Unified approach to Quantum and Classical Dualities

Details Unified approach to Quantum and Classical Dualities Unified approach to Quantum and Classical Dualities

2009-07-06

arxiv.org/abs/0907.0733v3

Phys. Rev. Lett. 104:020402,2010

Physics

Condensed Matter

Statistical Mechanics

4+3 pages, 3 figures

Scientific paper

We show how classical and quantum dualities, as well as duality relations that appear only in a sector of certain theories ("emergent dualities"), can be unveiled, and systematically established. Our method relies on the use of morphisms of the "bond algebra" of a quantum Hamiltonian. Dualities are characterized as unitary mappings implementing such morphisms, whose even powers become symmetries of the quantum problem. Dual variables -which were guessed in the past- can be derived in our formalism. We obtain new self-dualities for four-dimensional Abelian gauge field theories.

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