Wheeler Propagator of the Lorentz Invariant Thermal Energy Propagation

Abstract

Two decades ago it was made the first steps to establish a really Hamiltonian description of field theory of dissipative transport processes in order to apply all of the tools of modern field theories for these kind of processes. The great breakthrough was to introduce such scalar potential fields for the measurable quantities-temperature, pressure, etc.-, by which the complete Lagrangian-Hamiltonian formalism could be developed. Later it has been managed to create the differential equation for the relativistic invariant heat propagation by the help of the scalar field, which field can generate a dynamical temperature immediately. In the present paper it is focused on a farther step in the Lorentz invariant thermal energy propagation. Now, the temperature field satisfies a covariant field equation of a (wave-like) thermal energy propagation with finite speed-less than the speed of light. In our previous works the connection has been clarified between this scalar field and the usual local equilibrium temperature including the classical Fourier's heat conduction. The existence of a dynamical phase transition between the two kinds of propagation, between a wave and a non-wave, i.e., a dynamical phase transition between a non-dissipative and a dissipative thermal process is also found. Presently, it is pointed out that the so-called Wheeler propagator can be obtained without any difficulty for this process inspite of the existence of the dynamical phase transition and it can be seen that the causality condition is completed at the same time.

Application of Potentials in the Description of Transport Processes

“…The general solution is not known at the time of this writing. We can conclude that there is a successful description for the thermal energy propagation with the help of the potential theory [15,16]. Accordingly, this means that the laws of thermodynamics are completed in the Lorentz invariant formulation [17,18].…”

A Repulsive Interaction in Classical Electrodynamics

“…The structure of equation is similar to the equations (1) and (2) (such as in Refs. [1][2][3][4][5][6][7]) that includes a dynamical phase transition depending on the parameter as a consequence of a spinodal instability [19,20]. The equation for the vector potential can be also formulated, starting from Eq.…”

“…It can be seen that for all of the field equationsequations (9), (11), (16) and 18have the same structure. We know from the former studies [1][2][3][4][5][6][7]15] that these Klein-Gordon equations with a negative "mass term" are resulted from repulsive interactions. Thus, it seems to us that the interaction in the present case is a repulsive-like force which appears mathematically in the second Maxwell's equation, in Eq.…”

“…Mechanical [1,2], thermodynamic [2][3][4] and further field theoretical examples [5][6][7] for the Klein-Gordon equation with negative "mass term" involve the same dynamical phase transition that operates between the diffusive and the wave type dynamics. Studying the existence of these kinds of phenomena we may assume that the occurrence of these are more general and not restricted exclusively to a certain part of physics.…”

Can a Lorentz Invariant Equation Describe Thermal Energy Propagation Problems?

“…Finally, it is important to mention and emphasize that the participating particles of the above treated thermal energy propagation cannot be observable directly as Bollini's and Rocca's detailed studies (Bollini & Rocca, 1997a;b;Bollini et al, 1999) show. This is a consequence of the fact that the tachyons do not move as free particles, thus they can be considered as the mediators of the dynamic phase transition (Gambár & Márkus, 2007;Márkus & Gambár, 2010).…”