VECTOR COHERENT STATES AND NON-ABELIAN GAUGE STRUCTURES IN QUANTUM MECHANICS

1990 ◽  
Vol 05 (22) ◽  
pp. 4311-4331 ◽  
Author(s):  
G. GIAVARINI ◽  
E. ONOFRI
Keyword(s):  
Quantum Mechanics ◽  
Lie Group ◽  
Coherent States ◽  
Quantum Systems ◽  
Semisimple Lie Group ◽  
Abelian Gauge ◽  
Geometric Properties ◽  
Generalized Coherent States ◽  
Abelian Case ◽  
Vector Coherent States

We set the general formalism for calculating Berry's phase in quantum systems with Hamiltonian belonging to the algebra of a semisimple Lie group of any rank in the framework of generalized coherent states. Within this approach the geometric properties of Berry's connection are also studied, both in the Abelian and non-Abelian cases. In particular we call attention to the non-Abelian case where we make use of a vectorial generalization of coherent states. In this respect a thorough and self-contained exposition of the formalism of vector coherent states is given. The specific examples of the groups SU(3) and Sp(2) are worked out in detail.

Generalized Coherent States and Operator Descriptions in Quantum Mechanics

2003 ◽  
Vol 18 (33n35) ◽  
pp. 2405-2414
Author(s):  
N. Mukunda
Keyword(s):  
Quantum Mechanics ◽  
Lie Group ◽  
Coherent States ◽  
Group Representation ◽  
Sufficient Conditions ◽  
Classical Type ◽  
Noncommuting Operators ◽  
Generalized Coherent States ◽  
Diagonal Representation ◽  
Necessary And Sufficient

"The possibility of describing noncommuting operators in quantum mechanics by classical type functions, and the associated expression of operator multiplication, is of considerable interest. The well known Wigner-Weyl-Moyal theory is an important example. Another is the diagonal representation of operators using standard coherent states. We develop general necessary and sufficient conditions for the existence of the diagonal representation in the context of a family of generalised coherent states associated with any unitary irreducible Lie group representation. Several examples illustrating these conditions, and interesting results in the Heisenberg-Weyl case, are presented".

SUSY coherent states and enhanced canonical quantizations for Pauli model

2021 ◽  
pp. 2150105
Author(s):  
Jean Vignon Hounguevou ◽  
Daniel Sabi Takou ◽  
Gabriel Y. H. Avossevou
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Coherent States ◽  
Differential Operators ◽  
Canonical Quantization ◽  
Point Of View ◽  
Supersymmetric Quantum Mechanics ◽  
Geometric Properties

In this paper, we study coherent states for a quantum Pauli model through supersymmetric quantum mechanics (SUSYQM) method. From the point of view of canonical quantization, the construction of these coherent states is based on the very important differential operators in SUSYQM call factorization operators. The connection between classical and quantum theory is given by using the geometric properties of these states.

scholarly journals Time and classical equations of motion from quantum entanglement via the Page and Wootters mechanism with generalized coherent states

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Caterina Foti ◽  
Alessandro Coppo ◽  
Giulio Barni ◽  
Alessandro Cuccoli ◽  
Paola Verrucchi
Keyword(s):  
Classical Limit ◽  
Coherent States ◽  
Equations Of Motion ◽  
Quantum Systems ◽  
Physical Systems ◽  
Quantum Time ◽  
First Case ◽  
Hamilton Equations ◽  
Generalized Coherent States ◽  
Evolving System

AbstractWe draw a picture of physical systems that allows us to recognize what “time” is by requiring consistency with the way that time enters the fundamental laws of Physics. Elements of the picture are two non-interacting and yet entangled quantum systems, one of which acting as a clock. The setting is based on the Page and Wootters mechanism, with tools from large-N quantum approaches. Starting from an overall quantum description, we first take the classical limit of the clock only, and then of the clock and the evolving system altogether; we thus derive the Schrödinger equation in the first case, and the Hamilton equations of motion in the second. This work shows that there is not a “quantum time”, possibly opposed to a “classical” one; there is only one time, and it is a manifestation of entanglement.

Generalized Coherent States and theU(n) Lie Group

1979 ◽  
Vol 47 (3) ◽  
pp. 1003-1009 ◽  
Author(s):  
A. Jannussis ◽  
N. Patargias ◽  
L. Papaloucas
Keyword(s):  
Lie Group ◽  
Coherent States ◽  
Generalized Coherent States
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