• Corpus ID: 119577086

Homotopy Poisson-n Algebras from N-plectic Structures

@article{Richter2015HomotopyPA,
  title={Homotopy Poisson-n Algebras from N-plectic Structures},
  author={Mirco Richter},
  journal={arXiv: Differential Geometry},
  year={2015}
}
  • M. Richter
  • Published 3 June 2015
  • Mathematics
  • arXiv: Differential Geometry
We associate a homotopy Poisson-n algebra to any higher symplectic structure, which generalizes the common symplectic Poisson algebra of smooth functions. This provides robust n-plectic prequantum data for most approaches to quantization. 
1 Citations

Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-Time

The functional Schrödinger representation of a nonlinear scalar quantum field theory in curved space-time is shown to emerge as a singular limit from the formulation based on precanonical

References

SHOWING 1-10 OF 17 REFERENCES

On the universal enveloping algebra of a Lie algebroid

We review the extent to which the structure of the universal enveloping algebra of a Lie algebroid over a manifold M resembles a Hopf algebra, and prove a Cartier-Milnor-Moore theorem for this type

Homotopy algebra and iterated integrals for double loop spaces

This paper provides some background to the theory of operads, used in the first author's papers on 2d topological field theory (hep-th/921204, CMP 159 (1994), 265-285; hep-th/9305013). It is intended

THE POISSON BRACKET FOR POISSON FORMS IN MULTISYMPLECTIC FIELD THEORY

We present a general definition of the Poisson bracket between differential forms on the extended multiphase space appearing in the geometric formulation of first order classical field theories and,

Higher Symplectic Geometry

Author(s): Rogers, Christopher Lee | Advisor(s): Baez, John C | Abstract: In higher symplectic geometry, we consider generalizations of symplectic manifolds called n-plectic manifolds. We say a

Poisson cohomology and quantization.

Let R be a commutative ring, and let A be a Poisson algebra over R. We construct an (R,A)-Lie algebra structure, in the sense of Rinehart, on the A-module of K\"ahler differentials of A depending

Homotopy Batalin–Vilkovisky algebras

This paper provides an explicit cobrant resolution of the operad encoding Batalin{Vilkovisky algebras. Thus it denes the notion of homotopy Batalin{Vilkovisky algebras with the required homotopy

DIFFERENTIAL FORMS ON GENERAL COMMUTATIVE ALGEBRAS

Introduction. Let K be a commutative ring with ulnit, and let R be a commutative unitary K-algebra. We shall be concerned with variously defined cohomology theories based on algebras of differential

Loop Spaces, Characteristic Classes and Geometric Quantization

This book deals with the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Recent developments in mathematical

The Schouten-Nijenhuis bracket and interior products