Foundations of thermodynamics in special theory of relativity are considered. We argue that from the phenomenological point of view the correct relativistic transformations of heat and absolute temperature are given by the formulas proposed by H. Ott, H. Arzeliès and C. Møller. It is shown that the same transformation rules can be also found from the relativistic Gibbs distribution for ideal gas. This distribution has been recently verified by the computer simulations. Phenomenological and statistical thermometers in relativistic thermodynamics are analyzed.
The construction of the * -product proposed by Fedosov is implemented in terms of the theory of fibre bundles. The geometrical origin of the Weyl algebra and the Weyl bundle is shown. Several properties of the product in the Weyl algebra are proved. Symplectic and abelian connections in the Weyl algebra bundle are introduced. Relations between them and the symplectic connection on a phase space M are established. Elements of differential symplectic geometry are included. Examples of the Fedosov formalism in quantum mechanics are given.
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