相关论文: Properties of derivative expansion approximations …
We formulate a method of performing non-perturbative calculations in quantum field theory, based upon a derivative expansion of the exact renormalization group. We then proceed to apply this method to the calculation of critical exponents…
By writing the flow equations for the continuum Legendre effective action (a.k.a. Helmholtz free energy) with respect to a particular form of smooth cutoff, and performing a derivative expansion up to some maximum order, a set of…
These two lectures cover some of the advances that underpin recent progress in deriving continuum solutions from the exact renormalization group. We concentrate on concepts and on exact non-perturbative statements, but in the process will…
Equations related to the Polchinski version of the exact renormalisation group equations for scalar fields which extend the local potential approximation to first order in a derivative expansion, and which maintain reparameterisation…
We incorporate running parameters and anomalous dimensions into the framework of the exact renormalization group. We modify the exact renormalization group differential equations for a real scalar field theory, using the anomalous…
Direct verification of the existence of an infinite set of multicritical non-perturbative FPs (Fixed Points) for a single scalar field in two dimensions, is in practice well outside the capabilities of the present standard approximate…
Nonperturbative renormalization group techniques have recently proven a powerful tool to tackle the nontrivial infrared dynamics of light scalar fields in de Sitter space. In the present article, we develop the formalism beyond the local…
We investigate the renormalization of ``nonlocal" interactions which arise as an infinite sum of higher derivative interactions in an effective field theory. Using dimensional regularization with minimal subtraction in a general scalar…
The method of self-consistent expansions is a powerful tool for handling strong coupling problems that might otherwise be beyond the reach of perturbation theory, providing surprisingly accurate approximations even at low order. First…
The conventional absence of field renormalization in the local potential approximation (LPA) --implying a zero value of the critical exponent \eta -- is shown to be incompatible with the logic of the derivative expansion of the exact…
On the example of the three-dimensional Ising model, we show that nonperturbative renormalization group equations allow one to obtain very accurate critical exponents. Implementing the order $\partial^4$ of the derivative expansion leads to…
The functional flow equations for the Legendre effective action, with respect to changes in a smooth cutoff, are approximated by a derivative expansion; no other approximation is made. This results in a set of coupled non-linear…
A perturbative approach for non renormalizable theories is developed. It is shown that the introduction of an extra expansion parameter allows one to get rid of divergences and express physical quantities as series with finite coefficients.…
The perturbative evaluation of the effective action can be expanded in powers of derivatives of the external field. We apply the renormalization group equation to the term in the effective action that is second order in the derivatives of…
On the perturbatively non-renormalizable and non-perturbatively finite examples (delta-function type potential in non-relativistic quantum mechanics and the mathematical model of the propagator by Redmond and Uretsky in quantum field…
We give a review of the exact renormalization group (ERG) approach and illustrate its applications in scalar and fermionic theories. The derivative expansion and approximations based on the derivative expansion with further truncation in…
Renormalization procedure is generalized to be applicable for non renormalizable theories. It is shown that introduction of an extra expansion parameter allows to get rid of divergences and express physical quantities as series of finite…
We introduce an approach to compute the renormalisation group flow of relational observables in quantum gravity which evolve from their microscopic expressions towards the full quantum expectation value. This is achieved by using the…
We study the optimization of nonperturbative renormalization group equations truncated both in fields and derivatives. On the example of the Ising model in three dimensions, we show that the Principle of Minimal Sensitivity can be…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…