Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userQuantization of Hamiltonian coactions via twist
62
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this paper we introduce a notion of quantum Hamiltonian (co)action of Hopf algebras endowed with Drinfeld twist structure (resp., 2-cocycles). First, we define a classical Hamiltonian action in the setting of Poisson Lie groups compatible with the 2-cocycle stucture and we discuss a concrete example. This allows us to construct, out of the classical momentum map, a quantum momentum map in the setting of Hopf coactions and to quantize it by using Drinfeld approach.
rate research
Read More
We show that the associative algebra structure can be incorporated in the BRST quantization formalism for gauge theories such that extension from the corresponding Lie algebra to the associative algebra is achieved using operator quantization of reducible gauge theories. The BRST differential that encodes the associativity of the algebra multiplication is constructed as a second-order quadratic differential operator on the bar resolution.
Fedosovs simple geometrical construction for deformation quantization of symplectic manifolds is generalized in three ways without introducing new variables: (1) The base manifold is allowed to be a supermanifold. (2) The star product does not have to be of Weyl/symmetric or Wick/normal type. (3) The initial geometric structures are allowed to depend on Plancks constant.
In a seminal paper Drinfeld explained how to associate to every classical r-matrix for a Lie algebra $lie g$ a twisting element based on $mathcal{U}(lie g)[[hbar]]$, or equivalently a left invariant star product of the corresponding symplectic structure $omega$ on the 1-connected Lie group G of g. In a recent paper, the authors solve the same problem by means of Fedosov quantization. In this short note we provide a connection between the two constructions by computing the characteristic (Fedosov) class of the twist constructed by Drinfeld and proving that it is the trivial class given by $ frac{[omega]}{hbar}$.
We present a superfield construction of Hamiltonian quantization with N=2 supersymmetry generated by two fermionic charges Q^a. As a byproduct of the analysis we also derive a classically localized path integral from two fermionic objects Sigma^a that can be viewed as ``square roots of the classical bosonic action under the product of a functional Poisson bracket.
We study the deformation complex of the dg wheeled properad of $mathbb{Z}$-graded quadratic Poisson structures and prove that it is quasi-isomorphic to the even M. Kontsevich graph complex. As a first application we show that the Grothendieck-Teichmuller group acts on the genus completion of that wheeled properad faithfully and essentially transitively. As a second application we classify all universal quantizations of $mathbb{Z}$-graded quadratic Poisson structures together with the underlying (so called) homogeneous formality maps.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
