In this project, we propose to analyze some theoretical issues related to field theories defined on spatial regions with boundary.
These systems are relevant in areas like condensed matter physics, quantum computation, general relativity, and theoretical physics.
The main topics that we want to explore are:
i) The geometric understanding of the so-called boundary degrees of freedom in the classical and quantum context.
Examples of theories in which these are supposed to exist, are Chern-Simons, BF, and Maxwell-Chern-Simons models.
ii) In the context of gravitational physics, we have found a rich interplay between the dynamics of the theory in the bulk (Husain-Kuchar model) and the induced one on the boundary (gravitational theories).
Both are very interesting by themselves and the fact that they can be so related is a remarkable result.
A deep understanding of this kind of interplay is mandatory, in this example and other theories.
During this project I expect to acquire new knowledge in different research areas, such as quantum information theory, percolation theory, statistical mechanics and quantum gravity.
Related publications
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Dirac geometric approach for the unimodular Holst action
Bogar Díaz, Eduardo J.S. Villaseñor, and Diana Zomeño
Mathematics 12 (2024) 980
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Classical analogs of generalized purities, entropies, and logarithmic negativity
Bogar Díaz, Diego González, Marcos J. Hernández, and J. David Vergara
Physical Review A 108 (2023) 012411
[arXiv: 2305.02887]
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Structure of the medium formed in heavy ion collisions
J. R. Alvarado García, D. Rosales Herrera, A. Fernández Téllez, Bogar Díaz, and J. E. Ramírez
Universe 9 (2023) 291
[arXiv: 2305.14860]
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Poisson brackets in Sobolev spaces: a mock holonomy-flux algebra
J. Fernando Barbero G., Marc Basquens, Bogar Díaz, and Eduardo J.S. Villaseñor
Physica Scripta 97 (2022) 125202 [arXiv:
2207.00342]
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Edge observables of the Maxwell-Chern-Simons theory
J. Fernando Barbero G., Bogar Díaz, Juan Margalef-Bentabol, and Eduardo J.S. Villaseñor
Physical Review D 106 (2022) 025011 [arXiv:
2204.06073]
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Adiabatic lapse rate of real gases
Bogar Díaz, Miguel Ángel García-Ariza, and J.E. Ramírez
Physical Review E 106 (2022) 014108 [arXiv:
2203.12040]
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Classical analogs of the covariance matrix, purity, linear entropy, and von Neumann entropy
Bogar Díaz, Diego González, Daniel Gutiérrez-Ruiz, and J. David Vergara
Physical Review A 105 (2022) 062412 [arXiv:
2112.10899]
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Consistent and non-consistent deformations of gravitational theories
J. Fernando Barbero G., Marc Basquens, Bogar Díaz, and Eduardo J.S. Villaseñor
Journal of High Energy Physics 05 (2022) 175, [arXiv:
2202.07997]
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Mobility strategies based on percolation theory to avoid the spread of diseases: COVID-19
Diana Rosales Herrera, J.E. Ramírez, Jorge Velázquez-Castro, Bogar Díaz, M. I. Martínez, P. Vázquez Juárez, and A. Fernández Téllez
Revista Mexicana de Física 68 (2022) 011701, [arXiv:
2105.10934]
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Interacting color strings as the origin of the liquid behavior of the quark-gluon plasma
J.E. Ramírez, Bogar Díaz, and C. Pajares
Physical Review D 103 (2021) 094029, [arXiv:
2012.07920]
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Hamiltonian Gotay-Nester-Hinds analysis of the parametrized unimodular extension of the Holst action
J. Fernando Barbero G., Bogar Díaz, Juan Margalef-Bentabol, and Eduardo J.S. Villaseñor
Physical Review D 103 (2021) 064062, [arXiv:
2101.12311]
