Laurent Baulieu

Covariant quantization of non-Abelian antisymmetric tensor gauge theories

Abstract The non-Abelian Freedman-Townsend gauge tensor model is quantized in large class of covariant gauges using the geometrical reinterpretation of the BRS equations. In addition to the now usual pyramid of gauge and ghost states, a pyramid of auxiliary fields is found in our construction. These fields enforce the consistency of equations of motion and the integrability of the BRS equations.

Anomalies and Gauge Symmetry

Abstract Anomalies are known to have an intrinsic geometrical meaning. Using a formalism where the gauge condition is never made explicit we reanalyze the gauge theory anomaly problem. By requiring simultaneously the BRS and anti-BRS invariances, we do not need to use in our study the gauge dependent anti-ghost equation of motion. Then all equations definining the anomaly are independent of all parameters specifying the lagrangian. Not only does this stress explicitly the geometrical nature of the anomaly problem, but it allows for a single analysis for all possible BRS and anti-BRS invariant gauges, including those with four-ghost interactions. Our method for solving the anomaly equations is as a new sign of the relevance of the formalism in which the ghost components are unified with those of the classical gauge field, the ghost fields playing the role of a “connection” along unphysical directions. We recover the ABJ anomaly directly from the structure of BRS equations, as a straightforward application of the Chern-Weil theorem in some enlarged space. The method can be formally extended to higher space-time dimensions, and a general formula for “anomalies” in any even dimension is given.

Beltrami parametrization and string theory

Abstract By introducing Beltrami differentials to describe the conformal structure of the worldsheet, we prove the factorization of two-dimensional diffeomorphisms and of the corresponding BRS symmetry which is relevant for the string theory. Weyl invariance appears as a fundamental symmetry of the problem. Factorization of the connected tree diagrams is proven.

On the covariant quantization of the free bosonic string

Abstract The covariant quantization of the free bosonic string in the Landau-type background-metric gauge is formulated in terms of the Slavnov identity which constraints the correlation functions of the energy-momentum tensor. The resulting theory is a “conformal” one.

Path integral on the quantum plane

Abstract We construct the path integral representation of quantum mechanics on the quantum plane with coordinates satisfying z z =q 2 z z . To this end, we introduce a new differential and integral calculus, and generalize the holomorphic representations of Fermi and Bose particles. When q2 is a root of unity, we obtain an extension of Berezin calculus. We discuss also the irrational case, for which the formulae turn out to be similar.

Monopoles and topological field theory

Abstract We present a topological quantum field theory for magnetic monopoles in an SU( N ) Yang-Mills-Higgs model. This field theory is obtained by gauge fixing the topological action defining the monopole charge. This work extends to the three-dimensional case the quantization of invariant polynomials in four dimensions. We choose the Bogomolny self-duality equations as gauge conditions for the magnetic monopole topological field theory. In this way the geometrical equation discussed e.g. in Atiyah and Hitchins work are recovered as ghost equations of motion. We give the cocycles of the corresponding topological symmetry. In the N →∞ limit interesting phenomena occur. The functional integration is forced to cover only the moduli space and the role of the ghosts stemming from the gauge fixing process is to provide a smooth semiclassical approximation.

Cohomological Yang-Mills theory in eight-dimensions

We construct nearly topological Yang-Mills theories on eight dimensional manifolds with a special holonomy group. These manifolds are the Joyce manifold with

BRST symmetry for finite-dimensional invariances: Applications to global zero modes in string theory

Spin(7)

Beltrami parametrization for superstrings

holonomy and the Calabi-Yau manifold with SU(4) holonomy. An invariant closed four form

Quantum structure of the unified N = 1 supergravity and N = 1 super-Yang-Mills theory

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