### About

### Quantum Theory, Groups and Representations

### Not Even Wrong: The Book

### Categories

- Book Reviews (96)
- BRST (12)
- Experimental HEP News (148)
- Fake Physics (4)
- Favorite Old Posts (46)
- Langlands (32)
- Multiverse Mania (143)
- Not Even Wrong: The Book (27)
- Obituaries (19)
- Quantum Mechanics (10)
- Quantum Theory: The Book (6)
- Strings 2XXX (16)
- This Week's Hype (100)
- Uncategorized (1,153)

### Recent Comments

- Losing the Nobel Prize 23

A.J., Low Math, Meekly Interacting, Shantanu, Peter Woit, piscator, S [...] - Math News 14

LMR, Jim Given, LMR, S, Jim Given, Michael Gogins [...] - Are We In the Swampland? 18

Peter Woit, Curious Mayhem, Peter Woit, DrDave, Petite Kabylie, Peter Woit [...] - What is Real? 74

Curious Mayhem, Tim Maudlin, Peter Woit, Peter Woit, Mark Hillery, Dave Miller [...] - From Princeton to Prison 6

william e emba, In Hell's Kitchen (NYC), troubled@dot.com, Peter Woit, G. S., Swany

- Losing the Nobel Prize 23
### Archives

### Links

### Mathematics Weblogs

- Alex Youcis
- Alexandre Borovik
- Anton Hilado
- Cathy O'Neil
- Daniel Litt
- Danny Calegari
- David Hansen
- David Mumford
- Emmanuel Kowalski
- Harald Helfgott
- Jesse Johnson
- Johan deJong
- Lieven Le Bruyn
- Mathematics Without Apologies
- Michael Hutchings
- Motivic Stuff
- Noncommutative Geometry
- Pieter Belmans
- Qiaochu Yuan
- Quomodocumque
- Rigorous Trivialities
- Secret Blogging Seminar
- Terence Tao
- The n-Category Cafe
- Timothy Gowers

### Physics Weblogs

- Alexey Petrov
- AMVA4NewPhysics
- Andrew Jaffe
- Angry Physicist
- Capitalist Imperialist Pig
- Chad Orzel
- Charles Day
- Clifford Johnson
- Cormac O’Raifeartaigh
- Doug Natelson
- EPMG Blog
- Georg von Hippel
- Gordon Watts
- Jackson Clarke
- Jacques Distler
- Jennifer Ouellette
- Jim Baggott
- Joe Conlon
- John Horgan
- Kyle Cranmer
- Lubos Motl
- Makoto Sakurai
- Mark Goodsell
- Matt Strassler
- Matthew Buckley
- Michael Schmitt
- Norbert Bodendorfer
- Peter Orland
- Physics World
- Reimagine Physics
- Resonaances
- Robert Helling
- Ross McKenzie
- Sabine Hossenfelder
- Scott Aaronson
- Sesh Nadathur
- Shaun Hotchkiss
- Shores of the Dirac Sea
- Stacy McGaugh
- Steve Hsu
- Tommaso Dorigo

### Twitter

### Meta

# Category Archives: BRST

## BRST and Dirac Cohomology

For the last couple years I’ve been working on the idea of using what mathematicians call “Dirac Cohomology” to replace the standard BRST formalism for handling gauge symmetries. So far this is just in a toy model: gauge theory in … Continue reading

Posted in BRST
16 Comments

## Notes on BRST IX: Clifford Algebras and Lie Algebras

Note: I’ve started putting together the material from these postings into a proper document, available here, which will be getting updated as time goes on. I’ll be making changes and additions to the text there, not on the blog postings. … Continue reading

Posted in BRST
4 Comments

## Notes on BRST VIII: Clifford Algebras

Clifford Algebras Clifford algebras are well-known to physicists, in the guise of matrix algebras generated by the -matrices first used in the Dirac equation. They also have a more abstract formulation, which will be the topic of this posting. One … Continue reading

Posted in BRST
6 Comments

## Notes on BRST VII: The Harish-Chandra Homomorphism

The Casimir element discussed in the last posting of this series is a distinguished quadratic element of the center (note, here is a complex semi-simple Lie algebra), but there are others, all of which will act as scalars on irreducible … Continue reading

Posted in BRST
2 Comments

## Notes on BRST VI: Casimir Operators

For the case of , it is well-known from the discussion of angular momentum in any quantum mechanics textbook that irreducible representations can be labeled either by j, the highest weight (here, highest eigenvalue of ), or by , the … Continue reading

Posted in BRST
8 Comments

## BRST News

I should finish writing the next installment of the Notes on BRST series soon, but thought I’d post here about two pieces of BRST-related news, concerning the “B” and the “T”. The “T” in BRST is I.V. Tyutin, whose Lebedev … Continue reading

Posted in BRST
4 Comments

## Notes on BRST V: Highest Weight Theory

In the last posting we discussed the Lie algebra cohomology for a semi-simple Lie algebra. Because the invariants functor is exact here, this tells us nothing about the structure of irreducible representations in this case. In this posting we’ll consider … Continue reading

Posted in BRST
4 Comments

## Notes on BRST IV: Lie Algebra Cohomology for Semi-simple Lie Algebras

In this posting I’ll work out some examples of Lie algebra cohomology, still for finite dimensional Lie algebras and representations. If is a compact, connected Lie group, it can be thought of as a compact manifold, and as such one … Continue reading

Posted in BRST
2 Comments

## Notes on BRST III: Lie Algebra Cohomology

The Invariants Functor The last posting discussed one of the simplest incarnations of BRST cohomology, in a formalism familiar to physicists. This fits into a much more abstract mathematical context, and that’s what we’ll turn to now. Given a Lie … Continue reading

Posted in BRST
6 Comments

## Notes on BRST II: Lie Algebra Cohomology, Physicist’s Version

My initial plan was to have the second part of these notes be about gauge symmetry and the problems physicists have encountered in handling it, but as I started writing it quickly became apparent that explaining this in any detail … Continue reading

Posted in BRST
15 Comments