We reinterpret the spectral dimension of spacetimes as the scaling of an effective self-energy transition amplitude in quantum field theory, 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 non-relativistic diffusion equation in an abstract diffusion time; (b) it solves the problem of negative probabilities known for higher-order and non-local 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 $\ds^{\rm UV}\leq D$ in the ultraviolet (UV). We apply this general result to Stelle theory of renormalizable gravity, which attains the universal value $\ds^{\rm UV}=2$ for any dimension $D$.

Calcagni, G., Modesto, L., Nardelli, G., Quantum spectral dimension in quantum field theory, <<INTERNATIONAL JOURNAL OF MODERN PHYSICS D>>, 2016; 25 (05): N/A-N/A. [doi:10.1142/S0218271816500589] [http://hdl.handle.net/10807/76210]

Quantum spectral dimension in quantum field theory

Calcagni, Gianluca
Primo
;
Nardelli, Giuseppe
Ultimo
2016

Abstract

We reinterpret the spectral dimension of spacetimes as the scaling of an effective self-energy transition amplitude in quantum field theory, 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 non-relativistic diffusion equation in an abstract diffusion time; (b) it solves the problem of negative probabilities known for higher-order and non-local 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 $\ds^{\rm UV}\leq D$ in the ultraviolet (UV). We apply this general result to Stelle theory of renormalizable gravity, which attains the universal value $\ds^{\rm UV}=2$ for any dimension $D$.
Inglese
Calcagni, G., Modesto, L., Nardelli, G., Quantum spectral dimension in quantum field theory, <<INTERNATIONAL JOURNAL OF MODERN PHYSICS D>>, 2016; 25 (05): N/A-N/A. [doi:10.1142/S0218271816500589] [http://hdl.handle.net/10807/76210]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/76210
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