nLab
duality in physics

Context

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Duality

Contents

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.

Examples

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

for more.

Relation to mathematical duality

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:

duality between algebra and geometry in physics:

algebrageometry
Poisson algebraPoisson manifold
deformation quantizationgeometric quantization
algebra of observablesspace of states
Heisenberg pictureSchrödinger picture
AQFTFQFT
higher algebrahigher geometry
Poisson n-algebran-plectic manifold
En-algebrashigher symplectic geometry
BD-BV quantizationhigher geometric quantization
factorization algebra of observablesextended quantum field theory
factorization homologycobordism representation

Revised on September 17, 2014 05:41:11 by Urs Schreiber (185.26.182.30)