Unified approach to Quantum and Classical Dualities

Bloomington; E. Cobanera (1); G. Ortiz (1); IN; (2) Dep. of Physics; Indiana University; Mo); St. Louis; Washington University; Z. Nussinov (2) ((1) Dep. of Physics

arxiv: 0907.0733 · v3 · pith:JWJTINDOnew · submitted 2009-07-06 · ❄️ cond-mat.stat-mech · cond-mat.str-el· hep-th· quant-ph

Unified approach to Quantum and Classical Dualities

E. Cobanera (1) , G. Ortiz (1) , Z. Nussinov (2) ((1) Dep. of Physics , Indiana University , Bloomington , IN; (2) Dep. of Physics , Washington University , St. Louis

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classification ❄️ cond-mat.stat-mech cond-mat.str-elhep-thquant-ph

keywords dualitiesquantumclassicalmorphismstheoriesabelianalgebraappear

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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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