Mathematical basis of computational statistical physics and quantum analysis

D. Ya. Petrina

Doreen Fraser

Philosophical analysis of spontaneous symmetry breaking (SSB) in particle physics has been hindered by the unavailability of rigorous formulations of models in quantum field theory (QFT). A strategy for addressing this problem is to use the rigorous models that have been constructed for SSB in quantum statistical mechanics (QSM) systems as a basis for drawing analogous conclusions about SSB in QFT. On the basis of an analysis of this strategy as an instance of the application of the same mathematical formalism to different domains and as an instance of drawing analogies between domains, I conclude that certain structural explanations can be exported from QSM to QFT but that causal explanations cannot.

Doreen Fraser

Philosophical analysis of spontaneous symmetry breaking (SSB) in particle physics has been hindered by the unavailability of rigorous formulations of models in quantum field theory (QFT). A strategy for addressing this problem is to use the rigorous models that have been constructed for SSB in quantum statistical mechanics (QSM) systems as a basis for drawing analogous conclusions about SSB in QFT. Based on an analysis of this strategy as an instance of the application of the same mathematical formalism to different domains and as an instance of drawing analogies between domains, I conclude that certain structural explanations can be exported from QSM to QFT, but that causal explanations cannot.

Milan Vinduška

Louis Fishman

A. Ya. Khinchin, Aleksandr I︠A︡kovlevich Khinchin

A coherent, well-organized look at the basis of quantum statistics' computational methods, the determination of the mean values of occupation numbers, the foundations of the statistics of photons and material particles, thermodynamics.