Some Classical and Quantum Algebras
نویسندگان
چکیده
We discuss the notion of a Batalin-Vilkovisky (BV) algebra and give several classical examples from differential geometry and Lie theory. We introduce the notion of a quantum operator algebra (QOA) as a generalization of a classical operator algebra. In some examples, we view a QOA as a deformation of a commutative algebra. We then review the notion of a vertex operator algebra (VOA) and show that a vertex operator algebra is a QOA with some additional structures. Finally, we establish a connection between BV algebras and VOAs.
منابع مشابه
فرمولبندی هندسی کوانتش تغییرشکل برزین
In this paper we try to formulate the Berezin quantization on projective Hilbert space P(H) and use its geometric structure to construct a correspondence between a given classical theory and a given quantum theory. It wil be shown that the star product in berezin quantization is equivalent to the Posson bracket on coherent states manifold M, embodded in P(H), and the Berezin method is used to...
متن کاملConstacyclic Codes over Group Ring (Zq[v])/G
Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...
متن کاملOn quantum and classical Poisson algebras
Results on derivations and automorphisms of some quantum and classical Poisson algebras, as well as characterizations of manifolds by the Lie structure of such algebras, are revisited and extended. We prove in particular somehow unexpected fact that the algebras of linear differential operators acting on smooth sections of two real vector bundles of rank 1 are isomorphic as Lie algebras if and ...
متن کاملSome Introductory Notes on Quantum Groups, Quantum Algebras, and Their Applications †
Some very elementary ideas about quantum groups and quantum algebras are introduced and a few examples of their physical applications are mentioned. Concepts of quantum groups and algebras emerged from two directions : • Studies on quantum integrable models using the quantum inverse scattering method ([1]-[4]) led to certain deformations, or quantizations, of classical matrix groups and the cor...
متن کاملمروری بر شبکه های عصبی کوانتومی
In this paper the development of quantum neural networks (QNN), and some of presented models and physical implementation are reviewed. How of making use of double-slit experiment for implementing QNN and methods of designing as well as examples of two-layer hybrid networks in QNN constructed from quantum neurons and classical neurons are represented. Some application models of the networks (QNN...
متن کامل