Statistical Physics (Book)
Statistical physics is commonly introduced in physics education as the physics of thermodynamics in gases and solids. This is wrong. Firstly, the standard courses neglect what Landau does, deriving the macroscopic concepts from probabilistic (but ultimately deterministic) microscopic motion. There are also numerous other applications of the subject from chemistry to crystals to phase transitions. Souriau takes this further. Statistical mechanics like classical mechanics is based on symplectic geometry, but with the added ingredient of measures. This geometric approach to statistical mechanics leads us eventually to statistical field theory and stochastic quantization with lattice statistical mechanics as a stepping stone to the continuum limit - this makes the connection to quantum field theory manifest. Statistical field theory and stochastic quantization were first coined and motivated by Parisi, who started to make the analogies between e.g. statistical correlation functions and quantum field theory propagators rigorous.
| Statistical Physics | |
| |
| Information | |
|---|---|
| Author | Lev Landau |
| Language | English |
| Series | Course of Theoretical Physics |
| Publisher | Butterworth Heinemann |
| Publication Date | 1982 |
| Pages | 564 |
| ISBN-13 | 978-0-08-057046-4 |
From the physics, other genuinely new types of mathematical objects appear:
- scale symmetry/renormalization and critical phenomena
- continuous random processes
- statistical learning (to be elaborated on in the future)
Understanding the fundamentals of statistical mechanics and its geometric consequences may lead directly to an understanding of complex phenomena at all scales - from weather to neuronal cognition.
ApplicationsEdit
Structure of dynamical systems: a Symplectic View of Physics
Structure of dynamical systems: a Symplectic View of Physics by Jean-Marie Souriau.
Exactly Solved Models In Statistical Mechanics
Exactly Solved Models In Statistical Mechanics by Rodney Baxter.
Quantum Groups: From Coalgebras to Drinfeld Algebras
Quantum Groups: From Coalgebras to Drinfeld Algebras by Shlomo Sternberg and Steven Shnider.
Statistical Field Theory Volume 1
Statistical Field Theory Volume 1: From Brownian Motion to Renormalization and Lattice Gauge Theory by Claude Itzykson and Jean-Michel Drouffe.
Statistical Field Theory Volume 2
Statistical Field Theory Volume 2: Strong Coupling, Monete Carlo Methods, Conformal Field Theory, and Random Systems by Claude Itzykson and Jean-Michel Drouffe.
Stochastic Quantization
Stochastic Quantization by Mikio Namiki
Mathematical Theory of Bayesian Statistics
Mathematical Theory of Bayesian Statistics by Sumio Watanabe
Algebraic Geometry and Statistical Learning Theory
Algebraic Geometry and Statistical Learning Theory by Sumio Watanabe