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Quantum-field theories as representations of a single $^\ast$-algebra (1302.4057v2)
Published 17 Feb 2013 in math-ph and math.MP
Abstract: We show that many well-known quantum field theories emerge as representations of a single $\ast$-algebra. These include free quantum field theories in flat and curved space-times, lattice quantum field theories, Wightman quantum field theories, and string theories. We prove that such theories can be approximated on lattices, and we give a rigorous definition of the continuum limit of lattice quantum field theories.
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