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A perturbative approach for non renormalizable theories is developed. It is shown that the introduction of an extra expansion parameter allows one to get rid of divergences and express physical quantities as series with finite coefficients.…
Based on the analysis of biquaternion quadratic forms of field, it is shown that Maxwell equations arise as a consequence of the principle of conservation of the energy-momentum flow of field in space-time. It turns out that this principle…
Einstein's distinction between principle theories and constructive theories is methodological rather than metaphysical. Principle theories such as thermodynamics and relativity articulate empirically distilled constraints that delimit…
Recent work has shown the existence of a relativistic effect present in a single component non-equilibrium fluid, corresponding to a heat flux due to an electric field. The treatment in that work was limited to a four-dimensional Minkowksi…
Ever since the appearance of renormalization theory there have been several differently motivated attempts at non-localized (in the sense of not generated by point-like fields) relativistic particle theories, the most recent one being at…
We investigate the long time behavior of a system of viscoelastic particles modeled with the homogeneous Boltzmann equation. We prove the existence of a universal Maxwellian intermediate asymptotic state and explicit the rate of convergence…
A self-consistent extended Einstein-Maxwell model for relativistic non-stationary polarizable-magnetizable anisotropic media is presented. Based on the analogy with relativistic extended irreversible (transient) thermodynamics, the extended…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is employed to address the hitherto nonrenormalizable gravitational interaction following which the…
We address the Riemann and Cauchy problems for systems of $n$ conservation laws in $m$ unknowns which are subject to $m-n$ constraints ($m\geq n$). Such constrained systems generalize systems of conservation laws in standard form to include…
A proof is given, at a greater level of generality than previous 'no-go' theorems, of the impossibility of formulating a modal interpretation that exhibits 'serious' Lorentz invariance at the fundamental level. Particular attention is given…
The complex form of Maxwell equations has been constructed as one equation for 3-dimensional complex A-vector. The real and imaginary parts of this vector are described with use of electric and magnetic tensions accordingly. With using a…
Continuum electrodynamics is an axiomatic formal theory based on the macroscopic Maxwell equations and the constitutive relations. We apply the formal theory to a thermodynamically closed system consisting of an antireflection coated block…
We consider a complex covariant form of the macroscopic Maxwell equations, in a moving medium or at rest, following the original ideas of Minkowski. A compact, Lorentz invariant, derivation of the energy-momentum tensor and the…
We investigate the existence of "generic derivations" in exponential fields. We show that exponential fields without additional compatibility conditions between derivation and exponentiation cannot support a generic derivation.
We show from first principles the emergence of classical Boltzmann equations from relativistic nonequilibrium quantum field theory as described by the Kadanoff-Baym equations. Our method applies to a generic quantum field, coupled to a…
In quantum field theory there is now a well developed technique, effective field theory, which allows one to obtain low energy quantum predictions in ``non-renormalizable'' theories, using only the degrees of freedom and interactions…
Studies of geometrical theories suggest that fundmental problems of quantization arise from the disparate usage of displacement operators. These may be the source of a concealed inconsistency in the accepted formalism of quantum physics.…
It is argued that the one-loop effective action for a space-like noncommutative scalar field theory does not exist. This indicates that such theories are not renormalizable already at one loop order and suggests supersymmetrization and…
Augmented variational principles are introduced in order to provide a definition of relative conservation laws. As it is physically reasonable, relative conservation laws define in turn relative conserved quantities which measure, for…
We study the Boltzmann equation near a global Maxwellian in the case of bounded domains. We consider the boundary conditions to be either specular reflections or Maxwellian diffusion. Starting from the reference work of Guo in…