# Symmetries in Quantum Field Theory and superselection structure

July 18, 2023

“Symmetry” is an extremely broad and versatile concept in physics in general. The realization
of symmetries acquires more facets and shadings in quantum theory, than it already exhibits
in classical physics. Rather than attempting a full coverage of the topic, I just start by recalling
in a schematic way of the richness of the notion in quantum theory, before I turn to a more
specific discussion of symmetries in the context of quantum field theory, and finally turn to
concentrate on its relation with superselection structure. This relation strongly depends on
the number of spacetime dimensions.

Commissioned by the Encyclopedia of Mathematical Physics, M. Bojowald and R.J. Szabo (eds.). To be published by Elsevier.

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Keywords:

Symmetries, Superselection sectors, Conformal quantum field theory, two-dimensional models