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In a quantum field theory, one may calculate an effective or running coupling constant that defines the coupling of the theory measured at a given momentum scale. One example of such a coupling constant is the electric charge.
In theoretical physics, it is usually possible to organize physical phenomena according to the energy scale or distance scale. The theory of renormalization group is based on this paradigm. The short-distance, ultraviolet (UV) physics does not directly affect qualitative features of the long-distance, infrared (IR) physics, and vice versa.
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In theoretical physics, functional renormalization group (FRG) is an implementation of the renormalization group (RG) concept which is used in quantum and statistical field theory, especially when dealing with strongly interacting systems. The method combines functional methods of quantum field theory with the intuitive renormalization group idea of Kenneth G. Wilson. This technique allows to interpolate smoothly between the known microscopic laws and the complicated macroscopic phenomena in physical systems. In this sense, it bridges the transition from simplicity of microphysics to complexity of macrophysics. Figuratively speaking, FRG acts as a microscope with a variable resolution. One starts with a high-resolution picture of the known microphysical laws and subsequently decreases the resolution to obtain a coarse-grained picture of macroscopic collective phenomena. The method is nonperturbative, meaning that it does not rely on an expansion in a small coupling constant. Mathematically, FRG is based on an exact functional differential equation for a scale-dependent effective action.
Asymptotic safety is a concept in quantum field theory which aims at finding a consistent and predictive quantum theory of the gravitational field. Its key ingredient is a nontrivial fixed point of the theory's renormalization group flow which controls the behavior of the coupling constants in the ultraviolet (UV) regime and renders physical quantities safe from divergences. Although originally proposed by Steven Weinberg to find a theory of quantum gravity, the idea of a nontrivial fixed point providing a possible UV completion can be applied also to other field theories, in particular to perturbatively nonrenormalizable ones. In this respect, it is similar to quantum triviality.
References
- 1 2 3 Moffat, J. W. "Ultraviolet Complete Quantum Field Theory and Particle Model". The European Physical Journal Plus. 134 (9): 443. doi:10.1140/epjp/i2019-12973-6. ISSN 2190-5444.
- ↑ Demir, Durmuş; Karahan, Canan; Sargın, Ozan (2023-02-08). "Dimensional regularization in quantum field theory with ultraviolet cutoff". Physical Review D. 107 (4): 045003. doi:10.1103/PhysRevD.107.045003.
- 1 2 "Ultraviolet and Infrared Divergences in Superstring Theory" (PDF).
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