Theoretical Physics Department, Institut National des Sciences et Techniques Nucléaires (INSTN- Madagascar), BP 4279 101-Antananarivo, Madagascar
: Received: 19 August 2016 / Approved: 20 August 2016 / Online: 20 August 2016 (10:55:58 CEST)
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Andriambololona, R.; Ranaivoson, R.; Randriamisy, H.; Rakotoson, H. Dispersion Operators Algebra and Linear Canonical Transformations. Preprints2016, 2016080185 (doi: 10.20944/preprints201608.0185.v1).
Andriambololona, R.; Ranaivoson, R.; Randriamisy, H.; Rakotoson, H. Dispersion Operators Algebra and Linear Canonical Transformations. Preprints 2016, 2016080185 (doi: 10.20944/preprints201608.0185.v1).
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.
Dispersion operator; Lie algebra; Linear Canonical Transformation; Quantum theory; Phase space representation