A geometric construction for obtaining a prolongation of a connection to a connection of a bundle of connections is presented. This determines a natural extension of the notion of canonical energy-tensor which suits gauge and gravitational fields, and shares the main properties of the energy-tensor of a matter field in the jet space formulation of Lagrangian field theory, in particular with regards to symmetries of the Poincaré-Cartan form. Accordingly, the joint energy-tensor for interacting matter and gauge fields turns out to be a natural geometric object, whose definition needs no auxiliary structures. Various topics related to energy-tensors, symmetries and the Einstein equations in a theory with interacting matter, gauge and gravitational fields can be viewed under a clarifying light. Finally, the symmetry determined by the ``Komar super potential'' is expressed as a symmetry of the gravitational Poincar\'e-Cartan form.
Overconnections and the energy-tensors of gauge and gravitational fields / Canarutto, Daniel. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - ELETTRONICO. - (2016), pp. 0-0. [10.1016/j.geomphys.2016.03.027]
Overconnections and the energy-tensors of gauge and gravitational fields
CANARUTTO, DANIEL
2016
Abstract
A geometric construction for obtaining a prolongation of a connection to a connection of a bundle of connections is presented. This determines a natural extension of the notion of canonical energy-tensor which suits gauge and gravitational fields, and shares the main properties of the energy-tensor of a matter field in the jet space formulation of Lagrangian field theory, in particular with regards to symmetries of the Poincaré-Cartan form. Accordingly, the joint energy-tensor for interacting matter and gauge fields turns out to be a natural geometric object, whose definition needs no auxiliary structures. Various topics related to energy-tensors, symmetries and the Einstein equations in a theory with interacting matter, gauge and gravitational fields can be viewed under a clarifying light. Finally, the symmetry determined by the ``Komar super potential'' is expressed as a symmetry of the gravitational Poincar\'e-Cartan form.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.