Bosonic Representation of Matrices and Angular Momentum Probabilistic Representation of Cyclic States.

Julio A López-Saldívar, Olga V Man'ko, Margarita A Man'ko, Vladimir I Man'ko

Abstract read

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Article in Entropy (Basel, Switzerland), 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

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5 · Who and what money

Authors and funding

4 authors.

Julio A López-SaldívarInstituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apdo. Postal 70-543, Ciudad de Mexico 04510, Mexico.ORCID 0000-0001-5489-698X

Olga V Man'koLebedev Physical Institute, Leninskii Prospect 53, Moscow 119991, Russia.

Margarita A Man'koLebedev Physical Institute, Leninskii Prospect 53, Moscow 119991, Russia.

Vladimir I Man'koDepartment of Theoretical Physics, Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow 141700, Russia.

Funding

Russian Science Foundation 19-71-10092

6 · The paper itself

Abstract

The Jordan-Schwinger map allows us to go from a matrix representation of any arbitrary Lie algebra to an oscillator (bosonic) representation. We show that any Lie algebra can be considered for this map by expressing the algebra generators in terms of the oscillator creation and annihilation operators acting in the Hilbert space of quantum oscillator states. Then, to describe quantum states in the probability representation of quantum oscillator states, we express their density operators in terms of conditional probability distributions (symplectic tomograms) or Husimi-like probability distributions. We illustrate this general scheme by examples of qubit states (spin-1/2 su(2)-group states) and even and odd Schrödinger cat states related to the other representation of su(2)-algebra (spin-

Indexed as

angular momentumcoherent statescontinuous variable systemsJordan-Schwinger mapLie algebrastomographic representation

Identifiers

PMID38136507

DOI10.3390/e25121628

PMCPMC10743218

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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.