madhusudhan raman

senior research fellow
theoretical physics group
institute of mathematical sciences

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Constraints, BRST and Supersymmetry

August - December '14

In order to better understand the notion of gauge invariance, we began this seminar with a discussion of (i) Dirac's work on constrained dynamical systems and (ii) the BRST formalism.

We decided then that a discussion of supersymmetry was appropriate, given the similarities between the BRST charge \( \mathcal{Q} \) and the supersymmetry charges \( Q_{\alpha} \). We plan to end the seminar with a discussion of Seiberg-Witten theory.

Each meeting will go on for an hour and a half. We meet every Saturday at 5:00 pm in Hall 123.

Note: An asterisk (*) next to a reference means it was mentioned in passing and is only tangentially related to the material discussed in the talk.


Date Speaker Topic Notes/References
6th December Renjan John The Moduli Space and \( S \)-Duality [12], [13]
15th November M Instantons and Seiberg's Nonrenormalization Theorems [14]
25th October Renjan John The \( \mathcal{N} = 2 \) Supersymmetric Yang-Mills Action [11], [13]
18th October Renjan John \( \mathcal{N}=1 \) Superspace: Chiral and Vector Superfields [11], [12]
11th October Renjan John The Supersymmetry Algebra and Its Representations [11]
8th October M BRST III: Quantum \( \mathcal{Q} \) Cohomology and Topological Field Theories [8], [9], [10]
27th September M BRST II: Ghosts and \( \mathcal{Q} \) Cohomology [5], [8]
20th September Pulak Banerjee Renormalization I: Loops and Divergences ...
13th September M BRST I: Phase Space and Local Charges [8]
6th September Dr. Vivek M. Vyas Constrained Theories III: Examples [2], [6], [7]
30th August Dr. Vivek M. Vyas Constrained Theories II: Dirac Brackets and Constraint Classes [5]
26rd August Dr. Vivek M. Vyas Constrained Theories I: Motivations, Multipliers and Singular Lagrangians [1], [3], [4*]


  1. P. A. M. Dirac: Lectures on Quantum Mechanics, Dover Publications (2001).
  2. A. Das: Lectures on Quantum Field Theory, World Scientific (2008).
  3. H. J. Rothe, K. D. Rothe: Classical and Quantum Dynamics of Constrained Hamiltonian Systems, World Scientific (2010).
  4. M. Ornigotti, A. Aiello: The Faddeev-Popov Method Demystified.
    Preprint available at arXiv:1407.7256.
  5. M. Henneaux, C. Teitelboim: Quantization of Gauge Systems, Princeton University Press (1994).
  6. S. Seahra: Quantization of Constrained Systems.
    Lecture notes available here.
  7. A. Scardicchio: Classical and Quantum Dynamics of a Particle Constrained on a Circle, Phys. Lett. A 300 (2002), 7-17.
    Preprint available at arXiv:quant-ph/0106029.
  8. J. W. van Holten: Aspects of BRST Quantization.
    Preprint available at arXiv:hep-th/0201124.
  9. D. Birmingham et al.: Topological Field Theories, Phys. Rep. 209 (1991), 129-340.
  10. Y.-H. Gao: Topological Twisting.
    Lecture notes available here.
  11. A. Bilal: Introduction to Supersymmetry.
    Lecture notes available at arXiv:hep-th/0101055.
  12. L. Alvarez-Gaume, S. F. Hassan: Introduction to \( S \)-Duality in \( \mathcal{N}=2 \) Supersymmetric Gauge Theory, Fortsch. Phys. 45 (1997), 159-236.
    Preprint available at arXiv:hep-th/9701069.
  13. N. Seiberg, E. Witten: Electric-Magnetic Duality, Monopole Condensation, And Confinement in \( \mathcal{N}=2 \) Supersymmetric Yang-Mills Theory, Nucl. Phys. B 426 (1994), 19-52.
    Preprint available at arXiv:hep-th/9407087.
  14. N. Seiberg: Naturalness Versus Supersymmetric Non-Renormalization Theorems, Phys. Lett. B 318 (1993), 469-475.
    Preprint available at arXiv:hep-ph/9309335.