Related papers: Geometry of Quantum Group invariant systems
We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically…
The two-fluid Interacting Vector Boson Model (IVBM) with the U(6) as a dynamical group possesses a rich algebraic structure of physical interesting subgroups that define its distinct exactly solvable dynamical limits. The classical images…
We define and study kinematical observables involving fermion spin, such as the total spin of a collection of particles, in loop quantum gravity. Due to the requirement of gauge invariance, the relevant quantum states contain strong…
The paper is the first of two parts of the work devoted to the investigation of constructing quantum theory of a closed universe as a system without asynptotic states. In Part I the role of asymptotic states in quantum theory of gravity is…
Algebraic approach to the integrability condition called shape invariance is briefly reviewed. Various applications of shape-invariance available in the literature are listed. A class of shape-invariant bound-state problems which represent…
The transverse group associated to some continuous quantum measuring processes is analyzed in the presence of nonvanishing gravitational fields. This is done considering, as an exmaple, the case of a particle whose coordinates are being…
Using the analogy between acoustic perturbations in an ideal fluid and the description of a Klein-Gordon scalar field in a curved spacetime, we study the quasinormal modes of a quantum system: the rotating Bose-Einstein condensate. To…
We show how particle-vortex duality implies the existence of a large non-abelian discrete symmetry group which relates the electromagnetic response for dual two-dimensional systems in a magnetic field. For conductors with charge carriers…
The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert…
In this Thesis we examine the interplay between the encoding of information in quantum systems and their geometrical and topological properties. We first study photonic qubit probes of space-time curvature, showing how gauge-independent…
We develop a general framework for the open dynamics of an ensemble of quantum particles subject to spacetime fluctuations about the flat background. An arbitrary number of interacting bosonic and fermionic particles are considered. A…
One of the most celebrated accomplishments of modern physics is the description of fundamental principles of nature in the language of geometry. As the motion of celestial bodies is governed by the geometry of spacetime, the motion of…
We study relations between different kinds of non-commutative spheres which have appeared in the context of ADS/CFT correspondences recently, emphasizing the connections between spaces that have manifest quantum group symmetry and spaces…
We consider the geometry of quantum states associated with different classes of random matrix Hamiltonians, in particular ensembles that show integrability to chaotic transition in terms of the nearest neighbour energy level spacing…
The usual concepts of topological physics, such as the Berry curvature, cannot be applied directly to non-Hermitian systems. We show that another object, the quantum metric, which often plays a secondary role in Hermitian systems, becomes a…
In loop quantum gravity the discrete nature of quantum geometry acts as a natural regulator for matter theories. Studies of quantum field theory in quantum space-times in spherical symmetry in the canonical approach have shown that the main…
It is shown that the recently geometric formulation of quantum mechanics implies the use of Weyl geometry. It is discussed that the natural framework for both gravity and quantum is Weyl geometry. At the end a Weyl invariant theory is…
The problem of gauge invariance of the physical sector of (2+1)-dimensional Maxwell-Chern-Simons quantum electrodynamics (QED$_{2+1}$) is studied. It is shown that using Proca mass term for the infrared regularization one obtains…
We study the quantum symmetric spaces for quantum general linear groups modulo symplectic groups. We first determine the structure of the quotient quantum group and completely determine the quantum invariants. We then derive the…
Group theory is extremely successful in characterizing the symmetries in quantum systems, which greatly simplifies and unifies our treatments of quantum systems. Here we introduce the concept of the symmetry for a quantum Boltzmann machine…