Symmetries of Snyder--de Sitter space and relativistic particle dynamics

We study the deformed conformal-Poincare symmetries consistent with the Snyder--de Sitter space. A relativistic particle model invariant under these deformed symmetries is given. This model is used to provide a gauge independent derivation of the Snyder--de Sitter algebra. Our results are valid in the leading order in the parameters appearing in the model.Comment: 12 pages, LaTeX, version appearing in JHEP, minor changes to match published versio

Extended thermodynamics for dense gases up to whatever order

The 14 moments model for dense gases, introduced in the last years by Arima, Taniguchi Ruggeri, Sugiyama, is here considered. They have found the closure of the balance equations up to second order with respect to equilibrium; here the closure is found up to whatever order with respect to equilibrium, but for a more constrained system where more symmetry conditions are imposed and this in agreement with the suggestion of the kinetictheory. The results, when restricted at second order with respect to equilibrium, are the same of the previously cited model but under the further restriction of full symmetries

Extended Thermodynamics of charged gases with many moments

Recently amodel with many moments for the description of relativistic gases has been studied and an exact closure has been found, depending on an arbitrary set of single variable functions. In the case of a charged gas and when the electromagnetic field acts as an external force, the exploitation of the entropy principle produces an additional condition. A closure compatible with this further condition has been found, when the highest order moment has an even number of free indexes. It amounts in restrictions on the arbitrary single variable functions appearing in the general case. They are polynomials of increasing degree with respect to equilibrium, which coefficients are arbitrary constants. When the highest order moment has an odd number M of free indexes the further condition is different from that appearing in the case M even and alternative techniques must be used to find a closure compatible with it. In this paper we take into account this last model and we find a closure compatible with the further condition. As well as in the case M even, also in the case M odd we find that the arbitrary single variable functions of the general theory are polynomials of increasing degree with respect to equilibrium, which coefficients are arbitrary constant

REPRESENTATION THEOREMS IN A 4-DIMENSIONAL EUCLIDEAN SPACE. THE CASE WITH ONLY SKEW-SYMMETRIC TENSORS

In a 4-dimensional Euclidean space, representation theorems have been recently obtained for isotropic functions depending on an arbitrary number of scalars, skew-symmetric second order tensors and symmetric second order tensors; the cases has been treated where at least one of these last ones has an eigenvalue with multiplicity 1 or two distinct eigenvalues with multiplicity 2. The case with at least a non null vector, among the independent variables, was already treated in literature. There remain the case where every symmetric tensor has an eigenvalue with multiplicity 4; but, in this case, it plays a role only through its trace. Consequently, it remains the case where the independent variables, besides scalars, are skew-symmetric tensors. This case is treated in the present paper. As in the other cases, the result is a finite set of scalar valued isotropic functions such that every other scalar function of the same variables can be expressed as a function of the elements of this set. Similarly, a set of tensor valued isotropic functions is found such that every other tensor valued function of the same variables can be expressed as a linear combination, trough scalar coefficients, of the elements of this set. This result is achieved both for symmetric functions , and for skew-symmetric functions