Symmetries as Topological Operators

Abstract: In this talk I'll discuss extended symmetry defect operators and how they naturally arise from symmetries in the quantum theory.

The focus will be on ordinary symmetries; these are referred to as 0-form topological group-like symmetries in the modern literature. First I will discuss classical symmetries of Lagrangian field theory. In the second part I will discuss their analogues in the quantised theory, and outline and a sketch a proof of their properties.

condensed matterHEP - theorymathematical physicsdifferential geometry

Audience: advanced learners

( paper | slides )

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Europe and Pacific Theoretical Physics

Series comments: European and Pacific Theoretical Physics is a group that runs online seminars and talks across broad topics in mathematical and theoretical physics. Our goal is to share concepts across continents to bring about a deeper understanding of cutting-edge topics in physics.

The talks are informal, and anyone can participate, so please reach out if you would like to present one week!

Extended notes & presentation material are uploaded to "Past talks". Please click on the title of a talk, and then click on "paper" or "slides" to see more. Our focus for 2025 was on Generalised (Categorical) Symmetries, following the lecture notes found here: arxiv.org/pdf/2411.09082.

The reading course seminars are scheduled to resume in 2026. If you would like to present material, please reach out.

Zoom link: unibe-ch.zoom.us/j/6801537904

Talks may be uploaded to YouTube: www.youtube.com/@eupactp

Mailing list sign-up: forms.gle/StswcjC7RbXWuvAr8

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