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.

MAGNETIC GROUP ON THE PSEUDOSPHERE

1992 ◽  
Vol 06 (21) ◽  
pp. 3525-3537 ◽  
Author(s):  
V. BARONE ◽  
V. PENNA ◽  
P. SODANO
Keyword(s):  
Magnetic Field ◽  
Hilbert Space ◽  
Quantum Mechanics ◽  
Constant Magnetic Field ◽  
Coherent States ◽  
Compact Operators ◽  
Point Of View ◽  
Algebraic Point ◽  
Planar Limit ◽  
Discrete Part

The quantum mechanics of a particle moving on a pseudosphere under the action of a constant magnetic field is studied from an algebraic point of view. The magnetic group on the pseudosphere is SU(1, 1). The Hilbert space for the discrete part of the spectrum is investigated. The eigenstates of the non-compact operators (the hyperbolic magnetic translators) are constructed and shown to be expressible as continuous superpositions of coherent states. The planar limit of both the algebra and the eigenstates is analyzed. Some possible applications are briefly outlined.

scholarly journals Quantum mechanics, gravity and modified quantization relations

2015 ◽  
Vol 373 (2047) ◽  
pp. 20140244 ◽  
Author(s):  
Xavier Calmet
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Scale Dependence ◽  
Energy Scale ◽  
Point Of View ◽  
Planck’S Constant ◽  
Phenomenological Point ◽  
Quantization Rules

In this paper, we investigate a possible energy scale dependence of the quantization rules and, in particular, from a phenomenological point of view, an energy scale dependence of an effective (reduced Planck’s constant). We set a bound on the deviation of the value of at the muon scale from its usual value using measurements of the anomalous magnetic moment of the muon. Assuming that inflation has taken place, we can conclude that nature is described by a quantum theory at least up to an energy scale of about 10 16  GeV.

scholarly journals COHERENT STATES AND THE QUANTIZATION OF (1+1)-DIMENSIONAL YANG–MILLS THEORY

2001 ◽  
Vol 13 (10) ◽  
pp. 1281-1305 ◽  
Author(s):  
BRIAN C. HALL
Keyword(s):  
Phase Space ◽  
Gauge Symmetry ◽  
Coherent States ◽  
Complex Structure ◽  
Canonical Quantization ◽  
Point Of View ◽  
Joint Work ◽  
Bargmann Transform ◽  
Yang Mills ◽  
New Family

This paper discusses the canonical quantization of (1+1)-dimensional Yang–Mills theory on a spacetime cylinder from the point of view of coherent states, or equivalently, the Segal–Bargmann transform. Before gauge symmetry is imposed, the coherent states are simply ordinary coherent states labeled by points in an infinite-dimensional linear phase space. Gauge symmetry is imposed by projecting the original coherent states onto the gauge-invariant subspace, using a suitable regularization procedure. We obtain in this way a new family of "reduced" coherent states labeled by points in the reduced phase space, which in this case is simply the cotangent bundle of the structure group K. The main result explained here, obtained originally in a joint work of the author with B. Driver, is this: The reduced coherent states are precisely those associated to the generalized Segal–Bargmann transform for K, as introduced by the author from a different point of view. This result agrees with that of K. Wren, who uses a different method of implementing the gauge symmetry. The coherent states also provide a rigorous way of making sense out of the quantum Hamiltonian for the unreduced system. Various related issues are discussed, including the complex structure on the reduced phase space and the question of whether quantization commutes with reduction.

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.

scholarly journals THE PROBLEM OF REALITY IN THE TEXTS OF NIELS BOHR

2019 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Point Of View ◽  
Niels Bohr ◽  
Stationary States ◽  
Physical Processes ◽  
Specific Behavior ◽  
Physical Experiments ◽  
Interpretation Of Quantum Theory ◽  
Philosophical Questions

The article discusses a new understanding of the reality in the 20th century. Since the key figure in these changes was the Danish physicist Niels Bohr, we refer to his early and later articles to analyze the use of the term “reality”. Through an analysis of the terms, it is shown that Bohr describes discoveries in earlier articles that are inconsistent with old concepts in physics, and it is these questions that will further lead him to a new understanding of reality. In the article we also indicate how many times and in what contexts the term “reality” is used. Further, we find that the term “reality” is more common in later articles than in his earlier works (Copenhagen’s interpretation of quantum theory had not yet been formulated at the time of writing the early works). Through the analyzing of usage of certain terms, we show how the emphasis in the early and late Bohr’s articles shifts. For many years, the Danish physicist has sought to clarify quantum theory. In some later articles, we note that the problems affect not only physical, but also other areas of knowledge. We also analyze the use of the term in later articles. This analysis shows how Niels Bohr’s discoveries in the nature of the objects of the micro-world lead him to questions about the nature of reality. How discoveries in the microcosm affect the new conception of reality is best traced in controversy with other physicists. As the most striking example, we took the article “Discussion with Einstein on epistemological problems in atomic physics”. In this article, Bohr describes the specific behavior of micro-objects, features of physical experiments and proves the idea that a fundamentally new (including ontological plan) understanding of physical processes is needed. An analysis of the terms shows that, from Bohr’s point of view, reality itself is as described by its quantum mechanics. We strive to show the evolution of Bohr’s views in the context of how they influenced the revision of all physics. We conclude that the discovery of stationary states in an atom is the first step to rethinking philosophical questions of a nature of reality.

scholarly journals Susy for Non-Hermitian Hamiltonians, with a View to Coherent States

2020 ◽  
Vol 23 (3) ◽  
Author(s):  
F. Bagarello
Keyword(s):  
Quantum Mechanics ◽  
Physical System ◽  
Coherent States ◽  
Supersymmetric Quantum Mechanics ◽  
Extended Version ◽  
Black Scholes

Abstract We propose an extended version of supersymmetric quantum mechanics which can be useful if the Hamiltonian of the physical system under investigation is not Hermitian. The method is based on the use of two, in general different, superpotentials. Bi-coherent states of the Gazeau-Klauder type are constructed and their properties are analyzed. Some examples are also discussed, including an application to the Black-Scholes equation, one of the most important equations in Finance.

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