Geometric Lagrangian approach to the physical degree of freedom count in field theory

dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.contributor.authorDíaz Jiménez, Bogar
dc.contributor.authorMontesinos, Merced
dc.description.abstractTo circumvent some technical difficulties faced by the geometric Lagrangian approach to the physical degree of freedom count presented in the work of Díaz, Higuita, and Montesinos [J. Math. Phys. 55, 122901 (2014)] that prevent its direct implementation to field theory, in this paper, we slightly modify the geometric Lagrangian approach in such a way that its resulting version works perfectly for field theory (and for particle systems, of course). As in previous work, the current approach also allows us to directly get the Lagrangian constraints, a new Lagrangian formula for the counting of the number of physical degrees of freedom, the gauge transformations, and the number of first- and second-class constraints for any action principle based on a Lagrangian depending on the fields and their first derivatives without performing any Dirac’s canonical analysis. An advantage of this approach over the previous work is that it also allows us to handle the reducibility of the constraints and to get the off-shell gauge transformations. The theoretical framework is illustrated in 3-dimensional generalized general relativity (Palatini and Witten’s exotic actions), Chern-Simons theory, 4-dimensional BF theory, and 4-dimensional general relativity given by Palatini’s action with a cosmological constant.en
dc.description.sponsorshipWe thank Mariano Celada, Gerardo F. Torres del Castillo, Mercedes Velázquez, and José D. Vergara for their valuable comments on this work. Merced Montesinos’ sabbatical year at Benemérita Universidad Autónoma de Puebla was supported by CONACYT, Grant No. 266062, and by Benemérita Universidad Autónoma de Puebla.en
dc.identifier.bibliographicCitationDíaz, B. & Montesinos, M. (2018). Geometric Lagrangian approach to the physical degree of freedom count in field theory. Journal of Mathematical Physics, 59(5), 052901.en
dc.identifier.publicationtitleJournal of Mathematical Physicsen
dc.publisherAmerican Institute of Physics (AIP)en
dc.rights© 2018 Author(s). Published by AIP Publishing.en
dc.rights.accessRightsopen access
dc.subject.otherChern-Simons theoriesen
dc.subject.otherOperator theoryen
dc.subject.otherVector fieldsen
dc.subject.otherGauge fixingen
dc.subject.otherHamiltonian mechanicsen
dc.subject.otherDifferentiable manifolden
dc.subject.otherGeneral relativityen
dc.subject.otherBf modelen
dc.subject.otherCosmological constanten
dc.subject.otherDifferential geometryes
dc.titleGeometric Lagrangian approach to the physical degree of freedom count in field theoryen
dc.typeresearch article*
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
811.27 KB
Adobe Portable Document Format