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Physica A Statistical Mechanics and its Applications

Relativistic kinetic theory of quantum systems

Ch.G. van Weert, Wim P.H. de Boer

Published Jan 1, 1975• 17 citations
Publisher
DOI
10.1016/0378-4371(75)90076-x

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In this thesis, we discussed the derivation of quantum kinetic equations appropriate for applications in nuclear physics, both in a non-relativistic and in a relativistic context. In each case we obtained a kinetic equation together with an equation for the effective interaction. The latter serves as the dynamical input of the former. In the kinetic equation both mean-field and collision effects are described in a self-consistent way because both are expressed in terms of the effective interaction. This self-consistency enforces us to solve a statistical problem (kinetic equation) and a dynamical problem (effective interaction) simultaneously. The interaction, that we obtained as a result of our considerations, is a generalized version of the usual Brueckner G-matrix in the sense that single-particle energies are corrected for collision effects by the so called rearrangement-term. 0nly in this way kinetic theory and interaction are consistent with one another and therefore constitute a conserving approximation.... Zie epilogue
It is shown that the well-known relativistic correction of quantum Hamiltonian that is present in textbooks appears after quantization of oversimplified relativistic kinetic energy decomposition. Using the proper expression one obtains the kinetic energy operator which relation with the ususal one is consistent with corresponding relation of kinetic energies in special relativity theory. The Schrödinger equation with this operator gives new interesting possibilities for quantum phenomena description.