Jump to content

Statistical Physics (Book): Difference between revisions

references/application books added
(started summary)
Β 
(references/application books added)
Line 8: Line 8:
|publisher=Butterworth Heinemann
|publisher=Butterworth Heinemann
|publicationdate=1982
|publicationdate=1982
|pages=669
|pages=564
|isbn13=978-0-08-050346-2
|isbn13=978-0-08-057046-4
}}
}}


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