Related papers: Group Theoretical Quantization of Phase and Modulu…
Beginning with a skew-symmetric matrix, we define a certain Poisson--Lie group. Its Poisson bracket can be viewed as a cocycle perturbation of the linear (or "Lie-Poisson") Poisson bracket. By analyzing this Poisson structure, we gather…
We study moduli spaces of lattice-polarized K3 surfaces in terms of orbits of representations of algebraic groups. In particular, over an algebraically closed field of characteristic 0, we show that in many cases, the nondegenerate orbits…
We formulate quantum mechanics on SO(3) using a non-commutative dual space representation for the quantum states, inspired by recent work in quantum gravity. The new non-commutative variables have a clear connection to the corresponding…
Let V(KG) be a normalised unit group of the modular group algebra of a finite p-group G over the field K of p elements. We introduce a notion of symmetric subgroups in V(KG) as subgroups invariant under the action of the classical…
In this work, a class of semiclassical Fourier Integral Operators (FIOs) with complex phase associated to some canonical transformation of the phase space $T^*\R^d$ is constructed. Upon some general boundedness assumptions on the symbol and…
In this article, we show that Fourier eigenmeasures supported on spheres with radii given by a locally finite sequence, which we call $k$-spherical measures, correspond to Fourier series exhibiting a modular-type transformation behaviour…
Chern-Simons Theories with gauge super-groups appear naturally in string theory and they possess interesting applications in mathematics, e.g. for the construction of knot and link invariants. This paper is the first in a series where we…
This is an introduction to the group algebras of the symmetric groups, written for a quarter-long graduate course. After recalling the definition of group algebras (and monoid algebras) in general, as well as basic properties of…
We study a new class of infinite dimensional Lie algebras, which has important applications to the theory of integrable equations. The construction of these algebras is very similar to the one for automorphic functions and this motivates…
The aim of this paper is to study the classification of generic coherent state representations of a Lie group and its connection to the structure theory of K\"{a}hler algebras. The group we deal with is the holomorphic automorphism group of…
Notwithstanding known obstructions to this idea, we formulate an attempt to turn quantization into a functorial procedure. We define a category PO of Poisson manifolds, whose objects are integrable Poisson manifolds and whose arrows are…
The Lie and module (Rinehart) algebraic structure of vector fields of compact support over C infinity functions on a (connected) manifold M define a unique universal non-commutative Poisson * algebra. For a compact manifold, a…
We investigate refined algebraic quantisation with group averaging in a finite-dimensional constrained Hamiltonian system that provides a simplified model of general relativity. The classical theory has gauge group SL(2,R) and a…
Starting with an operator in the universal enveloping algebra of a semi-simple, complex Lie group the nearest neighbor statistics of the spectra of this operator along a sequence of representations are discussed. After a short introduction…
A general model independent approach using the `off-shell Bethe Ansatz' is presented to obtain an integral representation of generalized form factors. The general techniques are applied to the quantum sine-Gordon model alias the massive…
The Feynman path integral is used to quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U_q(su(2)). This is achieved by finding explicit Darboux coordinates and then using a…
We construct a counter example showing, for the quadratic quantization, the identity $(\Gamma(T))^*= \Gamma(T^*)$ is not necessarily true. We characterize all operators on the one-particle algebra whose quadratic quantization are…
Determining the relationship between composite systems and their subsystems is a fundamental problem in quantum physics. In this paper we consider the spectra of a bipartite quantum state and its two marginal states. To each spectrum we can…
A number of problems in theoretical physics share a common nucleus of combinatoric nature. It is argued here that Hopf algebraic concepts and techiques can be particularly efficient in dealing with such problems. As a first example, a brief…
The domain of application of quantization methods is traditionally restricted to smooth classical observables. We show that the coherent states or "anti-Wick" quantization enables us to construct fairly reasonable quantum versions of…