Related papers: On the algebra of quantum observables for a certai…
It is proved that for a vector space W, any set of parafermion-like vertex operators on W in a certain canonical way generates a generalized vertex algebra in the sense of [DL2] with W as a natural module. This result generalizes a result…
We construct and characterize quantum Garnier systems in two variables including degenerate cases by certain holomorphic properties under the quantum canonical transformations.
Let us consider a polynomial algebra in three variables equipped with an integer grading. We construct a system of group-generating automorphisms that preserve a given grading.
Using the formalism of discrete quantum group gauge theory, one can construct the quantum algebras of observables for the Hamiltonian Chern-Simons model. The resulting moduli algebras provide quantizations of the algebra of functions on the…
Gauge symmetries generally appear as a constraint algebra, under which one expects all physical states to be singlets. However, quantum anomalies and boundary conditions introduce central charges and change this picture, thus causing…
The recent construction of integrable quantum field theories on two-dimensional Minkowski space by operator-algebraic methods is extended to models with a richer particle spectrum, including finitely many massive particle species…
In this paper the q-deformed $W$ algebra $\WW_q$ is constructed, whose nontrivial quantum group structure is presented.
It is shown how the programme of decoherence can be applied in the context of quantum field theory. To illustrate the role of gauge invariance, we first discuss the charge superselection rule in quantum electrodynamics in some detail. We…
We address the construction and interpretation of diffeomorphism-invariant observables in a low-energy effective theory of quantum gravity. The observables we consider are constructed as integrals over the space of coordinates, in analogy…
We study here the algebraic structure of the conserved generators from which the microcanonical and canonical ensembles are constructed on an underlying generalized quantum dynamics, and the flows they induce on the phase space. We also…
MV-algebras can be viewed either as the Lindenbaum algebras of Lukasiewicz infinite-valued logic, or as unit intervals [0,u] of lattice-ordered abelian groups in which a strong order unit u>0 has been fixed. They form an equational class,…
There is a relatively well understood class of deformable W-algebras, resulting from Drinfeld-Sokolov (DS) type reductions of Kac-Moody algebras, which are Poisson bracket algebras based on finitely, freely generated rings of differential…
The rotation group is formulated based on the abstract $B(X)$-module framework. Although the infinitesimal generators of rotation group include differential operators, the rotation group is formulated utilizing the framework of bounded…
It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum…
The objective of this paper is to determine the finite dimensional, indecomposable representations of the algebra that is generated by two complex structures over the real numbers. Since the generators satisfy relations that are similar to…
We show an algebra morphism between Yangians and some finite W-algebras. This correspondence is nicely illustrated in the framework of the Non Linear Schrodinger hierarchy. For such a purpose, we give an explicit realization of the Yangian…
Beginning with ordinary quantum mechanics for spinless particles, together with the hypothesis that all experimental measurements consist of positional measurements at different times, we characterize directly a class of nonlinear quantum…
The concept of ergodicity---the convergence of the temporal averages of observables to their ensemble averages---is the cornerstone of thermodynamics. The transition from a predictable, integrable behavior to ergodicity is one of the most…
We discuss the notion about physical quantities as having values represented by real numbers, and its limiting to describe nature to be understood in relation to our appreciation that the quantum theory is a better theory of natural…
The infinitesimal action of Kappa-Poincar'e group on Kappa-Minkowski space is computed both for generators of Kappa-Poincar'e algebra and those of Woronowicz generalized Lie algebra. The notion of invariant operators is introduced and…