Related papers: A Topological Study of Induced Representation
We study 2-d $\phi F$ gauge theories with the objective to understand, also at the quantum level, the emergence of induced gravity. The wave functionals - representing the eigenstates of a vanishing flat potential - are obtained in the…
We investigate the tomography of unknown unitary quantum processes within the framework of a finite-dimensional Wigner-type representation. This representation provides a rich visualization of quantum operators by depicting them as shapes…
Dynamical inverse problem of representation theory, which has its origin in a classical paper of E.P.Wigner on a determination of commutation relations of quantum mechanical quantities by the quantum dynamical equations, is illustrated on…
Represented spaces form the general setting for the study of computability derived from Turing machines. As such, they are the basic entities for endeavors such as computable analysis or computable measure theory. The theory of represented…
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…
Topological transforms have been very useful in statistical analysis of shapes or surfaces without restrictions that the shapes are diffeomorphic and requiring the estimation of correspondence maps. In this paper we introduce two…
Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…
We propose a topological model of induced gravity (pregeometry) where both Newton's coupling constant and the cosmological constant appear as integration constants in solving field equations. The matter sector of a scalar field is also…
In this work we present the formal background used to develop the methods used in earlier works to extend the truncated Wigner representation of quantum and atom optics in order to address multi-time problems. The truncated Wigner…
Structures in low-dimensional topology and low-dimensional geometry -- often combined with ideas from (quantum) field theory -- can explain and inspire concepts in algebra and in representation theory and their categorified versions. We…
We study the tomography of multispin quantum states in the context of finite-dimensional Wigner representations. An arbitrary operator can be completely characterized and visualized using multiple shapes assembled from linear combinations…
Wigner's method of induced representations is applied to the N=1 super-Poincare group, and by using a state corresponding to the basic vector of the little group as a Clifford vacuum we show that the spin operator of a supersymmetric point…
Let $G$ be a locally compact second countable groupoid with a Haar system. In this article, we introduce the induced representation of $G$ from a continuous unitary representation of a closed wide subgroupoid $H$ with a Haarsystem provided…
We study the quantum mechanics of a system of topologically interacting particles in 2+1 dimensions, which is described by coupling the particles to a Chern-Simons gauge field of an inhomogeneous group. Analysis of the phase space shows…
This paper studies ways to represent an ordered topological vector space as a space of continuous functions, extending the classical representation theorems of Kadison and Schaefer. Particular emphasis is put on the class of semisimple…
These notes of a course given at IRMA in April 2009 cover some aspects of the representation theory of fundamental groups of manifolds of dimension at most 3 in compact Lie groups, mainly $\su$. We give detailed examples, develop the…
Theory of representations of F-algebra is a natural development of the theory of F-algebra. Exploring of morphisms of the representation leads to the concepts of generating set and basis of representation. In the book I considered the…
We study the tomography of propagators for spin systems in the context of finite-dimensional Wigner representations, which completely characterize and visualize operators using shapes assembled from linear combinations of spherical…
We show that a modification of Wigner's induced representation for the description of a relativistic particle with spin can be used to construct spinors and tensors of arbitrary rank, with invariant decomposition over angular momentum. In…
We construct Quantum Representation Theory which describes quantum analogue of representations in frame of "non-commutative linear geometry" developed by Manin. To do it we generalise the internal hom-functor to the case of adjunction with…