nLab
duality in physics

Idea

In fundamental physics, notably in quantum field theory and string theory one often says that a non-trivial equivalence between two models (in theoretical physics) is a duality.

While most of these dualities refer to equivalences between quantum field theories, they find their conceptual explanation in string theory. See at

for more.

In some cases such as Montonen-Olive duality/S-duality the equivalence involves some actual duality in the mathematical sense, as in replacing the gauge group by its Langlands dual group. In T-duality only simple cases exhibit such obviously “dual” behaviour and in general cases such as U-duality really only the notion of equivalence remains.

There is also a duality in the description of physics:

algebra	geometry
Poisson algebra	Poisson manifold
deformation quantization	geometric quantization
algebra of observables	space of states
Heisenberg picture	Schrödinger picture
AQFT	FQFT

higher algebra	higher geometry
Poisson n-algebra	n-plectic manifold
En-algebras	higher symplectic geometry
BD-BV quantization	higher geometric quantization
factorization algebra of observables	extended quantum field theory
factorization homology	cobordism representation

Revised on October 25, 2012 23:29:15 by Urs Schreiber (82.169.65.155)