Vacuum energy and renormalization of the field-independent term
Year: 2022
Authors: Màriàn I.G., Jentschura U.D., Defenu N., Trombettoni A., Nandori I.
Autors Affiliation: MTA DE Particle Phys Res Grp, POB 51, H-4001 Debrecen, Hungary; Univ Debrecen, POB 105, H-4010 Debrecen, Hungary; Missouri Univ Sci & Technol, Dept Phys, Rolla, MO 65409 USA; MTA Atomki, POB 51, H-4001 Debrecen, Hungary; Swiss Fed Inst Technol, Inst Theoret Phys, Wolfgang Pauli Str 27, Zurich, Switzerland; Univ Trieste, Dept Phys, Str Costiera 11, I-34151 Trieste, Italy; CNR IOM DEMOCRITOS Simulat Ctr, Via Bonomea 265, I-34136 Trieste, Italy; SISSA, Via Bonomea 265, I-34136 Trieste, Italy; Ist Nazl Fis Nucl, Sez Trieste, Via Bonomea 265, I-34136 Trieste, Italy.
Abstract: Due to its construction, the nonperturbative renormalization group (RG) evolution of the constant, field-independent term (which is constant with respect to field variations but depends on the RG scale k) requires special care within the Functional Renormalization Group (FRG) approach. In several instances, the constant term of the potential has no physical meaning. However, there are special cases where it receives important applications. In low dimensions (d = 1), in a quantum mechanical model, this term is associated with the ground-state energy of the anharmonic oscillator. In higher dimensions (d = 4), it is identical to the A term of the Einstein equations and it plays a role in cosmic inflation. Thus, in statistical field theory, in flat space, the constant term could be associated with the free energy, while in curved space, it could be naturally associated with the cosmological constant. It is known that one has to use a subtraction method for the quantum anharmonic oscillator in d = 1 to remove the k 2 term that appears in the RG flow in its high-energy (UV) limit in order to recover the correct results for the ground-state energy. The subtraction is needed because the Gaussian fixed point is missing in the RG flow once the constant term is included. However, if the Gaussian fixed point is there, no further subtraction is required. Here, we propose a subtraction method for k(4) and k(2) terms of the UV scaling of the RG equations for d = 4 dimensions if the Gaussian fixed point is missing in the RG flow with the constant term. Finally, comments on the application of our results to cosmological models are provided.
Journal/Review: JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS
Volume: (3) Pages from: 62-1 to: 62-28
More Information: This work was supported by the uNKP-20-4-I New National Excellence Program of the Ministry for Innovation and Technology from the source of the National Research, Development and Innovation Fund and by the National Science Foundation (Grant PHY-2110294) . Useful discussions with Z. Trocsanyi and G. Somogyi are gratefully acknowledged. This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC2181/1-390900948 (the Heidelberg STRUCTURES Excellence Cluster) . The CNR/MTA Italy-Hungary 2019-2021 Joint Project Strongly interacting systems in confined geometries also is gratefully acknowledged.KeyWords: particle physics; cosmology connection; dark energy theory; cosmological parameters from CMBR; inflationDOI: 10.1088/1475-7516/2022/03/062Citations: 3data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-10-20References taken from IsiWeb of Knowledge: (subscribers only)