Abstract
The Olbertian partition function is reformulated in terms of continuous (Abelian) fields described by the Landau–Ginzburg action, respectively, Hamiltonian. In order to make some progress, the Gaussian approximation to the partition function is transformed into the Olbertian prior to adding the quartic Landau–Ginzburg term in the Hamiltonian. The final result is provided in the form of an expansion suitable for application of diagrammatic techniques once the nature of the field is given, that is, once the field equations are written down such that the interactions can be formulated.
Highlights
Particle spectra in near-Earth space as well as in cosmic rays very frequently exhibit power law tails at high energies which since their introduction by [4] have been interpreted as Olbert distributions (κ-distributions).1, Cosmic ray spectra in particular extend as power laws over many decades reminding of several ultra-relativistic Olbert distributions adding up continuously [5]
Field partition functions play a substantial role in field theory when interacting fields are under scrutiny
The partition function is the key to the identification of phase transitions on the one hand, and on the other in managing renormalization [23, 35] and elimination of divergences
Summary
Particle spectra in near-Earth space (e.g., see [1,2,3]) as well as in cosmic rays very frequently exhibit power law tails at high energies which since their introduction by [4] have been interpreted as Olbert distributions (κ-distributions)., Cosmic ray spectra in particular extend as power laws over many decades reminding of several ultra-relativistic Olbert distributions adding up continuously [5]. Olbert distributions have been inferred in plasma turbulence and many other occasions as for instance in front [6] and behind [7] collisionless shocks [8] as for example, in the heliosphere and its heliosheath [9, 10], which may serve as the paradigm of a stellar wind that is terminated by its interaction with the interstellar galactic medium They were derived in plasma wave–wave interaction theory [11,12,13]. We show how the Olbertian field partition function can be constructed giving it an operational representation that is suitable for application This is interesting in as far as the extra parameter κ which is fundamental to the Olbert theory provides an external degree of freedom which may become useful in applications like renormalization and phase transition where convergence is obliterated
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