scholarly journals The relation between the symplectic group Sp(4,R) and its Lie algebra: Applications to polymer quantum mechanics

2021 ◽  
Vol 104 (12) ◽  
Author(s):  
Guillermo Chacón-Acosta ◽  
Angel Garcia-Chung
Keyword(s):  
Quantum Mechanics ◽  
Lie Algebra ◽  
Symplectic Group

scholarly journals Gaussian pure states in quantum mechanics and the symplectic group

1988 ◽  
Vol 37 (8) ◽  
pp. 3028-3038 ◽  
Author(s):  
R. Simon ◽  
E. C. G. Sudarshan ◽  
N. Mukunda
Keyword(s):  
Quantum Mechanics ◽  
Symplectic Group ◽  
Pure States

scholarly journals THE STABILIZED POINCARE–HEISENBERG ALGEBRA: A CLIFFORD ALGEBRA VIEWPOINT

2007 ◽  
Vol 16 (09) ◽  
pp. 1519-1529 ◽  
Author(s):  
N. G. GRESNIGT ◽  
P. F. RENAUD ◽  
P. H. BUTLER
Keyword(s):  
Quantum Mechanics ◽  
Clifford Algebra ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Clifford Algebras ◽  
Heisenberg Algebra ◽  
Stability Conditions ◽  
Relativistic Kinematics ◽  
Evolutionary Step

The stabilized Poincare–Heisenberg algebra (SPHA) is a Lie algebra of quantum relativistic kinematics generated by fifteen generators. It is obtained from imposing stability conditions after combining the Lie algebras of quantum mechanics and relativity. In this paper, we show how the sixteen-dimensional real Clifford algebras Cℓ(1,3) and Cℓ(3,1) can both be used to generate the SPHA. The Clifford algebra path to the SPHA avoids the traditional stability considerations. It is conceptually easier and more straightforward to work with a Clifford algebra. The Clifford algebra path suggests that the next evolutionary step toward a theory of physics at the interface of GR and QM might be to depart from working in spacetime and instead to work in spacetime–momentum.

scholarly journals Lie algebra in quantum physics by means of computer algebra

2017 ◽  
Author(s):  
Ichio Kikuchi ◽  
Akihito Kikuchi
Keyword(s):  
Quantum Mechanics ◽  
Angular Momentum ◽  
Lie Algebra ◽  
Computer Algebra ◽  
Quantum Physics ◽  
Character Formula ◽  
Weyl Character Formula ◽  
Weight Modules

This article explains how to apply the computer algebra package GAP (www.gap-system.org) in the computation of the problems in quantum physics, in which the application of Lie algebra is necessary. The article contains several exemplary computations which readers would follow in the desktop PC: such as, the brief review of elementary ideas of Lie algebra, the angular momentum in quantum mechanics, the quark eight-fold-way model, and the usage of Weyl character formula (in order to construct weight modules, and to count correctly the degeneracy

scholarly journals Dispersion Operators Algebra and Linear Canonical Transformations

2016 ◽  
Author(s):  
Raoelina Andriambololona ◽  
Ravo Tokiniaina Raymond Ranaivoson ◽  
Hasimbola Damo Emile Randriamisy ◽  
Hanitriarivo Rakotoson
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Lie Algebra ◽  
Canonical Transformation ◽  
Space Representation ◽  
Canonical Transformations ◽  
Linear Canonical Transformation ◽  
Multidimensional Generalization ◽  
Phase Space Representation ◽  
Operators Algebra

This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given.

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