Termodinâmica de um gás de fótons no contexto de eletrodinâmicas não-lineares
The objective of this dissertation is the development of a general formalism to analyze the thermodynamical properties of a photon gas under the context of nonlinear electrodynamics (NLED). To this end it is obtained, through the systematic analysis of Maxwell s electromagnetism (EM) properties, the...
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Formato: | Dissertação |
Idioma: | por |
Publicado em: |
Universidade Federal do Rio Grande do Norte
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Endereço do item: | https://repositorio.ufrn.br/jspui/handle/123456789/18608 |
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Resumo: | The objective of this dissertation is the development of a general formalism to
analyze the thermodynamical properties of a photon gas under the context of nonlinear
electrodynamics (NLED). To this end it is obtained, through the systematic
analysis of Maxwell s electromagnetism (EM) properties, the general dependence of
the Lagrangian that describes this kind of theories. From this Lagrangian and in
the background of classical field theory, we derive the general dispersion relation
that photons must obey in terms of a background field and the NLED properties. It
is important to note that, in order to achieve this result, an aproximation has been
made in order to allow the separation of the total electromagnetic field into a strong
background electromagnetic field and a perturbation. Once the dispersion relation
is in hand, the usual Bose-Einstein statistical procedure is followed through which
the thermodynamical properties, energy density and pressure relations are obtained.
An important result of this work is the fact that equation of state remains identical
to the one obtained under EM. Then, two examples are made where the thermodynamic
properties are explicitly derived in the context of two NLED, Born-Infelds
and a quadratic approximation. The choice of the first one is due to the vast appearance
in literature and, the second one, because it is a first order approximation
of a large class of NLED. Ultimately, both are chosen because of their simplicity.
Finally, the results are compared to EM and interpreted, suggesting possible tests to
verify the internal consistency of NLED and motivating further developement into
the formalism s quantum case |
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