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dc.contributor.author
Cirilo, Diego Julio
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dc.contributor.author
Sanchez, Norma G.
dc.date.available
2024-06-14T10:44:50Z
dc.date.issued
2024-01
dc.identifier.citation
Cirilo, Diego Julio; Sanchez, Norma G.; Quantum-Spacetime Symmetries: A Principle of Minimum Group Representation; MDPI; Universe; 10; 1; 1-2024; 1-16
dc.identifier.issn
2218-1997
dc.identifier.uri
http://hdl.handle.net/11336/238105
dc.description.abstract
We show that, as in the case of the principle of minimum action in classical and quantummechanics, there exists an even more general principle in the very fundamental structure of quantum spacetime: this is the principle of minimal group representation, which allows us to consistently and simultaneously obtain a natural description of spacetime’s dynamics and the physical states admissible in it. The theoretical construction is based on the physical states that are average values of the generators of the metaplectic group Mp(n), the double covering of SL(2C) in a vector representation, with respect to the coherent states carrying the spin weight. Our main results here are: (i) There exists a connection between the dynamics given by the metaplectic-group symmetry generators and the physical states (the mappings of the generators through bilinear combinations of the basic states). (ii) The ground states are coherent states of the Perelomov–Klauder type defined by the action of the metaplectic group that divides the Hilbert space into even and odd states that are mutually orthogonal. They carry spin weight of 1/4 and 3/4, respectively, from which two other basic states can be formed. (iii) The physical states, mapped bilinearly with the basic 1/4- and 3/4-spin-weight states, plus their symmetric and antisymmetric combinations, have spin contents s = 0, 1/2, 1, 3/2 and 2. (iv) The generators realized with the bosonic variables of the harmonic oscillator introduce a natural supersymmetry and a superspace whose line element is the geometrical Lagrangian of our model. (v) From the line element as operator level, a coherent physical state of spin 2 can be obtained and naturally related to the metric tensor. (vi) The metric tensor is naturally discretized by taking the discrete series given by the basic states (coherent states) in the n number representation, reaching the classical (continuous) spacetime for n → ∞. (vii) There emerges a relation between the eigenvalue α of our coherent-state metric solution and the black-hole area (entropy) as Abh/4l ^2 p = |α|, relating the phase space of the metric found, gab, and the black hole area, Abh, through the Planck length lp^2 and the eigenvalue |α| of the coherent states. As a consequence of the lowest level of the quantum-discrete spacetime spectrum—e.g., the ground state associated to n = 0 and its characteristic length—thereexists a minimum entropy related to the black-hole history.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
MDPI
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by/2.5/ar/
dc.subject
QUANTUM SPACETIME
dc.subject
FUNDAMENTAL PRINCIPLE
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MINIMUM GROUP REPRESENTATION
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SYMMETRY
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METAPLECTIC GROUP
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PHASE SPACE
dc.subject
QUANTUM COHERENT STATES
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Física de Partículas y Campos
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Ciencias Físicas
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CIENCIAS NATURALES Y EXACTAS
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Astronomía
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Ciencias Físicas
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CIENCIAS NATURALES Y EXACTAS
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Matemática Aplicada
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Matemáticas
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CIENCIAS NATURALES Y EXACTAS
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dc.title
Quantum-Spacetime Symmetries: A Principle of Minimum Group Representation
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2024-06-13T11:23:44Z
dc.journal.volume
10
dc.journal.number
1
dc.journal.pagination
1-16
dc.journal.pais
Suiza
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dc.description.fil
Fil: Cirilo, Diego Julio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física del Plasma. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física del Plasma; Argentina
dc.description.fil
Fil: Sanchez, Norma G.. Centre National de la Recherche Scientifique; Francia
dc.journal.title
Universe
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.mdpi.com/2218-1997/10/1/22
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.3390/universe10010022
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