Artículo

Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

The relation between fundamental spacetime structures and dynamical symmetries are treated beyond the geometrical and topological viewpoint. To this end analyze, taking into account the concept of categories and quasi hamiltonian structures, a recent research (Cirilo-Lombardo and Arbuzov in Int J Geom Methods Mod Phys 15(01):1850005, 2017) where one linear and one quadratic in curvature models were constructed and where a dynamical breaking of the SO(4 , 2) group symmetry arises. We explain there how and why coherent states of the Klauder-Perelomov type are defined for both cases taking into account the coset geometry and some hints on the possibility to extend they to the categorical (functorial) status are given. The new spontaneous compactification mechanism that was defined in the subspace invariant under the stability subgroup is commented in the context of future developments as the main tool for the treatment of the internal symmetries, as the electroweak in the Standard Model (SM). The physical implications of the symmetry rupture as the introduction of a noncommutative structure in the context of non-linear realizations and direct gauging are analyzed and briefly discussed in this new theoretical framework. © 2018, Springer (India) Private Ltd., part of Springer Nature.

Registro:

Documento: Artículo
Título:Dynamical Symmetries, Super-coherent States and Noncommutative Structures: Categorical and Geometrical Quantization Analysis
Autor:Cirilo-Lombardo, D.J.
Filiación:Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Universidad de Buenos Aires, National Institute of Plasma Physics (INFIP), Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Buenos Aires, 1428, Argentina
Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, 141980, Russian Federation
Palabras clave:Categories; Coherent states; Dynamical symmetries; Geometrical quatization; Group manifolds; UFT
Año:2018
Volumen:4
Número:3
DOI: http://dx.doi.org/10.1007/s40819-018-0518-6
Título revista:International Journal of Applied and Computational Mathematics
Título revista abreviado:Internat. J. Appl. Comput. Math.
ISSN:23495103
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_23495103_v4_n3_p_CiriloLombardo

Referencias:

