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Hamiltonian Structure of Poincaré Gauge Theory and Separation of Non‐Dynamical Variables in Exact Torsion Solutions
Author(s) -
Baekler Peter,
Mielke Eokehard W.
Publication year - 1988
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190360704
Subject(s) - hamiltonian lattice gauge theory , mathematical physics , physics , torsion (gastropod) , poincaré conjecture , gauge theory , gauge fixing , gauge symmetry , hamiltonian constraint , tetrad , covariant hamiltonian field theory , curvature , classical mechanics , lorentz transformation , lorenz gauge condition , hamiltonian (control theory) , mathematics , gauge anomaly , hamiltonian system , gauge boson , quantum mechanics , geometry , quantum gravity , medicine , mathematical optimization , surgery , loop quantum gravity , quantum
The canonical Hamiltonian of the Poincaré gauge theory of gravity is reanalyzed for generic Lagrangians. It is shown that the time components e 0 α and Γ 0 αβ of the tetrad and the linear connection fields of a Riemann‐Cartan space‐time U 4 constitute gauge degrees of freedom which remain non‐dynamical during the time evolution of the system. Whereas the e 0 α are to be identified with the lapse and shift functions N α known from the ADM formalism in Einstein's theory, the additional Lorentz degrces of freedom Γ 0 αβ are pertinent to Poincaré gauge models. These non‐dynamical variables are instrumental in the derivation of exact torsion solutions obeying modified double duality conditions for the U 4 ‐curvature. Thereby, in the case of spherical symmetry and for the charged Taub‐NUT metric, we obtain the most general torsion configuration for a large class of quadratic Lagrangians. Previously found solutions are contained therein and can be recovered after fixing special “gauge”.