Consistency conditions for fundamentally discrete theories

Martin Bojowald, Ghanashyam Date

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

The dynamics of physical theories is usually described by differential equations. Difference equations then appear mainly as an approximation which can be used for a numerical analysis. As such, they have to fulfil certain conditions to ensure that the numerical solutions can reliably be used as approximations to solutions of the differential equation. There are, however, also systems where a difference equation is deemed to be fundamental, mainly in the context of quantum gravity. Since difference equations in general are harder to solve analytically than differential equations, it can be helpful to introduce an approximating differential equation as a continuum approximation. In this paper implications of this change in viewpoint are analysed to derive the conditions that the difference equation should satisfy. The difference equation in such a situation cannot be chosen freely but must be derived from a fundamental theory. Thus, the conditions for a discrete formulation can be translated into conditions for acceptable quantizations. In the main example, loop quantum cosmology, we show that the conditions are restrictive and serve as a selection criterion among possible quantization choices.

Original languageEnglish (US)
Pages (from-to)121-143
Number of pages23
JournalClassical and Quantum Gravity
Volume21
Issue number1
DOIs
StatePublished - Jan 7 2004

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difference equations
differential equations
approximation
cosmology
numerical analysis
gravitation
continuums
formulations

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

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Consistency conditions for fundamentally discrete theories. / Bojowald, Martin; Date, Ghanashyam.

In: Classical and Quantum Gravity, Vol. 21, No. 1, 07.01.2004, p. 121-143.

Research output: Contribution to journalArticle

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