31,518 research outputs found
Lagrangian supersymmetries depending on derivatives. Global analysis and cohomology
Lagrangian contact supersymmetries (depending on derivatives of arbitrary
order) are treated in very general setting. The cohomology of the variational
bicomplex on an arbitrary graded manifold and the iterated cohomology of a
generic nilpotent contact supersymmetry are computed. In particular, the first
variational formula and conservation laws for Lagrangian systems on graded
manifolds using contact supersymmetries are obtained.Comment: 28 pp., appears in 'Communications in Mathematical Physics
Conservation laws for under determined systems of differential equations
This work extends the Ibragimov's conservation theorem for partial
differential equations [{\it J. Math. Anal. Appl. 333 (2007 311-328}] to under
determined systems of differential equations. The concepts of adjoint equation
and formal Lagrangian for a system of differential equations whose the number
of equations is equal to or lower than the number of dependent variables are
defined. It is proved that the system given by an equation and its adjoint is
associated with a variational problem (with or without classical Lagrangian)
and inherits all Lie-point and generalized symmetries from the original
equation. Accordingly, a Noether theorem for conservation laws can be
formulated
Entropy of Self-Gravitating Systems from Holst's Lagrangian
We shall prove here that conservation laws from Holst's Lagrangian, often
used in LQG, do not agree with the corresponding conservation laws in standard
GR. Nevertheless, these differences vanish on-shell, i.e. along solutions, so
that they eventually define the same classical conserved quantities.
Accordingly, they define in particular the same entropy of solutions, and the
standard law S=A/4 is reproduced for systems described by Holst's Lagragian.
This provides the classical support to the computation usually done in LQG for
the entropy of black holes which is in turn used to fix the Barbero-Immirzi
parameter.Comment: 4 pages, no figures; just acknowledgments change
The Cartan form for constrained Lagrangian systems and the nonholonomic Noether theorem
This paper deals with conservation laws for mechanical systems with
nonholonomic constraints. It uses a Lagrangian formulation of nonholonomic
systems and a Cartan form approach. We present what we believe to be the most
general relations between symmetries and first integrals. We discuss the
so-called nonholonomic Noether theorem in terms of our formalism, and we give
applications to Riemannian submanifolds, to Lagrangians of mechanical type, and
to the determination of quadratic first integrals.Comment: 25 page
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