-dependent formulation of gauge theories and the origin of field copies in the non-Abelian case

The introduction of path-dependent potentials, as new relevant objects, allows us to relate in a natural way the path-dependent formulation of gauge theories to other point-function formulations. The absence of field copies in a very general class of gauges is proven in a rather obvious geometric way.

Quantization of supersymmetric gauge theories

We consider the quantization of supersymmetric gauge theories in a rather general class of gauges. A generating functional is constructed that is supersymmetric, for which we formulate the Ward--Takahashi identities of the local gauge invariance. The existence of a supermultiplet of ghost fields is established. We present several examples to demonstrate the consistency of our approach. (AIP)