Vacuum energy and renormalization of the field-independent term

• Verfasst von: Márián, István Gábor [VerfasserIn]
• Verfasst von: Jentschura, Ulrich D. [VerfasserIn]
• Verfasst von: Defenu, Nicolò [VerfasserIn]
• Verfasst von: Trombettoni, Andrea [VerfasserIn]
• Verfasst von: Nandori, I. [VerfasserIn]
• Titel: Vacuum energy and renormalization of the field-independent term
• Verf.angabe: I. G. Marian, U.D. Jentschura, N. Defenu, A. Trombettoni and I. Nandori
• Ausgabe: Version v2
• E-Jahr: 2022
• Jahr: 31 Mar 2022
• Umfang: 19 S.
• Fussnoten: Version 1 vom 24 Juni 2021, Version 2 vom 31 März 2022 ; Gesehen am 18.10.2022
• Weitere Titel: Titel der Preprint-Version: Renormalization of field-independent term in the cosmological constant problem
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [S.l.] : Arxiv.org, 1991
• Jahr Quelle: 2022
• Band/Heft Quelle: (2022), Artikel-ID 2107.06069, Seite 1-19
• DOI: doi:10.48550/arXiv.2107.06069
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Astrophysics - Cosmology and Nongalactic Astrophysics
• Sach-SW: General Relativity and Quantum Cosmology
• Sach-SW: High Energy Physics - Theory
• K10plus-PPN: 1819105563

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 $\Lambda$ 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.