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Article Dans Une Revue Physical Review D Année : 2022

Discretizing parametrized systems: The magic of Dittrich invariance

Résumé

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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hal-00611582 , version 1 (02-02-2024)

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Carlo Rovelli. Discretizing parametrized systems: The magic of Dittrich invariance. Physical Review D, 2022, 106 (10), pp.104062. ⟨10.1103/PhysRevD.106.104062⟩. ⟨hal-00611582⟩
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