-
Fadeev-Popov ghosts, continued
This post has been migrated from my old blog, the math-physics learning seminar. Last time I sketched how we can represent an integral over a submanifold \(M \subset \mathbb{R}^n\) by an integral of the form
Read more… -
Fadeev-Popov ghosts
This post has been migrated from my old blog, the math-physics learning seminar. Today I want to review the Fadeev-Popov procedure, with a view toward BRST and eventually BV. Gauge-Invariance and Gauge-Fixing
Read more… -
The Weyl and Wigner transforms
This post has been migrated from my old blog, the math-physics learning seminar. Today I’d like to try to understand better how deformation quantization is related to the usual canonical quantization, and especially how the latter might be used to deduce the former, i.
Read more… -
Equations of motion and Noether's theorem in the functional formalism
This post has been migrated from my old blog, the math-physics learning seminar. First, let us recall the derivation of the equations of motion and Noether’s theorem in classical field theory.
Read more… -
The Moyal product
This post has been migrated from my old blog, the math-physics learning seminar. Today I want to understand the Moyal product, as we will need to understand it in order to construct quantizations of symplectic quotients.
Read more… -
An exercise in quantum Hamiltonian reduction
This post has been migrated from my old blog, the math-physics learning seminar. Semiclassical Setup Let the group \(GL(2)\) act on \(V = \mathrm{Mat}_{2\times n}\) and consider the induced symplectic action on \(T^\ast V\).
Read more… -
The 1PI effective action
This post has been migrated from my old blog, the math-physics learning seminar. In this post I’d like to try to understand the 1PI effective action that is often of interest.
Read more… -
Spontaneous symmetry breaking in QFT
This post has been migrated from my old blog, the math-physics learning seminar. In this post I want to try to understand symmetry breaking and the origin of the moduli space of vacua.
Read more… -
Seiberg-Witten theory and the Riemann-Hilbert problem
This post has been migrated from my old blog, the math-physics learning seminar. References: Introduction to Seiberg-Witten theory and its stringy origin Seiberg-Witten and follow-up The Classical Moduli Space of Vacua For definiteness, we’ll consider just the case of \(SU(2)\) considered by Seiberg and Witten.
Read more… -
BPS states and wall-crossing
This post has been migrated from my old blog, the math-physics learning seminar. This is the first in what I hope will become a series of posts on BPS state counting and wall-crossing.
Read more…