2019/03/20 by Adnan Aboulalaâ, Aboulalaa, Adnan
Physics and Astronomy · #60F10 #60G60 #60K35 #81T08 #81T16 #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Particle physics theoretical and experimental studies #Probability (math.PR) #Quantum Electrodynamics and Casimir Effect
paper · pdf · doi:10.48550/arxiv.1903.09621
openalex publication_date 2019/03/20 · openalex created_date 2023/01/25 · openalex updated_date 2026/07/28
The issue of the existence and possible triviality of the Euclidean quantum\nscalar field in dimension 4 is investigated by using some large deviations\ntechniques. As usual, the field \φd4 is obtained as a limit of\nregularized fields \φk4 associated with a probability measures\n\μk,V, where k, V represent ultraviolet and volume cutoffs. The result\nobtained is that in a fixed volume, the almost sure limit (as k \→\n\∞) of the density of \μk,V, with respect to the Gaussian free field\nmeasure, exists and is equal to 0, when the coupling constant is not\nvanishing. This implies that \μk,V can not have a strong limit as the\nultraviolet cutoff is removed. Furthermore, the normalization sequence\nZk,V=E e^- cal Ak,V is divergent as k \→ \∞ for\ndimensions d\≥4 when the vacuum renormalization is lower than some\nthreshold, which leads to the non ultraviolet stability of the field in this\ncase. These assertions are also valid for vector fields and can be extended to\npolynomial Lagrangians.\n