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Quantum spectral dimension in quantum field theory

AuthorsCalcagni, Gianluca CSIC ORCID ; Modesto, Leonardo; Nardelli, Giuseppe
KeywordsField theory
Quantum gravity
Spectral dimension
Issue Date28-Mar-2016
PublisherWorld Scientific Publishing
CitationInternational Journal of Modern Physics D 25: 1650058 (2016)
AbstractWe reinterpret the spectral dimension of spacetimes as the scaling of an effective self-energy transition amplitude in quantum field theory (QFT), when the system is probed at a given resolution. This picture has four main advantages: (a) it dispenses with the usual interpretation (unsatisfactory in covariant approaches) where, instead of a transition amplitude, one has a probability density solving a nonrelativistic diffusion equation in an abstract diffusion time; (b) it solves the problem of negative probabilities known for higher-order and nonlocal dispersion relations in classical and quantum gravity; (c) it clarifies the concept of quantum spectral dimension as opposed to the classical one. We then consider a class of logarithmic dispersion relations associated with quantum particles and show that the spectral dimension dS of spacetime as felt by these quantum probes can deviate from its classical value, equal to the topological dimension D. In particular, in the presence of higher momentum powers it changes with the scale, dropping from D in the infrared (IR) to a value dSUV ≤ D in the ultraviolet (UV). We apply this general result to Stelle theory of renormalizable gravity, which attains the universal value dSUV = 2 for any dimension D.
Description26 pags.; 3 figs.; app. ; PACS numbers: 04.60.-m, 11.10.-z, 11.10.Hi
Publisher version (URL)
Identifiersdoi: 10.1142/S0218271816500589
issn: 0218-2718
Appears in Collections:(CFMAC-IEM) Artículos

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