2018/04/30 by Eduardo Antonio dos Reis, G. Krein, Gastão Krein +2
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Covariant transformation #Curvature #Curved space #Geometry #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Path integral formulation #Physics #Quantization (signal processing) #Quantum #Quantum field theory in curved spacetime #Quantum gravity #Quantum mechanics #Scalar (mathematics) #Scalar curvature #Scalar field #Semiclassical physics #Spacetime #Stochastic quantization #hep-lat #hep-th #msc:81T16 #msc:81T20 #msc:81T25 #msc:83C47
paper · pdf · doi:10.1016/j.physletb.2019.134925
Corrected formulations, some two-loop results added. Fits the version accepted in Physics Letters B
openalex created_date 2018/04/24 · openalex publication_date 2019/09/10 · arxiv created 2019/09/19 · arxiv updated 2019/09/25 · openalex updated_date 2026/08/06
We employ stochastic quantization for a self-interacting nonminimal massive scalar field in curved spacetime. The covariant background field method and local momentum space representation are used to obtain the Euclidean correlation function and evaluate multi-loop quantum corrections through simultaneous expansions in the curvature tensor and its covariant derivatives and in the noise fields. The stochastic correlation function for a quartic self-interaction reproduces the well-known one-loop result by Bunch and Parker and is used to construct the effective potential in curved spacetime in an arbitrary dimension D up to the first order in curvature. Furthermore, we present a sample of numerical simulations for D=3 in the first order in curvature. We consider the model with spontaneous symmetry breaking and obtain fully nonperturbative solutions for the vacuum expectation value of the scalar field and compare them with one- and two-loop solutions.