We introduce the concepts of a multisymplectic structure and a polysymplectic structure on a general fiber bundle over a general base manifold, define the concept of the symbol of a multisymplectic form, which is a polysymplectic form representing its leading order contribution, and prove Darboux theorems for the existence of canonical local coordinates.

This paper addresses the interplay between vacuum and thermal local averages for massless scalar radiation near a plane wall of a large cavity where the Dirichlet boundary condition is assumed to hold. The main result is that stable thermodynamic equilibrium is possible only if the curvature coupling parameter is restricted to a certain range. In more than three spacetime dimensions such a range contains the conformal coupling, but it does not contain the minimal coupling. Since this same range for possible values of the curvature coupling parameter also applies to massive scalar radiation, it may be relevant in settings where arbitrarily coupled scalar fields are present.

Based upon the intrinsic symmetries approach to inhomogeneous cosmologies, we propose an exact solution to Einstein’s field equations where the spatial sections are flat and the source is a nonperfect fluid such that the dissipative terms can be written in terms of spatial gradients of the energy density under a suitable choice of the coordinate system. It is shown through the calculation of the luminosity distance as a function of the redshift that the presence of such inhomogeneities may lead to an effective deceleration parameter compatible with either the standard [Formula: see text]CDM model or LTB models depending on the choice of boundary conditions with no exotic matter. This fact is another evidence that different inhomogeneous models should be carefully investigated in order to verify which model may be compatible with observations and still be as close as possible to the standard model regarding the underlying assumptions, without resorting necessarily to exotic matter components.

The mean square fluctuation and the expectation value of the stress-energymomentum tensor of a neutral massive scalar field at finite temperature are determined near an infinite plane Dirichlet wall, and also near an infinite plane Neumann wall. The flat background has an arbitrary number of dimensions and the field is arbitrarily coupled to the vanishing curvature. It is shown that, unlike vacuum contributions, thermal contributions are free from boundary divergences, and that the thermal behaviour of the scalar field near a Dirichlet wall differs considerably from that near a Neumann wall. Far from the wall the study reveals a local version of dimensional reduction, namely, corrections to familiar blackbody expressions are linear in the temperature, with the corresponding coefficients given only in terms of vacuum expectation values in a background with one less dimension. It is shown that such corrections are "classical" (i.e., not dependent on Planck's constant) only if the scalar field is massless. A natural conjecture that arises is that the "local dimensional reduction" is universal since it operates for massless and massive fields alike and regardless of the boundary conditions.

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