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Covariant Theory of Asymptotic Symmetries, Conservation Laws and Central Charges
, 2001
"... Under suitable assumptions on the boundary conditions, it is shown that there is a bijective correspondence between non trivial asymptotic reducibility parameters and non trivial asymptotically conserved n 2 forms in the context of Lagrangian gauge theories. The asymptotic reducibility parameters ar ..."
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Cited by 132 (17 self)
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Under suitable assumptions on the boundary conditions, it is shown that there is a bijective correspondence between non trivial asymptotic reducibility parameters and non trivial asymptotically conserved n 2 forms in the context of Lagrangian gauge theories. The asymptotic reducibility parameters are the parameters of gauge transformations that vanish suciently fast when evaluated at the background. A universal formula for asymptotically conserved n 2 forms in terms of the reducibility parameters is derived. Sucient conditions for niteness of the charges built out of the asymptotically conserved n 2 forms and for the existence of a Lie algebra g among equivalence classes of asymptotic reducibility parameters are given. The representation of g in terms of the charges may be centrally extended. An explicit and covariant formula for the central charges is constructed. They are shown to be 2cocycles on the Lie algebra g. The general considerations and formulas are applied to electrodynamics, YangMills theory and Einstein gravity where they reproduce familiar results.
Local BRST cohomology in the antifield formalism. I. General theorems
 COMM. MATH. PHYS
, 1995
"... ..."
Tensor constructions of open string theories I
 Foundations,” Nucl. Phys. B
, 1997
"... The possible tensor constructions of open string theories are analyzed from first principles. To this end the algebraic framework of open string field theory is clarified, including the role of the homotopy associative A ∞ algebra, the odd symplectic structure, cyclicity, star conjugation, and twist ..."
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Cited by 105 (7 self)
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The possible tensor constructions of open string theories are analyzed from first principles. To this end the algebraic framework of open string field theory is clarified, including the role of the homotopy associative A ∞ algebra, the odd symplectic structure, cyclicity, star conjugation, and twist. It is also shown that two string theories are offshell equivalent if the corresponding homotopy associative algebras are homotopy equivalent in a strict sense. It is demonstrated that a homotopy associative star algebra with a compatible even bilinear form can be attached to an open string theory. If this algebra does not have a spacetime interpretation, positivity and the existence of a conserved ghost number require that its cohomology is at degree zero, and that it has the structure of a direct sum of full matrix algebras. The resulting string theory is shown to be physically equivalent to a string theory with a familiar open string gauge group.
Threedimensional quantum geometry and black holes
"... We review some aspects of threedimensional quantum gravity with emphasis in the ‘CFT → Geometry ’ map that follows from the BrownHenneaux conformal algebra. The general solution to the classical equations of motion with antide Sitter boundary conditions is displayed. This solution is parametrized ..."
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Cited by 70 (3 self)
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We review some aspects of threedimensional quantum gravity with emphasis in the ‘CFT → Geometry ’ map that follows from the BrownHenneaux conformal algebra. The general solution to the classical equations of motion with antide Sitter boundary conditions is displayed. This solution is parametrized by two functions which become Virasoro operators after quantisation. A map from the space of states to the space of classical solutions is exhibited. Some recent proposals to understand the BekensteinHawking entropy are reviewed in this context. The origin of the boundary degrees of freedom arising in 2+1 gravity is analysed in detail using a Hamiltonian ChernSimons formalism. 1
Courant algebroids and strongly homotopy Lie algebras
 Lett. Math. Phys
, 1998
"... Abstract. Courant algebroids are structures which include as examples the doubles of Lie bialgebras and the bundle TM ⊕ T ∗ M with the bracket introduced by T. Courant for the study of Dirac structures. Within the category of Courant algebroids one can construct the doubles of Lie bialgebroids, the ..."
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Cited by 68 (5 self)
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Abstract. Courant algebroids are structures which include as examples the doubles of Lie bialgebras and the bundle TM ⊕ T ∗ M with the bracket introduced by T. Courant for the study of Dirac structures. Within the category of Courant algebroids one can construct the doubles of Lie bialgebroids, the infinitesimal objects for Poisson groupoids. We show that Courant algebroids can be considered as strongly homotopy Lie algebras. 1.
Canonical structure of classical field theory in the polymomentum phase space
 Rep. Math. Phys
, 1998
"... Canonical structure of classical field theory in n dimensions is studied within the covariant polymomentum Hamiltonian formulation of De Donder–Weyl (DW). The bivertical (n + 1)form, called polysymplectic, is put forward as a generalization of the symplectic form in mechanics. Although not given i ..."
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Cited by 67 (10 self)
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Canonical structure of classical field theory in n dimensions is studied within the covariant polymomentum Hamiltonian formulation of De Donder–Weyl (DW). The bivertical (n + 1)form, called polysymplectic, is put forward as a generalization of the symplectic form in mechanics. Although not given in intrinsic geometric terms differently than a certain coset it gives rise to an invariantly defined map between horizontal forms playing the role of dynamical variables and the socalled vertical multivectors generalizing Hamiltonian vector fields. The analogue of the Poisson bracket on forms is defined which leads to the structure of Zgraded Lie algebra on the socalled Hamiltonian forms for which the map above exists. A generalized Poisson structure appears in the form of what we call a “higherorder ” and a right Gerstenhaber algebra. The equations of motion of forms are formulated in terms of the Poisson bracket with the DW Hamiltonian nform H ˜ vol ( ˜ vol is the spacetime volume form, H is the DW Hamiltonian function) which is found to be related to the operation of the total exterior differentiation of forms. A few applications and a relation to the standard Hamiltonian formalism in field theory are briefly discussed. 1
Partial and Complete Observables for Hamiltonian Constrained Systems
 grqc/0411013 T. Thiemann, “Reduced Phase Space Quantization and Dirac Observables”, grqc/0411031
"... We will pick up the concepts of partial and complete observables introduced by Rovelli in [1] in order to construct Dirac observables in gauge systems. We will generalize these ideas to an arbitrary number of gauge degrees of freedom. Different methods to calculate such Dirac observables are develop ..."
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Cited by 63 (7 self)
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We will pick up the concepts of partial and complete observables introduced by Rovelli in [1] in order to construct Dirac observables in gauge systems. We will generalize these ideas to an arbitrary number of gauge degrees of freedom. Different methods to calculate such Dirac observables are developed. For background independent field theories we will show that partial and complete observables can be related to Kuchaˇr’s Bubble Time Formalism [2]. Moreover one can define a nontrivial gauge action on the space of complete observables and also state the Poisson brackets of these functions. Additionally we will investigate, whether it is possible to calculate Dirac observables starting with partially invariant partial observables, for instance functions, which are invariant under the spatial diffeomorphism group. 1
Consistent interactions between gauge fields: the cohomological approach
 In Henneaux et al. [54
"... Recent results on the cohomological reformulation of the problem of consistent interactions between gauge fields are illustrated in the case of the YangMills models. By evaluating the local BRST cohomology through descent equation techniques, it is shown (i) that there is a unique local, Poincaré i ..."
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Cited by 57 (3 self)
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Recent results on the cohomological reformulation of the problem of consistent interactions between gauge fields are illustrated in the case of the YangMills models. By evaluating the local BRST cohomology through descent equation techniques, it is shown (i) that there is a unique local, Poincaré invariant cubic vertex for free gauge vector fields which preserves the number of gauge symmetries to first order in the coupling constant; and (ii) that consistency to second order in the coupling constant requires the structure constants appearing in the cubic vertex to fulfill the Jacobi identity. The known uniqueness of the YangMills coupling is therefore rederived through cohomological arguments. 1.