We explore the possibility that, in a quantum field theory with Planck scale cutoff Λ ≃ mp , observable quantities for low-energy processes respect the Lorentz symmetry. In particular, we compute the one-loop radiative correction Π to the self-energy of a scalar field with λφ4 interaction, using a modified (non- invariant) propagator which vanishes in the trans-Planckian regime, as expected in the “classicalisation” scenario. We then show that, by imposing the result does not depend on Λ (in the limit Λ→mp), an explicit (albeit not unique) expression for Π can be derived, which is similar to the one simply obtained with the standard Feynman propagator and a cutoff Λ=mp.
Lorentz invariance without trans-Planckian physics? / Roberto Casadio. - In: PHYSICS LETTERS. SECTION B. - ISSN 0370-2693. - STAMPA. - 724:(2013), pp. 351-354. [10.1016/j.physletb.2013.06.040]
Lorentz invariance without trans-Planckian physics?
CASADIO, ROBERTO
2013
Abstract
We explore the possibility that, in a quantum field theory with Planck scale cutoff Λ ≃ mp , observable quantities for low-energy processes respect the Lorentz symmetry. In particular, we compute the one-loop radiative correction Π to the self-energy of a scalar field with λφ4 interaction, using a modified (non- invariant) propagator which vanishes in the trans-Planckian regime, as expected in the “classicalisation” scenario. We then show that, by imposing the result does not depend on Λ (in the limit Λ→mp), an explicit (albeit not unique) expression for Π can be derived, which is similar to the one simply obtained with the standard Feynman propagator and a cutoff Λ=mp.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.