  • Isaev, A.P., Quantum group covariant noncommutative geometry (1994) J. Math. Phys, 35, p. 6784
  • Aschieri, P., Castellani, L., Isaev, A.P., Discretized Yang-Mills and Born-Infeld actions on finite group geometries (2003) Int. J. Mod. Phys. A, 18, p. 3555
  • Blagojevic, M., (2002) Gravitation and Gauge Symmetries, p. 522. , IOP, Bristol
  • Hayashi, K., Shirafuji, T., Gravity from poincare gauge theory of the fundamental particles. 7. The axial vector model (1981) Prog. Theor. Phys., 66, p. 2258
  • Borisov, A.B., The unitary representations of the general covariant group algebra (1978) J. Phys. A, 11, p. 1057
  • Utiyama, R., Invariant theoretical interpretation of interaction (1956) Phys. Rev., 101, p. 1597
  • Capozziello, S., De Laurentis, M., Extended theories of gravity (2011) Phys. Rep., 509, p. 167. , [[gr-qc]]
  • Hehl, F.W., McCrea, J.D., Mielke, E.W., Ne’eman, Y., Metric affine gauge theory of gravity: field equations, Noether identities, world spinors, and breaking of dilation invariance (1995) Phys. Rep., 258, p. 1. , [gr-qc/9402012]
  • Ivanenko, D., Sardanashvily, G., The gauge treatment of gravity (1983) Phys. Rep., 94, p. 1
  • Obukhov, Y.N., Poincare gauge gravity: selected topics (2006) Int. J. Geom. Methods Mod. Phys., 3, p. 95. , [gr-qc/0601090]
  • Ne’eman, Y., Regge, T., Gauge theory of gravity and supergravity on a group manifold (1978) Riv. Nuovo Cim., 1N5, p. 1
  • Gotzes, S., Hirshfeld, A.C., A geometric formulation of the SO(3,2) theory of gravity (1990) Ann. Phys., 203, p. 410
  • Shirafuji, T., Suzuki, M., Gauge theory of gravitation: a unified formulation of poincare and anti-de sitter gauge theories (1988) Prog. Theor. Phys., 80, p. 711
  • Ivanov, E.A., Niederle, J., Gauge formulation of gravitation theories. 1. The poincare, de sitter and conformal cases (1982) Phys. Rev. D, 25, p. 976
  • Ivanov, E.A., Niederle, J., Gauge formulation of gravitation theories. 2. The special conformal case (1982) Phys. Rev. D, 25, p. 988
  • Leclerc, M., The Higgs sector of gravitational gauge theories (2006) Ann. Phys., 321, p. 708. , [gr-qc/0502005]
  • Stelle, K.S., West, P.C., Spontaneously broken de sitter symmetry and the gravitational holonomy group (1980) Phys. Rev. D, 21, p. 1466
  • Tseytlin, A.A., On the poincare and de sitter gauge theories of gravity with propagating torsion (1982) Phys. Rev. D, 26, p. 3327
  • Lord, E.A., Goswami, P., Gauge theory of a group of diffeomorphisms. 1. General principles (1986) J. Math. Phys., 27, p. 2415
  • Lord, E.A., Gauge theory of a group of diffeomorphisms. 2. The conformal and de sitter groups (1986) J. Math. Phys., 27, p. 3051
  • Greenberg, M., (1971) Lectures on Algebraic Topology, , W.A. Benjamin Inc., Menlo Park
  • Kobayashi, S., Nomizu, K., (1963) Foundations of Differential Geometry, , Wiley, New York
  • Sardanashvily, G., Classical gauge gravitation theory (2011) Int. J. Geom. Methods Mod. Phys., 8, p. 1869. , [[math-ph]]
  • Giachetta, G., Mangiarotti, L., Sardanashvily, G., (2009) Advanced Classical Field Theory, , World Scientific, Singapore
  • Kirsch, I., A Higgs mechanism for gravity (2005) Phys. Rev. D, 72
  • Keyl, M., About the geometric structure of symmetry breaking (1991) J. Math. Phys., 32, p. 1065
  • Nikolova, L., Rizov, V.A., Geometrical approach to the reduction of gauge theories with spontaneously broken symmetry (1984) Rep. Math. Phys., 20, p. 287
  • Sardanashvily, A., On the geometry of spontaneous symmetry breaking (1992) J. Math. Phys., 33, p. 1546
  • Sardanashvily, G., Geometry of classical Higgs fields (2006) Int. J. Geom. Methods Mod. Phys, 3, p. 139
  • Sardanashvily, G., Mathematical models of spontaneous symmetry breaking, , math-ph
  • Sardanashvily, G., : Classical Higgs fields (2014) Theor. Math. Phys, 181, p. 1598. , math-ph
  • Trautman, A., (1984) Differential Geometry For Physicists, p. 145. , Bibliopolis, Naples
  • Lawson, H.B., Michelsohn, M.L., (1989) Spin Geometry, , Princeton University Press, Princeton
  • Sardanashvily, G., Gravity as a goldstone field in the lorentz gauge theory (1980) Phys. Lett. A, 75, p. 257
  • Sardanashvily, G.A., Zakharov, O., (1992) Gauge Gravitation Theory, p. 122. , World Scientific, Singapore
  • Hawking, S.W., Ellis, G.F.R., (1973) The Large Scale Structure of Space-Time, p. 404. , Cambridge University Press, Cambridge
  • Sardanashvily, G., What are the poincare gauge fields? (1983) Czech. J. Phys. B, 33, p. 610
  • Volkov, D.V., Soroka, V.A., Higgs effect for goldstone particles with spin 1/2 (1973) JETP Lett., 18, p. 312
  • Volkov, D.V., Soroka, V.A., Higgs effect for goldstone particles with spin 1/2 (1973) Pisma Zh. Eksp. Teor. Fiz., 18, p. 529
  • Akulov, V.P., Volkov, D.V., Soroka, V.A., Gauge fields on superspaces with different holonomy groups (1975) JETP Lett., 22, p. 187
  • Akulov, V.P., Volkov, D.V., Soroka, V.A., Gauge fields on superspaces with different holonomy groups (1975) Pisma Zh. Eksp. Teor. Fiz., 22, p. 396
  • Nath, P., Arnowitt, R.L., Generalized supergauge symmetry as a new framework for unified gauge theories (1975) Phys. Lett., 56B, p. 177
  • Macdowell, S.W., Mansouri, F., Unified Geometric Theory of Gravity and Supergravity (1977) Phys. Rev. Lett, 38, p. 739. , Erratum: [Phys. Rev. Lett. 38, 1376 (1977)]
  • Volkov, D.V., Pashnev, A.I., Supersymmetric lagrangian for particles in proper time (1980) Theor. Math. Phys., 44, p. 770
  • Volkov, D.V., Pashnev, A.I., Supersymmetric Lagrangian for particles in proper time (1980) Teor. Mat. Fiz., 44, p. 321
  • Inonu, E., Wigner, E.P., On the contraction of groups and their represenations (1953) Proc. Nat. Acad. Sci., 39, p. 510
  • Cirilo-Lombardo, D.J., Non-compact groups, coherent states, relativistic wave equations and the Harmonic Oscillator (2007) Found. Phys., 37, p. 919
  • Cirilo-Lombardo, D.J., Non-compact groups, coherent states, relativistic wave equations and the Harmonic Oscillator (2007) Found. Phys., 37, p. 1149
  • Cirilo-Lombardo, D.J., Non-compact groups, coherent states, relativistic wave equations and the Harmonic Oscillator (2008) Found. Phys, 38, p. 99
  • de Azcarraga, J.A., Lukierski, J., Supersymmetric particle model with additional bosonic coordinates (1986) Z. Phys. C, 30, p. 221
  • Cirilo-Lombardo, D.J., Arbuzov, A., Electroweak Dynamical Symmetries beyond the SM and Coherent States, , Work in progress
  • Ogievetsky, V.I., Infinite-dimensional algebra of general covariance group as the closure of finite-dimensional algebras of conformal and linear groups (1973) Lett. Nuovo Cim., 8, p. 988
  • Volkov, D.V., Akulov, V.P., Is the neutrino a goldstone particle? (1973) Phys. Lett., 46B, p. 109
  • Capozziello, S., Cirilo-Lombardo, D.J., De Laurentis, M., The affine structure of gravitational theories: symplectic groups and geometry (2014) Int. J. Geom. Methods Mod. Phys., 11 (10), p. 1450081
  • Borisov, A.B., Ogievetsky, V.I., Theory of dynamical affine and conformal symmetries as gravity theory (1975) Theor. Math. Phys., 21, p. 1179
  • Borisov, A.B., Ogievetsky, V.I., Theory of dynamical affine and conformal symmetries as gravity theory (1974) Teor. Mat. Fiz., 21, p. 329
  • Cirilo-Lombardo, D.J., Non-compact groups, coherent states, relativistic wave equations and the harmonic osscillator II: physical and geometrical considerations (2009) Found. Phys., 39, pp. 373-396
  • Cirilo-Lombardo, D.J., The geometrical properties of Riemannian superspaces, exact solutions and the mechanism of localization (2008) Phys. Lett. B, 661, pp. 186-191
  • Cirilo-Lombardo, D.J., Algebraic structures, physics and geometry from a unified field theoretical framework (2015) Int. J. Theor. Phys., 54 (10), pp. 3713-3727
  • Ambrose, W., Singer, I.M., A theorem on holonomy (1953) Trans. Am. Math. Soc., 75 (3), pp. 428-443
  • Kostant, B., Graded manifolds, graded Lie theory and pre-quantization (1977) Differential Geometrical Methods in Mathematical Physics: Proceedings of the Symposium Held at the University of Bonn, 570, pp. 177-306. , Bleuler, K., Reetz, A., July 1–4, 1975. Lecture Notes in Mathematics, Springer, Berlin
  • Rothstein, M., The structure of supersymplectic supermanifolds (1991) Differential Geometric Methods in Theoretical Physics. Lecture Notes in Physics, 375. , Bartocci, C., Bruzzo, U., Cianci, R., Springer, Berlin
  • Bartocci, C., Bruzzo, U., Hernandez Ruiperez, D., (1991) The Geometry of Supermanifolds, , Kluwer, Dordrecht
  • Winnberg, J.O., Superfields as an extension of the spin representation of the orthogonal group (1977) J. Math. Phys., 18, p. 625
  • Pavsic, M., Spin Gauge Theory of Gravity in Clifford Space (2006) J. Phys. Conf. Ser., 33, pp. 422-427
  • Pavsic, M., A theory of quantized fields based on orthogonal and symplectic Clifford Algebras (2012) Adv. Appl. Clifford Algebras, 22, pp. 449-481
  • Albert, A.A., (1961) Structure of Algebras, , American Mathematical Society, Providence, RI
  • Salingaros, N.A., Wene, G.P., The Clifford algebra of differential forms (1985) Acta Appl. Math., 4 (27), pp. 1-292
  • Pavsic, M., On the unification of interactions by Clifford algebra (2010) Adv. Appl. Clifford Algebras, 20, pp. 781-801
  • Pavsic, M., Space inversion of spinors revisited: a possible explanation of chiral behavior in weak interactions (2010) Phys. Lett., B692, pp. 212-217
  • Cirilo-Lombardo, D.J., Geometrical properties of Riemannian superspaces, observables and physical states (2012) Eur. Phys. J., 100, p. 2079
  • Mickelsson, J., Boundary currents and hamiltonian quantization of fermions in background fields (1999) Phys. Lett. B, 456, pp. 124-128
  • Cirilo-Lombardo, D.J., Arbuzov, A., Dynamical symmetries, coherent states and nonlinear realizations: the SO(2,4) case (2017) Int. J. Geom. Methods Mod. Phys., 15 (1), p. 1850005
  • Agyo, S., Lei, C., Vourdas, A., The groupoid of bifractional transformations

