相关论文: Quantum Sp(2)-antibrackets and open groups
Canonical coordinates for the Schr\"odinger equation are introduced, making more transparent its Hamiltonian structure. It is shown that the Schr\"odinger equation, considered as a classical field theory, shares with Liouville completely…
We describe an $p$-mechanical (see funct-an/9405002 and quant-ph/9610016) brackets which generate quantum (commutator) and classic (Poisson) brackets in corresponding representations of the Heisenberg group. We \emph{do not} use any kind of…
Within a superfield approach, we formulate a simple quantum generating equation of the field - antifield formalism. Then, we derive the Schroedinger equation with the Hamiltonian whose $\Delta$ - exact part serves as a generator to the…
In this paper, following [1], we develop the theory of global pseudo-differential operators defined on the quantum group $SU_q(2)$, and provide some spectral results concerning these operators. We define a graduation for this algebra of…
We examine applications of polynomial Lie algebras $sl_{pd}(2)$ to solve physical tasks in $G_{inv}$-invariant models of coupled subsystems in quantum physics. A general operator formalism is given to solve spectral problems using…
We demonstrate that the matrix quantum group $SL_q(2)$ gives rise to nontrivial matrix product operator representations of the Lie group $SL(2)$, providing an explicit characterization of the nontrivial global $SU(2)$ symmetry of the XXZ…
A new type of algebras that represent a generalization of both quantum groups and braided groups is defined. These algebras are given by a pair of solutions of the Yang--Baxter equation that satisfy some additional conditions. Several…
The split involution quantization scheme, proposed previously for pure second--class constraints only, is extended to cover the case of the presence of irreducible first--class constraints. The explicit Sp(2)--symmetry property of the…
We complete the classification of quantum subgroups of $SL_q(2)$ with $q$ a root of unity of arbitrary order, that is, Hopf algebra quotients of the quantum function algebras $\mathcal{O}_{q} (SL_2(\mathbb{C}))$.
Global quantization of pseudo-differential operators on compact Lie groups is introduced relying on the representation theory of the group rather than on expressions in local coordinates. Operators on the 3-dimensional sphere and on group…
We give a simple geometrical picture of the basic structures of the covariant $Sp(2)$ symmetric quantization formalism -- triplectic quantization -- recently suggested by Batalin, Marnelius and Semikhatov. In particular, we show that the…
We give a general description of the spectral space of conjugacy classes of subgroups of Sp(2): it is a disjoint union of finitely many blocks, each dominated by a subgroup: of these blocks, 26 are of dimension 1, 6 are of dimension 2 and…
The geometric interpretation of the antibracket formalism given by Witten is extended to cover the anti-BRST symmetry. This enables one to formulate the quantum master equation for the BRST--anti-BRST formalism in terms of integration…
We propose a new formalism of quantum subsystems which allows to unify the existing and new methods of reduced description of quantum systems. The main mathematical ingredients are completely positive maps and correlation functions. In this…
The aim of this lecture is to present in a comprehensible way what the BRST quantization means and how the "classical" master equation, action and BRST transformations have to be prolonged towards the same "quantum" items. The presentation…
An extension of the non-local regularization scheme is formulated in the Sp(2) symmetric Lagrangian BRST quantization framework. It generates a systematic treatment of the anomalous quantum master equations and allows to substract the…
The universal enveloping algebra U(g) of a Lie algebra g acts on its representation ring R through D(R), the ring of differential operators on R. A quantised universal enveloping algebra (or "quantum group") is a deformation of a universal…
A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from \fun\ to \uqg\ , given by elements of the pure braid group. These operators --- the `reflection matrix' $Y \equiv…
An approach to study a generalization of the classical-quantum transition for general systems is proposed. In order to develop the idea, a deformation of the ladder operators algebra is proposed that contains a realization of the quantum…
The quantum master equation is usually formulated in terms of functionals of the components of mappings from a space-time manifold M into a finite-dimensional vector space. The master equation is the sum of two terms one of which is the…