2024/05/14 by S. A. Franchino-Viñas, Franchino-Viñas, S. A., S. Mignemi +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.2405.08934
openalex publication_date 2024/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We review recent discussions concerning the definition of a quantum field theory in a curved and noncommutative space, the Snyder--de Sitter space. For a quartic self-interacting scalar field in a spacetime of arbitrary dimension, we show how to perturbatively define the classical action in the small-deformation regime and give its explicit first-order expression. Afterwards, we compute the divergences of the one-loop effective action for the two- and four-dimensional cases. These are employed to calculate the beta functions of the couplings and to numerically analyze the corresponding renormalization group flow. Depending on the initial conditions of the couplings, in four dimensions it is possible to obtain an asymptotic-free theory or a flip in the sign of the cosmological constant as a consequence of the running.