Ensemble IISc
This is the official channel for Ensemble, the Undergraduate Physics Club at the Indian Institute of Science, Bangalore. We hold regular talks by students and professors of the institute and upload some selected talks on this channel.
Ensemble IISc
TLDR: In this talk, we will explore how field theories can be constructed from group theory for general groups.
Date: 03 March 2025
Time: 09:30 PM
Venue: F08-A, OPB
Speaker: Nikshay Chugh
We will begin with a brief overview of representation theory for finite groups, after which we will discuss projective representations and their connection to the second cohomology group, which is used in the classification of symmetries of fermions in Kitaev's periodic table.
If time permits, we will explore additional topics that further illustrate the interplay between group theory and field theory, focussing on continuous symmetries.
Pre-req: Basic group theory, quantum mechanics, and electrodynamics
Target audience: second- and third-year undergraduates.
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Group theory plays a fundamental role in modern physics, providing the mathematical framework for understanding symmetries in field theories. In this talk, we will explore how field theories can be constructed from group theory for general groups. We will begin with an overview of
representation theory for finite groups, introducing key concepts and their relevance in physical systems. Moving beyond ordinary representations, we will discuss projective representations and their connection to the second cohomology group, which is used in the classification of symmetries of fermions in Kitaev's periodic table. If time permits, we will explore additional topics that further illustrate the interplay between group theory and field theory, focussing on continuous symmetries.
The talk assumes familiarity with basic group theory, quantum mechanics, and electrodynamics and is aimed at second- and third-year undergraduates.
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