Non-Abelian antibrackets

Alfaro, Jorge; Damgaard, Poul H.

doi:10.1016/0370-2693(95)01533-7

Cited by 25 publications

(107 citation statements)

References 33 publications

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“…It may be remarked that the weakly canonical form of the antibrackets is somewhat reminiscent of the 'non-Abelian' antibrackets of [13], however a significant difference is that the non-Abelian antibracket involves some functions u A i that depend on the φ A fields in such a way that the derivations u A In this way, we obtain a vector field on the triplectic manifold which ensures the Sp(2) covariance of the weakly canonical, but not reducible, antibrackets of the form (3.18) in which e i α has the form (A.1), (A.6). It can also be shown that there exist Sp(2)-covariant vector fields V a that differentiate the antibrackets defined by the above c i j .…”

Section: Discussionmentioning

confidence: 99%

“…Thus, we have found a local coordinate system (x i , ξ 1j , ξ 2α ) in which (removing the tilde) 13) with all the other pairwise antibrackets of the coordinate functions vanishing. The symmetrized Jacobi identities for the antibrackets of the form (3.13) show that the functions λ ij depend only on ξ 1i , ξ 2α and satisfy the equations…”

Section: Finding Weak Canonical Coordinatesmentioning

confidence: 99%

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Canonical form of a pair of compatible antibrackets

Grigoriev

Semikhatov

1998

Physics Letters B

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In the triplectic quantization of general gauge theories, we prove a 'triplectic' analogue of the Darboux theorem: we show that the doublet of compatible antibrackets can be brought to a weakly-canonical form provided the general triplectic axioms of [2] are imposed together with some additional requirements that can be formulated in terms of marked functions of the antibrackets. The weakly-canonical antibrackets involve an obstruction to bringing them to the canonical form. We also classify the 'triplectic' odd vectors fields compatible with the weakly-canonical antibrackets and construct the Poisson bracket associated with the antibrackets and the odd vector fields. We formulate the Sp(2)-covariance requirement for the antibrackets and the vector fields; whenever the obstruction to the canonical form of the antibrackets vanishes, the Sp(2)-covariance condition implies the canonical form of the triplectic vector fields.

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Section: Discussionmentioning

confidence: 99%

Section: Finding Weak Canonical Coordinatesmentioning

confidence: 99%

Canonical form of a pair of compatible antibrackets

Grigoriev

Semikhatov

1998

Physics Letters B

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“…This works nicely for P = Lie, because we know what is a higher order coderivation of a cocommutative coalgebra. But we are not sure whether there exists a reasonable concept of higher-order coderivations without the cocommutativity, though the paper [4] seems to suggest this.…”

Section: Definitionmentioning

confidence: 98%

“…Conditions (3) and (4) also imply that the element := (−1) s s ⊗ s ∈ H ⊗2 rel is symmetric in the sense that (−1) s s ⊗ s = (−1) s s ⊗ s = −(−1) s s ⊗ s . (6) We use, in the previous formula as well as at many places in the rest of the paper, the Einstein convention of summing over repeated indices.…”

Section: Introductionmentioning

confidence: 99%

Loop Homotopy Algebras in Closed String Field Theory

Markl¹

2001

Commun. Math. Phys.

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Barton Zwiebach constructed the `string products' on the Hilbert space of combined conformal field theory of matter and ghosts. It is well-known that the `tree level' specialization of these products forms a strongly homotopy Lie algebra. A strongly homotopy Lie algebra is given by a square zero coderivation on the cofree cocommutative connected coalgebra, on the other hand, strongly homotopy Lie algebras are algebras over the cobar construction on the commutative algebras operad. The aim of our paper is to give two similar characterizations of the structure formed by the `string products' of arbitrary genera. Our first characterization will be based on the notion of a higher order coderivation, the second characterization will be based on the machinery of modular operads. We will also discuss possible generalizations to open string field theory.Comment: LaTeX 2.09, 29 pages. Section "Loop homotopy Lie algebras - operadic approach" substantially revise

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“…A first analysis of this more general framework was carried out in ref. [6], and it has more recently been considered from a different point of view [7,8]. The relevant mathematical structure can be described by a tower of higher antibrackets [9], and their associated algebra [8].…”

Section: Introductionmentioning

confidence: 99%

Second class constraints in a higher-order Lagrangian formalism

Batalin

Беринг

Damgaard³

1997

Physics Letters B

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We consider the description of second-class constraints in a Lagrangian path integral associated with a higher-order ∆-operator. Based on two conjugate higher-order ∆-operators, we also propose a Lagrangian path integral with Sp(2) symmetry, and describe the corresponding system in the presence of second-class constraints.NBI-HE-96-60 UUITP-09/97 hep-th/9703199 * Here, and in the following, [·, ·] equals the graded supercommutator: [A, B] = AB − (−1) ǫ A ǫ B BA.

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Non-Abelian antibrackets

Cited by 25 publications

References 33 publications

Canonical form of a pair of compatible antibrackets

Canonical form of a pair of compatible antibrackets

Loop Homotopy Algebras in Closed String Field Theory

Second class constraints in a higher-order Lagrangian formalism

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