Editing Statistical Physics (Book)

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{{InfoboxBook
{{InfoboxBook
|title=Statistical Physics
|title=Quantum Electrodynamics
|image=[[File:Landau statistical physics.jpg]]
|image=[[File:Landau statistical physics.jpg]]
|author=[https://en.wikipedia.org/wiki/Lev_Landau Lev Landau]
|author=[https://en.wikipedia.org/wiki/Lev_Landau Lev Landau]
Line 8: Line 8:
|publisher=Butterworth Heinemann
|publisher=Butterworth Heinemann
|publicationdate=1982
|publicationdate=1982
|pages=564
|pages=669
|isbn13=978-0-08-057046-4
|isbn13=978-0-08-050346-2
}}
}}


{{NavContainerFlex
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.
|content=
{{NavButton|link=[[Read#Landau|Read]]}}
{{NavButton|link=[[Statistical Mechanics]]}}
}}
Β 
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.
Β 
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)
Β 
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.


=== Applications ===
=== Applications ===
<div class="flex-container" style="clear: both;">
<div class="flex-container" style="clear: both;">
{{BookListing
{{BookListing
| cover = Souriaus ymplectic dynamics cover.jpg
| cover = Weinberg1new.jpg
| link = Structure of dynamical systems: a Symplectic View of Physics (Book)
| link = The Quantum Theory of Fields 1, Foundations (Book)
| title = === Structure of dynamical systems: a Symplectic View of Physics ===
| title = === The Quantum Theory of Fields 1, Foundations ===
| desc = Structure of dynamical systems: a Symplectic View of Physics by Jean-Marie Souriau.
| desc = Foundations of Quantum Field Theory by Steven Weinberg
}}
}}
{{BookListing
{{BookListing
| cover = Baxter statmech cover.jpg
| cover = Weinberg 2 QFT gauge theory cover.jpg
| link = Exactly Solved Models In Statistical Mechanics (Book)
| link = The Quantum Theory of Fields 2, Gauge Theory (Book)
| title = === Exactly Solved Models In Statistical Mechanics ===
| title = === Applications of Lie Groups to Differential Equations ===
| desc = Exactly Solved Models In Statistical Mechanics by Rodney Baxter.
| desc = The Quantum Theory of Fields 2, Gauge Theory by Steven Weinberg.
}}
}}
{{BookListing
{{BookListing
| cover = Sternberg quantgroup cover.jpg
| cover = Fieldsandstrings1 cover.jpg
| link = Quantum Groups: From Coalgebras to Drinfeld Algebras (Book Series)
| link = Quantum Fields and Strings: A Course for Mathematicians (Book Series)
| title = === Quantum Groups: From Coalgebras to Drinfeld Algebras ===
| title = === Quantum Fields and Strings: A Course for Mathematicians ===
| desc = Quantum Groups: From Coalgebras to Drinfeld Algebras by Shlomo Sternberg and Steven Shnider.
| desc = Axiomatic classical and quantum field theory for mathematicians.
}}
}}
{{BookListing
{{BookListing
| cover = Itzykson drouffe statfields1 cover.jpg
| cover = Haagqft cover.jpg
| link = Statistical Field Theory (Book Series)
| link = Local Quantum Physics: Fields, Particles, Algebras (Book)
| title = === Statistical Field Theory Volume 1 ===
| title = === Local Quantum Physics: Fields, Particles, Algebras ===
| desc = Statistical Field Theory Volume 1: From Brownian Motion to Renormalization and Lattice Gauge Theory by Claude Itzykson and Jean-Michel Drouffe.
| desc = C*-algebraic quantum field theory by Rudolph Haag.
}}
}}
{{BookListing
{{BookListing
| cover = Itzykson drouffe statfields2 cover.jpg
| cover = Connes Noncommutative Geometry, Quantum Fields and Motives cover.jpg
| link = Statistical Field Theory (Book Series)
| link = Noncommutative Geometry, Quantum Fields and Motives (Book)
| title = === Statistical Field Theory Volume 2 ===
| title = === Noncommutative Geometry, Quantum Fields and Motives ===
| desc = Statistical Field Theory Volume 2: Strong Coupling, Monete Carlo Methods, Conformal Field Theory, and Random Systems by Claude Itzykson and Jean-Michel Drouffe.
| desc = Noncommutative Geometry, Quantum Fields and Motives by Alain Connes and Matilde Marcolli.
}}
}}
{{BookListing
{{BookListing
| cover = Namiki stochasticquant cover.jpg
| cover = Costellorenormalization cover.jpg
| link = Stochastic Quantization (Book)
| link = Renormalization and Effective Field Theory (Book)
| title = === Stochastic Quantization ===
| title = === Renormalization and Effective Field Theory ===
| desc = Stochastic Quantization by Mikio Namiki
| desc = Renormalization and Effective Field theory by Kevin Costello
}}
}}
{{BookListing
{{BookListing
| cover = Watanabe bayesian cover.jpg
| cover = Senechalcft cover.jpg
| link = Mathematical Theory of Bayesian Statistics (Book)
| link = Conformal Field Theory (Book)
| title = === Mathematical Theory of Bayesian Statistics ===
| title = === Conformal Field Theory ===
| desc = Mathematical Theory of Bayesian Statistics by Sumio Watanabe
| desc = Conformal Field theory by Philippe Di Francesco, Pierre Mathieu, and David SΓ©nΓ©chal.
}}
}}
{{BookListing
{{BookListing
| cover = Watanabe alg learning cover.jpg
| cover = Kacvertex cover.jpg
| link = Algebraic Geometry and Statistical Learning Theory (Book)
| link = Vertex Algebras for Beginners (Book)
| title = === Algebraic Geometry and Statistical Learning Theory ===
| title = === Vertex Algebras for Beginners ===
| desc = Algebraic Geometry and Statistical Learning Theory by Sumio Watanabe
| desc = Vertex Algebras for Beginners by Victor Kac.
}}
{{BookListing
| cover = Frenkelvertex cover.jpg
| link = Vertex Algebras and Algebraic Curves (Book)
| title = === Vertex Algebras and Algebraic Curves ===
| desc = Vertex Algebras and Algebraic Curves by Edward Frenkel and David Ben-Zvi.
}}
}}
</div>
</div>
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