Publication: The U(1) lattice gauge theory universally connects all classical models with continuous variables, including background gravity
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2011-02-07
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IOP Publishing
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Abstract
We show that the partition function of many classical models with continuous degrees of freedom, e.g. abelian lattice gauge theories and statistical mechanical models, can be written as the partition function of an (enlarged) four–dimensional lattice gauge theory (LGT) with gauge group U(1). This result is very general that it includes models in different dimensions with different symmetries. In particular, we show that a U(1) LGT defined in a curved spacetime can be mapped to a U(1) LGT with a flat background metric. The result is achieved by expressing the U(1) LGT partition function as an inner product between two quantum states.
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© 2011 IOP Publishing Ltd and SISSA. The authors would like to thank Maarten Van den Nest for fruitful discussions and valuable suggestions. The work is supported by the FWF (SFB-F40) and the European Union (QICS, NAMEQUAM), the Spanish MICINN grant FIS2009-10061, CAM research consortium QUITEMAD S2009-ESP-1594, European Commission PICC: FP7 2007-2013. grant no. 249958, UCM-BS grant GICC-910758