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Topology in statistical physics - 1
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BSSP 2020 : Introduction to Topology in statistical physics
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Contents
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Lecture -1: Topology in statistical physics: What and why?
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Our course work in mathematical physics should tell us that a mathematical structures have two characteristic features
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Assume that you are familiar
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With this, I intent develop the course as follows
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The aim would be to try and tell you the story in a way you can start thinking for yourself.
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Example of topological quantum number and associated ideas
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In this sense Maxwell's equation describe a classical EFFECTIVE field theory
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Ultra-violet regulation : Define a small length, a and do all the calcula- tions.
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Sometimes it is easy to see what is a natural regular - Symmetries
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Now we modify the Maxwell's equation to incorporate the magnetic monopole This may come from more high energy theories which we would not discuss,
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Magnetic Monopole
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In the magnetostatic limit with the monopole at the origin, i.e. on = mor,
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Line singularity Dirac String : This singularity is not in a physical observable.
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General Forecast : Two types of Quantum Numbers.
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Term String
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Path Integral formulation of Quantum Mechanics
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Integrate out P
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Q&A
Description:
Explore the fundamental concepts of topology in statistical physics through this comprehensive lecture, part of the Bangalore School on Statistical Physics XI. Delve into the mathematical structures underlying physical phenomena, focusing on topological quantum numbers and their significance. Examine Maxwell's equations as a classical effective field theory, and investigate the incorporation of magnetic monopoles. Learn about ultraviolet regulation, symmetries, and the Dirac string. Gain insights into different types of quantum numbers and the path integral formulation of quantum mechanics. Engage with a detailed exploration of these advanced topics, designed to bridge the gap between master's-level courses and cutting-edge research in statistical physics.

Topology in Statistical Physics - Lecture 1

International Centre for Theoretical Sciences
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#Science #Physics #Statistical Physics #Quantum Mechanics #Quantum Field Theory #Effective Field Theory #Mathematics #Geometry #Topology #Electromagnetism #Maxwell's Equations
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Topology in statistical physics - 1