Discretizing parametrized systems: the magic of Ditt-invariance

Details Discretizing parametrized systems: the magic of Ditt-invariance Discretizing parametrized systems: the magic of Ditt-invariance

2011-07-12

arxiv.org/abs/1107.2310v3

Physics

High Energy Physics

High Energy Physics - Lattice

9 pages, 4 figures. (Revision: typos corrected and references added.)

Scientific paper

Peculiar phenomena appear in the discretization of a system invariant under reparametrization. The structure of the continuum limit is markedly different from the usual one, as in lattice QCD. First, the continuum limit does not require tuning a parameter in the action to a critical value. Rather, there is a regime where the system approaches a sort of asymptotic topological invariance ("Ditt-invariance"). Second, in this regime the expansion in the number of discretization points provides a good approximation to the transition amplitudes. These phenomena are relevant for understanding the continuum limit of quantum gravity. I illustrate them here in the context of a simple system.

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