senior research fellow

theoretical physics group

institute of mathematical sciences

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*] |

- P. A. M. Dirac:
*Lectures on Quantum Mechanics*, Dover Publications (2001). - A. Das:
*Lectures on Quantum Field Theory*, World Scientific (2008). - H. J. Rothe, K. D. Rothe:
*Classical and Quantum Dynamics of Constrained Hamiltonian Systems*, World Scientific (2010). - M. Ornigotti, A. Aiello:
*The Faddeev-Popov Method Demystified*.

Preprint available at arXiv:1407.7256. - M. Henneaux, C. Teitelboim:
*Quantization of Gauge Systems*, Princeton University Press (1994). - S. Seahra:
*Quantization of Constrained Systems*.

Lecture notes available here. - 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. - J. W. van Holten:
*Aspects of BRST Quantization*.

Preprint available at arXiv:hep-th/0201124. - D. Birmingham et al.:
*Topological Field Theories*, Phys. Rep.**209**(1991), 129-340. - Y.-H. Gao:
*Topological Twisting*.

Lecture notes available here. - A. Bilal:
*Introduction to Supersymmetry*.

Lecture notes available at arXiv:hep-th/0101055. - 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. - 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. - N. Seiberg:
*Naturalness Versus Supersymmetric Non-Renormalization Theorems*, Phys. Lett. B**318**(1993), 469-475.

Preprint available at arXiv:hep-ph/9309335.