Quantum field theories use Minkowski space whereas statictical mechanics uses 3-D Euclidean space with temperature as an additional variable. Both the theories deal with many particle systems and both consider point like particles only.
Is it possible to bridge the two theories and give an unified description. What are the major difficulties/obstacles of this approach and what are the success stories?
Such a unified description (if I understand your question correctly) exists. In the path integral formulation of quantum mechanics by Feynman it was noted that if you replace 1/kT by it you get similar expressions that need to be evaluated. B.M. McCoy had a recent paper on ArXiv devoted to this issue: "The Connection Between Statistical Mechanics and Quantum Field Theory", http://arxiv.org/pdf/hep-th/9403084v2.pdf
I suddenly remembered that I even have a book about this: "Quantum Physics, A Functional Integral Point of View, by J. Glimm and A. Jaffe. Springer, 1987. It is completely devoted to the unity of mathematical structure in quantum mechanics, quantum field theory, and statistical mechanics.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Quantum Physics