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Structure of BRSInvariant Local Functionals
, 1993
"... For a large class of gauge theories a nilpotent BRSoperator s is constructed and its cohomology in the space of local functionals of the offshell fields is shown to be isomorphic to the cohomology of ˜s = s + d on functions f ( ˜ C, T) of tensor fields T and of variables ˜ C which are constructed ..."
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Cited by 7 (2 self)
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For a large class of gauge theories a nilpotent BRSoperator s is constructed and its cohomology in the space of local functionals of the offshell fields is shown to be isomorphic to the cohomology of ˜s = s + d on functions f ( ˜ C, T) of tensor fields T and of variables ˜ C which are constructed of the ghosts and the connection forms. The result allows general statements about the structure of invariant classical actions and anomaly candidates whose BRSvariation vanishes offshell. The assumptions under which the result holds are thoroughly discussed. 1
M.: General solution of the consistency equation
 Phys. Lett
, 1992
"... We produce the general solution of the WessZumino consistency condition for gauge theories of the Yangmills type, for any ghost number and form degree. We resolve the problem of the cohomological independence of these solutions. In other words we fully describe the local version of the cohomology ..."
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Cited by 6 (0 self)
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We produce the general solution of the WessZumino consistency condition for gauge theories of the Yangmills type, for any ghost number and form degree. We resolve the problem of the cohomological independence of these solutions. In other words we fully describe the local version of the cohomology of the BRS operator, modulo the differential on space–time. This in particular includes the presence of external fields and non–trivial topologies of space–time.
bPhysique Th'eorique et Math'ematique, Universit'e Libre de Bruxelles, and
"... 1 Introduction Gauge symmetries are omnipresent in theoretical physics, especially in particle physics. Wellknown examples of gauge theories are QED and QCD. A common feature of gauge theories is the appearance of unphysical degrees of freedom in 1 ..."
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1 Introduction Gauge symmetries are omnipresent in theoretical physics, especially in particle physics. Wellknown examples of gauge theories are QED and QCD. A common feature of gauge theories is the appearance of unphysical degrees of freedom in 1
A Poincaré lemma for sigma models . . .
, 2009
"... For a sigma model of AKSZtype with target space a Qmanifold, we show that the cohomology in the space of local functionals of the differential associated to the BV master action is locally isomorphic to the cohomology of Q in target space. An analogous result is shown to hold for the cohomology in ..."
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For a sigma model of AKSZtype with target space a Qmanifold, we show that the cohomology in the space of local functionals of the differential associated to the BV master action is locally isomorphic to the cohomology of Q in target space. An analogous result is shown to hold for the cohomology in the space of functional multivectors. Applications in the context of the inverse problem of the calculus of variation for gauge systems are briefly discussed.
Physique Théorique et Mathématique, Université Libre de Bruxelles
"... ABSTRACT. For a sigma model of AKSZtype with target space a Qmanifold, we show that the cohomology in the space of local functionals of the differential associated to the BV master action is locally isomorphic to the cohomology of Q in target space. An analogous result is shown to hold for the coh ..."
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ABSTRACT. For a sigma model of AKSZtype with target space a Qmanifold, we show that the cohomology in the space of local functionals of the differential associated to the BV master action is locally isomorphic to the cohomology of Q in target space. An analogous result is shown to hold for the cohomology in the space of functional multivectors. Applications in the context of the inverse problem of the calculus of variation for gauge systems are briefly discussed.
unknown title
, 2000
"... Lectures on differentials, generalized differentials and on some examples related to theoretical physics Michel DuboisViolette Abstract. These notes contain a survey of some aspects of the theory of differential modules and complexes as well as of their generalization, that is, the theory of Ndiff ..."
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Lectures on differentials, generalized differentials and on some examples related to theoretical physics Michel DuboisViolette Abstract. These notes contain a survey of some aspects of the theory of differential modules and complexes as well as of their generalization, that is, the theory of Ndifferential modules and Ncomplexes. Several applications and examples coming from physics are discussed. The commun feature of these physical applications is that they deal with the theory of constrained or gauge systems. In particular different aspects of the BRS methods are explained and a detailed account of the Ncomplexes arising in the theory of higher spin gauge fields is given. 1.
unknown title
, 2000
"... Lectures on differentials, generalized differentials and on some examples related to theoretical physics Michel DuboisViolette Abstract. These notes contain a survey of some aspects of the theory of differential modules and complexes as well as of their generalization, that is, the theory of Ndiff ..."
Abstract
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Lectures on differentials, generalized differentials and on some examples related to theoretical physics Michel DuboisViolette Abstract. These notes contain a survey of some aspects of the theory of differential modules and complexes as well as of their generalization, that is, the theory of Ndifferential modules and Ncomplexes. Several applications and examples coming from physics are discussed. The commun feature of these physical applications is that they deal with the theory of constrained or gauge systems. In particular different aspects of the BRS methods are explained and a detailed account of the Ncomplexes arising in the theory of higher spin gauge fields is given. 1.
ON THE GEOMETRICAL STRUCTURE OF COVARIANT ANOMALIES IN YANGMILLS THEORY
, 1993
"... Covariant anomalies are studied in terms of the theory of secondary characteristic classes of the universal bundle of YangMills theory. A new set of descent equations is derived which contains the covariant current anomaly and the covariant Schwinger term. The counterterms relating consistent and c ..."
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Covariant anomalies are studied in terms of the theory of secondary characteristic classes of the universal bundle of YangMills theory. A new set of descent equations is derived which contains the covariant current anomaly and the covariant Schwinger term. The counterterms relating consistent and covariant anomalies are determined. A geometrical realization of the BRS/antiBRS algebra is presented which is used to understand the relationship between covariant anomalies in different approaches. *)Erwin Schrödinger fellow, supported by ”Fonds zur
Part I Local Cohomology and the
, 2008
"... The differential forms on the jet bundle J ∞ E of a bundle E → M over a compact nmanifold M of degree greater than n determine differential forms on the space Γ(E) of sections of E. The forms obtained in this way are called local forms on Γ(E), and its cohomology is called the local cohomology of Γ ..."
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The differential forms on the jet bundle J ∞ E of a bundle E → M over a compact nmanifold M of degree greater than n determine differential forms on the space Γ(E) of sections of E. The forms obtained in this way are called local forms on Γ(E), and its cohomology is called the local cohomology of Γ(E). More generally, if a group G acts on E, we can define the local Ginvariant cohomology. The local cohomology is computed in terms of the cohomology of the jet bundle by means of the variational bicomplex theory. A similar result is obtained for the local Ginvariant cohomology. Using these results and the techniques for the computation of the cohomology of invariant variational bicomplexes in terms of relative GelfandFuchs cohomology introduced in [3], we construct non trivial local cohomology classes in the important cases of Riemannian metrics with the action of diffeomorphisms, and connections on a principal bundle with the action of automorphisms. Key words and phrases: local cohomology, variational bicomplex, manifold of sections, space of metrics, space of connections.