相关论文: Vector coherent state representations, induced rep…
It is shown how the coherent states permit to find different geometrical objects as the geodesics, the conjugate locus, the cut locus, the Calabi's diastasis and its domain of definition, the Euler-Poincar\'e characteristic, the number of…
The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship…
The geometric quantization problem is considered from the point of view of the Davies and Lewis approach to quantum mechanics. The influence of the measuring device is accounted in the classical and quantum case and it is shown that the…
We unify three approaches within the vast body of gauge-theory research that have independently developed distinct representations of a geometrical surface-like structure underlying the vector-potential. The three approaches that we unify…
We analyze the elements characterizing the theory of induced representations of Lie groups, in order to generalize it to quantum groups. We emphasize the geometric and algebraic aspects of the theory, because they are more suitable for…
Quantum computation is based on tensor products and entangled states. We discuss an alternative to the quantum framework where tensor products are replaced by geometric products and entangled states by multivectors. The resulting theory is…
New quantal states which interpolate between the coherent states of the Heisenberg_Weyl and SU(1,1) algebras are introduced. The interpolating states are obtained as the coherent states of a closed and symmetric algebra which interpolates…
We describe a number of geometric contexts where categorification appears naturally: coherent sheaves, constructible sheaves and sheaves of modules over quantizations. In each case, we discuss how "index formulas" allow us to easily perform…
We start with definitions of the general notions of the theory of $\Bbb Z_{2}$-graded algebras. Then we consider theory of inductive families of $\Bbb Z_{2}$-graded semisimple finite-dimensional algebras and its representations in the…
We study and classify a class of representations (called generalized geometric representations) of a Coxeter group of finite rank. These representations can be viewed as a natural generalization of the geometric representation. The…
This paper presents State Algebra, a novel framework designed to represent and manipulate propositional logic using algebraic methods. The framework is structured as a hierarchy of three representations: Set, Coordinate, and Row…
We introduce the notion of (twisted) quiver representations in abelian categories and study the category of such representations. We construct standard resolutions and coresolutions of quiver representations and study basic homological…
p-Mechanics is a consistent physical theory which describes both quantum and classical mechanics simultaneously. We continue the development of p-mechanics by introducing the concept of states. The set of coherent states we introduce allow…
In this paper the generalized quantum states, i.e. positive and normalized linear functionals on $C^{*}$-algebras, are studied. Firstly, we study normal states, i.e. states which are represented by density operators, and singular states,…
A simple, and elegant geometrical representation is developed to describe the concept of coherence and squeezing for angular momentum operators. Angular momentum squeezed states were obtained by applying Bogoliubov transformation on the…
To a representation of $\O_N$ (the Cuntz algebra with $N$ generators) we associate a projection valued measure and we study the case when this measure has atoms. The main technical tool are the spaces invariant for all the operators…
This paper is based on my talk at ICM on recent progress in a number of classical problems of linear algebra and representation theory, based on new approach, originated from geometry of stable bundles and geometric invariant theory.
The representations of the observable algebra of a low dimensional quantum field theory form the objects of a braided tensor category. The search for gauge symmetry in the theory amounts to finding an algebra which has the same…
We present a general unified approach for finding the coherent states of polynomially deformed algebras such as the quadratic and Higgs algebras, which are relevant for various multiphoton processes in quantum optics. We give a general…
Informally, the 'linear representation hypothesis' is the idea that high-level concepts are represented linearly as directions in some representation space. In this paper, we address two closely related questions: What does "linear…