Abstract
We use the scalar field constructed in phase space to analyze the analogous Stefan-Boltzmann law and Casimir effect, both of them at finite temperature. The temperature is introduced by Thermo Field Dynamics (TFD) formalism and the quantities are analyzed once projected in the space of coordinates. We show that using the framework of phase space it is possible to introduce a thermal energy which is related to temperature as it vanishes when the temperature tends to zero. In fact given such a correlation the formalism of TFD is equivalent when project is in momenta space when compared to coordinates space.
Highlights
Eugene Paul Wigner [1, 2] introduced in 1932 the first formalism to quantum mechanics in phase space, motivated by finding a way to treat transport equations for superfluids
In this formalism of quantum mechanics, the observables are represented by operators of type â = a푤⋆, which are used to construct a representation of Galilei symmetries
In this article we explore how to implement Thermo Field Dynamics (TFD) in phase space; we analyze the scalar field in phase space at finite temperature
Summary
Eugene Paul Wigner [1, 2] introduced in 1932 the first formalism to quantum mechanics in phase space, motivated by finding a way to treat transport equations for superfluids. In case of nonrelativistic symmetries, this leads to a Schrodinger equation in phase space, where the wave function is directly associated with Wigner function, so with full physical meaning In this formalism of quantum mechanics, the observables are represented by operators of type â = a푤⋆, which are used to construct a representation of Galilei symmetries. The second one the socalled Thermo Field Dynamics (TFD) formalism; it is a Advances in High Energy Physics natural way to deal with dynamical systems It preserves the time-evolution once the temperature is identified with a rotation in a duplicated Fock space [7].
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