Tuesday, 19 April 2005
Symmetry and its Formalisms
Alexandre Guay, U. of Pittsburgh (HPS)
12:05 pm, 817R Cathedral of Learning
Abstract: Many philosophers and most physicists believe
that the operative use of the concept of symmetry is completely
captured by the mathematical concept of group. Some mathematicians
argue that the stronger formalism of groupoids is needed to represent
symmetries in all their generality. They insist that local/internal
symmetries cannot be represented adequately by groups. Physicists
could reply that the most important local/internal symmetry in physics
-- the local gauge symmetry -- is easily represented by groups.
What is the source of this apparent disagreement? In this talk I
will clarify how the concept of symmetry is related to the notions
of equivalence relation, group, groupoid, and harmony of parts.
I will show how the formalism of groupoids is the right framework
to discuss symmetries, why gauge symmetry can be represented by
groups nonetheless, and how the classical definition of symmetry
as the harmony of parts is also captured by groupoids.