2022-05-22T08:55:35Zhttps://digital.csic.es/dspace-oai/requestoai:digital.csic.es:10261/1520852020-05-18T12:45:53Zcom_10261_135com_10261_4col_10261_388
Quantum spectral dimension in quantum field theory
Calcagni, Gianluca
Modesto, Leonardo
Nardelli, Giuseppe
Consejo Superior de Investigaciones Científicas (España)
Field theory
Quantum gravity
Spectral dimension
26 pags.; 3 figs.; app. ; PACS numbers: 04.60.-m, 11.10.-z, 11.10.Hi
We 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.
G.C. and L.M. acknowledge the i-Link cooperation program of CSIC (project ID
i-Link0484) for partial sponsorship. The work of G.C. is under a Ramón y Cajal
contract.
Peer Reviewed
2017-06-27T11:26:24Z
2017-06-27T11:26:24Z
2016-03-28
2017-06-27T11:26:25Z
artículo
http://purl.org/coar/resource_type/c_6501
doi: 10.1142/S0218271816500589
issn: 0218-2718
International Journal of Modern Physics D 25: 1650058 (2016)
http://hdl.handle.net/10261/152085
10.1142/S0218271816500589
http://dx.doi.org/10.13039/501100003339
Preprint
http://doi.org/10.1142/S0218271816500589
Sí
open
World Scientific Publishing