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In this paper we propose a geometrization of the non-relativistic quantum mechanics for mixed states. Our geometric approach makes use of the Uhlmann's principal fibre bundle to describe the space of mixed states and as a novelty tool, to…

Mathematical Physics · Physics 2015-06-12 Vicent Gimeno , Jose Sotoca

We consider the problem of existence of the diagonal representation for operators in the space of a family of generalized coherent states associated with an unitary irreducible representation of a (compact) Lie group. We show that necessary…

Quantum Physics · Physics 2018-02-13 N. Mukunda , Arvind , S. Chaturvedi , R. Simon

We construct quantum states for a (1+1) dimensional gravity-matter model that is also a gauge theory based on the centrally extended Poincar\'e group. Explicit formulas are found, which exhibit interesting structures. For example wave…

High Energy Physics - Theory · Physics 2009-10-28 D. Cangemi , R. Jackiw

Monoidal product, braiding, balancing and weak duality are pieces of algebraic information that are well-known to have their origin in oriented genus zero surfaces and their mapping classes. More precisely, each of them correspond to…

Quantum Algebra · Mathematics 2025-09-09 Lukas Woike

The algebra of functions on kappa-Minkowski noncommutative spacetime is studied as algebra of operators on Hilbert spaces. The representations of this algebra are constructed and classified. This new approach leads to a natural construction…

High Energy Physics - Theory · Physics 2008-11-26 Alessandra Agostini

The unitary irreducible representations of a Lie group defines the Hilbert space on which the representations act. If this Lie group is a physical quantum dynamical symmetry group, this Hilbert space is identified with the physical quantum…

Mathematical Physics · Physics 2007-05-23 Stephen G. Low

Integral calculus on the space of gauge equivalent connections is developed. Loops, knots, links and graphs feature prominently in this description. The framework is well--suited for quantization of diffeomorphism invariant theories of…

General Relativity and Quantum Cosmology · Physics 2016-08-31 Abhay Ashtekar , Jerzy Lewandowski

I argue that scattering theory for massless particles in Minkowski space should be reformulated as a mapping between past and future representations of an algebra of densities on the conformal boundary. These densities are best thought of…

High Energy Physics - Theory · Physics 2015-11-05 Tom Banks

We give a method for obtaining states of massive particle representations of the two-parameter deformation of the Poincar\'e algebra proposed in q-alg/9601010, q-alg/9505030 and q-alg/9501026. We discuss four procedures to generate…

q-alg · Mathematics 2009-10-30 I. Yakushin

This is intended as a self-contained introduction to the representation theory developed in order to create a Poincare 2-category state sum model for Quantum Gravity in 4 dimensions. We review the structure of a new representation…

Quantum Algebra · Mathematics 2007-05-23 L. Crane , M. D. Sheppeard

In \cite{AminMoc} we defined the Minkowski superspace $SM(4,4\vert \lambda, \mu)$ as the invariant of the Poincare supergroup of supertransformations, which is a solution of Killing superequations. In the present paper we use formulae of…

General Relativity and Quantum Cosmology · Physics 2019-04-16 Asya V. Aminova , Mikhail Kh. Lyulinsky

An enumerative invariant theory in Algebraic Geometry, Differential Geometry, or Representation Theory, is the study of invariants which 'count' $\tau$-(semi)stable objects $E$ with fixed topological invariants $[E]=\alpha$ in some…

Algebraic Geometry · Mathematics 2022-09-26 Jacob Gross , Dominic Joyce , Yuuji Tanaka

Continuous mappings between compact Hausdorff spaces can be studied using homomorphisms between algebraic structures (lattices, Boolean algebras) associated with the spaces. This gives us more tools with which to tackle problems about these…

General Topology · Mathematics 2007-05-23 Klaas Pieter Hart

We apply geometric phase ideas to coherent states to shed light on interference phenomenon in the phase space description of continuous variable Cartesian quantum systems. In contrast to Young's interference characterized by path lengths,…

Quantum Physics · Physics 2018-12-19 Mayukh N. Khan , S. Chaturvedi , N. Mukunda , R. Simon

If a state is passive for uniformly accelerated observers in n-dimensional anti-de Sitter space-time (i.e. cannot be used by them to operate a perpetuum mobile), they will (a) register a universal value of the Unruh temperature, (b)…

Mathematical Physics · Physics 2009-11-10 Detlev Buchholz , Stephen J. Summers

A relativistic resonance which was defined by a pole of the $S$-matrix, or by a relativistic Breit-Wigner line shape, is represented by a generalized state vector (ket) which can be obtained by analytic extension of the relativistic…

High Energy Physics - Theory · Physics 2014-11-18 A. Bohm , H. Kaldass , S. Wickramasekara

In this paper is discussed description of some algebraic structures in quantum theory by using formal recursive constructions with "complex Poincar\'e group" ISO(4,C).

Mathematical Physics · Physics 2007-05-23 Alexander Yu. Vlasov

The structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group is related to a notion of Hilbert modules endowed with inner products taking values in spaces of unbounded operators. A…

Functional Analysis · Mathematics 2015-07-01 Davide Barbieri , Eugenio Hernández , Victoria Paternostro

A class of interacting classical random fields is constructed using deformed *-algebras of creation and annihilation operators. The fields constructed are classical random field versions of "Lie fields". A vacuum vector is used to construct…

Quantum Physics · Physics 2008-10-15 Peter Morgan

Matrix product states play an important role in quantum information theory to represent states of many-body systems. They can be seen as low-dimensional subvarieties of a high-dimensional tensor space. In these notes, we consider two…

Representation Theory · Mathematics 2023-12-05 Tim Seynnaeve