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Topology in statistical physics - 1
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Topology in Statistical Physics - Lecture 1
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- 1 Topology in statistical physics - 1
- 2 BSSP 2020 : Introduction to Topology in statistical physics
- 3 Contents
- 4 Lecture -1: Topology in statistical physics: What and why?
- 5 Our course work in mathematical physics should tell us that a mathematical structures have two characteristic features
- 6 Assume that you are familiar
- 7 With this, I intent develop the course as follows
- 8 The aim would be to try and tell you the story in a way you can start thinking for yourself.
- 9 Example of topological quantum number and associated ideas
- 10 In this sense Maxwell's equation describe a classical EFFECTIVE field theory
- 11 Ultra-violet regulation : Define a small length, a and do all the calcula- tions.
- 12 Sometimes it is easy to see what is a natural regular - Symmetries
- 13 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,
- 14 Magnetic Monopole
- 15 In the magnetostatic limit with the monopole at the origin, i.e. on = mor,
- 16 Line singularity Dirac String : This singularity is not in a physical observable.
- 17 General Forecast : Two types of Quantum Numbers.
- 18 Term String
- 19 Path Integral formulation of Quantum Mechanics
- 20 Integrate out P
- 21 Q&A
