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Statistical Physics (Book): Difference between revisions
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|publisher=Butterworth Heinemann | |publisher=Butterworth Heinemann | ||
|publicationdate=1982 | |publicationdate=1982 | ||
|pages= | |pages=564 | ||
|isbn13=978-0-08- | |isbn13=978-0-08-057046-4 | ||
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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. 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 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. 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. | ||
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) | |||
=== Applications === | === Applications === | ||
<div class="flex-container" style="clear: both;"> | <div class="flex-container" style="clear: both;"> | ||
{{BookListing | {{BookListing | ||
| cover = | | cover = Souriaus ymplectic dynamics cover.jpg | ||
| link = | | link = Structure of dynamical systems: a Symplectic View of Physics (Book) | ||
| title = === | | title = === Structure of dynamical systems: a Symplectic View of Physics === | ||
| desc = Structure of dynamical systems: a Symplectic View of Physics by Jean-Marie Souriau. | |||
| desc = | |||
}} | }} | ||
{{BookListing | {{BookListing | ||
| cover = | | cover = Baxter statmech cover.jpg | ||
| link = | | link = Exactly Solved Models In Statistical Mechanics (Book) | ||
| title = === | | title = === Exactly Solved Models In Statistical Mechanics === | ||
| desc = | | desc = Exactly Solved Models In Statistical Mechanics by Rodney Baxter. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
| cover = | | cover = Sternberg quantgroup cover.jpg | ||
| link = | | link = Quantum Groups: From Coalgebras to Drinfeld Algebras (Book Series) | ||
| title = === | | title = === Quantum Groups: From Coalgebras to Drinfeld Algebras === | ||
| desc = | | desc = Quantum Groups: From Coalgebras to Drinfeld Algebras by Shlomo Sternberg and Steven Shnider. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
| cover = | | cover = Itzykson drouffe statfields1 cover.jpg | ||
| link = | | link = Statistical Field Theory (Book Series) | ||
| title = === | | title = === Statistical Field Theory Volume 1 === | ||
| desc = | | desc = Statistical Field Theory Volume 1: From Brownian Motion to Renormalization and Lattice Gauge Theory by Claude Itzykson and Jean-Michel Drouffe. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
| cover = | | cover = Itzykson drouffe statfields2 cover.jpg | ||
| link = | | link = Statistical Field Theory (Book Series) | ||
| title = === | | title = === Statistical Field Theory Volume 1 === | ||
| desc = | | desc = Statistical Field Theory Volume 2: Strong Coupling, Monete Carlo Methods, Conformal Field Theory, and Random Systems by Claude Itzykson and Jean-Michel Drouffe. | ||
}} | }} | ||
{{BookListing | {{BookListing | ||
| cover = | | cover = Namiki stochasticquant cover.jpg | ||
| link = | | link = Stochastic Quantization (Book) | ||
| title = === | | title = === Stochastic Quantization === | ||
| desc = | | desc = Stochastic Quantization by Mikio Namiki | ||
}} | }} | ||
</div> | </div> | ||