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What is generalized geometry?
This post has been migrated from my old blog, the math-physics learning seminar. The following are my notes for a short introductory talk. References below are not intended to be comprehensive!
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Virasoro algebra from the free boson
This post has been migrated from my old blog, the math-physics learning seminar. Usual physics derivations of the Virasoro algebra from the free boson in two dimensions usually use some sort of regularization procedure to compute the central charge.
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The basic idea of the quantum BV complex
This post has been migrated from my old blog, the math-physics learning seminar. The original post can still be found here. This post was originally written by Dylan Butson (arxiv).
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Clifford algebras and spinors part 3: Bochner identity
Other articles in this series This post has been migrated from my old blog, the math-physics learning seminar. Let \(M\) be a Riemannian manifold, and let \(Cl(M)\) be its Clifford bundle.
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Clifford algebras and spinors, part 2: spin structures and Dirac operators
Other articles in this series This post has been migrated from my old blog, the math-physics learning seminar. A very good reference for today’s material is Dan Freed’s (unpublished) notes on Dirac operators, available here.
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Clifford algebras and spinors: part 1
Other articles in this series This post has been migrated from my old blog, the math-physics learning seminar. Clifford Algebras Today I’d like to write some brief notes about Clifford algebras and spinors.
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Clifford algebras and spinors: table of contents
Table of contents: Part 1 Part 2 Part 3
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Virasoro algebra
This post has been migrated from my old blog, the math-physics learning seminar. Conformal Invariance in 2D To begin, recall that in two dimensions, the conformal transformations are generated by holomorphic and anti-holomorphic transformations.
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BRST and Lie algebra cohomology
This post has been migrated from my old blog, the math-physics learning seminar. We saw in previous posts that gauge-fixing is intimately related to BRST cohomology. Today I want to explain the underlying mathematical formalism, as it is actually something very well-known: Lie algebra cohomology.
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BRST
This post has been migrated from my old blog, the math-physics learning seminar. Finally, I want to discuss gauge-invariant of the gauge-fixed theory. (!?) We saw in the previous posts that if we have a gauge theory with connection \(A\) and matter fields \(\psi\), in order to derive sensible Feynman rules we have to introduce a gauge-fixing function \(G\) as well as Fermionic fields \(c, \bar{c}\), the ghosts.
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