We investigate canonical aspects concerning the relation between symmetries and conservation laws in gauge-natural field theories. In particular, we find that a canonical spinor connection can be selected by the simple requirement of the global existence of canonical superpotentials for the Lagrangian describing the coupling of gravitational and Fermionic fields. In fact, the naturality of a suitably defined variational Lagragian implies the existence of an associated energy-momentum conserved current. Such a current defines a Hamiltonian form in the corresponding phase space; we show that an associated Hamiltonian connection is canonically defined along the kernel of the generalized gauge-natural Jacobi morphism and uniquely characterizes the canonical spinor connection.

Canonical Connections in Gauge-Natural Field Theories

FERRARIS, Marco;FRANCAVIGLIA, Mauro;PALESE, Marcella;
2008

Abstract

We investigate canonical aspects concerning the relation between symmetries and conservation laws in gauge-natural field theories. In particular, we find that a canonical spinor connection can be selected by the simple requirement of the global existence of canonical superpotentials for the Lagrangian describing the coupling of gravitational and Fermionic fields. In fact, the naturality of a suitably defined variational Lagragian implies the existence of an associated energy-momentum conserved current. Such a current defines a Hamiltonian form in the corresponding phase space; we show that an associated Hamiltonian connection is canonically defined along the kernel of the generalized gauge-natural Jacobi morphism and uniquely characterizes the canonical spinor connection.
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http://www.worldscinet.com/cgi-bin/details.cgi?id=voliss:ijgmmp_0506&type=toc
Jets; gauge-natural bundles; connections
M. FERRARIS; M. FRANCAVIGLIA; M. PALESE; E. WINTERROTH
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/53349
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