Citas:

---------- APA ----------
(2018) . Dynamical Symmetries, Super-coherent States and Noncommutative Structures: Categorical and Geometrical Quantization Analysis. International Journal of Applied and Computational Mathematics, 4(3).
http://dx.doi.org/10.1007/s40819-018-0518-6
---------- CHICAGO ----------
Cirilo-Lombardo, D.J. "Dynamical Symmetries, Super-coherent States and Noncommutative Structures: Categorical and Geometrical Quantization Analysis" . International Journal of Applied and Computational Mathematics 4, no. 3 (2018).
http://dx.doi.org/10.1007/s40819-018-0518-6
---------- MLA ----------
Cirilo-Lombardo, D.J. "Dynamical Symmetries, Super-coherent States and Noncommutative Structures: Categorical and Geometrical Quantization Analysis" . International Journal of Applied and Computational Mathematics, vol. 4, no. 3, 2018.
http://dx.doi.org/10.1007/s40819-018-0518-6
---------- VANCOUVER ----------
Cirilo-Lombardo, D.J. Dynamical Symmetries, Super-coherent States and Noncommutative Structures: Categorical and Geometrical Quantization Analysis. Internat. J. Appl. Comput. Math. 2018;4(3).
http://dx.doi.org/10.1007/s40819-018-0518-6