On the variational noncommutative poisson geometry

Journal Article · Sat Sep 15 00:00:00 EDT 2012 · Physics of Particles and Nuclei

DOI:https://doi.org/10.1134/S1063779612050188· OSTI ID:22977151

Kiselev, A. V., E-mail: [e-mail]

We outline the notions and concepts of the calculus of variational multivectors within the Poisson formalism over the spaces of infinite jets of mappings from commutative (non)graded smooth manifolds to the factors of noncommutative associative algebras over the equivalence under cyclic permutations of the letters in the associative words. We state the basic properties of the variational Schouten bracket and derive an interesting criterion for (non)commutative differential operators to be Hamiltonian (and thus determine the (non)commutative Poisson structures). We place the noncommutative jet-bundle construction at hand in the context of the quantum string theory.

• OSTI ID: 22977151
• Journal Information: Physics of Particles and Nuclei, Vol. 43, Issue 5; Other Information: Copyright (c) 2012 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-7796
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMMUTATION RELATIONS
DIFFERENTIAL OPERATORS
JET MODEL
SMOOTH MANIFOLDS
STRING THEORY
VARIATIONAL METHODS