Second-order approximate symmetries of the geodesic equations for the Reissner-Nordström metric and re-scaling of energy of a test particle.
Single-pole interaction of the particle with the string.
Some aspects of the homogeneous formalism in field theory and gauge invariance
We propose a suitable formulation of the Hamiltonian formalism for Field Theory in terms of Hamiltonian connections and multisymplectic forms where a composite fibered bundle, involving a line bundle, plays the role of an extended configuration bundle. This new approach can be interpreted as a suitable generalization to Field Theory of the homogeneous formalism for Hamiltonian Mechanics. As an example of application, we obtain the expression of a formal energy for a parametrized version of the Hilbert–Einstein...
Space-time diffeomorphisms in noncommutative gauge theories.
Spherical symmetry in classical and quantum Galilei general relativity
Supplementary balance laws for Cattaneo heat propagation
In this work we determine for the Cattaneo heat propagation system all the supplementary balance laws (shortly SBL) of the same order (zero) as the system itself and extract the constitutive relations (expression for the internal energy) dictated by the Entropy Principle. The space of all supplementary balance laws (having the functional dimension 8) contains four original balance laws and their deformations depending on 4 functions of temperature (). The requirements of the II law of thermodynamics...
Symmetries in finite order variational sequences
We refer to Krupka’s variational sequence, i.e. the quotient of the de Rham sequence on a finite order jet space with respect to a ‘variationally trivial’ subsequence. Among the morphisms of the variational sequence there are the Euler-Lagrange operator and the Helmholtz operator. In this note we show that the Lie derivative operator passes to the quotient in the variational sequence. Then we define the variational Lie derivative as an operator on the sheaves of the variational sequence. Explicit...
The averaging of nonlocal Hamiltonian structures in Whitham's method.
The calculus of variations on jet bundles as a universal approach for a variational formulation of fundamental physical theories
As widely accepted, justified by the historical developments of physics, the background for standard formulation of postulates of physical theories leading to equations of motion, or even the form of equations of motion themselves, come from empirical experience. Equations of motion are then a starting point for obtaining specific conservation laws, as, for example, the well-known conservation laws of momenta and mechanical energy in mechanics. On the other hand, there are numerous examples of physical...
The equivalence between the Hamiltonian and Lagrangian formulations for the parametrization-invariant theories.
The Problem of Invariance for Covariant hamiltonians
Towards an analytical mechanics of dissipative materials.
Towards unifying structures in higher spin gauge symmetry.
Variational calculus in several variables : a hamiltonian approach
Variational principles and symmetries on fibered multisymplectic manifolds
The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multisymplectic structure. Then, for the corresponding variational equations, conserved quantities (or, what is equivalent, conservation laws), symmetries, Cartan (Noether) symmetries, gauge symmetries and different versions of Noether's theorem are studied in this ambient. In this way, this constitutes a general geometric framework for all these topics that includes, as special...
Variations by generalized symmetries of local Noether strong currents equivalent to global canonical Noether currents
We will pose the inverse problem question within the Krupka variational sequence framework. In particular, the interplay of inverse problems with symmetry and invariance properties will be exploited considering that the cohomology class of the variational Lie derivative of an equivalence class of forms, closed in the variational sequence, is trivial. We will focalize on the case of symmetries of globally defined field equations which are only locally variational and prove that variations of local...