Fundamentals of the Exact Renormalization Group
By Oliver J. Rosten. 2010
357 citations recorded by the source corpus.
Abstract Various aspects of the Exact Renormalization Group (ERG) are explored, starting with a review of the concepts underpinning the framework and the circumstances under which it is expected to be useful. A particular emphasis is placed on the intuitive picture provided for both renormalization in quantum field theory and universality associated with second order phase transitions. A qualitative discussion of triviality, asymptotic freedom and asymptotic safety is presented. Focusing on scalar field theory, the construction of assorted flow equations is considered using a general approach, whereby different ERGs follow from field redefinitions. It is recalled that Polchinski’s equation can be cast as a heat equation, which provides intuition and computational techniques for what follows. The analysis of properties of exact solutions to flow equations includes a proof that the spectrum of the anomalous dimension at critical fixed-points is quantized. Two alternative methods for computing the β -function in λ ϕ 4 theory are considered. For one of these it is found that all explicit dependence on the non-universal differences between a family of ERGs cancels out, exactly. The Wilson–Fisher fixed-point is rediscovered in a rather novel way. The discussion of nonperturbative approximation schemes focuses on the derivative expansion, and includes a refinement of the arguments that, at the lowest order in this approximation, a function can be constructed which decreases monotonically along the flow. A new perspective is provided on the relationship between the renormalizability of the Wilsonian effective action and of correlation functions, following which the construction of manifestly gauge invariant ERGs is sketched, and some new insights are given. Drawing these strands together suggests a new approach to quantum field theory.
Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/3154b3fe58ae3d0091d76d253c58f60dd5636da2
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Atomic and Molecular Physics, and Optics
In Nuclear and High Energy Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- The nonperturbative functional renormalization group and its applications (2020, background): “int can actually be both; depending on the choice of RG trajectory, the fixed point is approached by the trajectory in the IR or serves as a repulsor of the trajectory in the UV, cf. the discussion in [68]. Therefore, the fixed points of relevance in statistical physics and the tentative gravitational”
- Keldysh field theory for driven open quantum systems (2015, background): “Indeed, it has proven a very versatile tool in many different physical context, ranging from quantum dots [234–236], ultracold atoms [233], strongly correlated electrons [237], classical stochastic models [238, 239], quantum chromodynamics [232, 240], to quantum gravity [241].”
- An Asymptotically Safe Guide to Quantum Gravity and Matter (2018, neutral): “For general introductions and reviews (see Berges et al., 2002; Polonyi, 2003; Pawlowski, 2007; Rosten, 2010; Braun, 2012; Delamotte, 2012; Gies, 2012, for gravity, see Reuter and Saueressig, 2012; Nink et al., 2013; Ashtekar et al., 2014; Percacci, 2017; Eichhorn, 2018a).”
- Quartic AdS interactions in higher-spin gravity from Conformal Field Theory (2015, neutral): “[116]), but in higherspin literature, the term “perturbatively local” is also sometimes used (see e.”