Renormalization in Minkowski space–time

The multiplicative and the functional renormalization group methods are applied for the four-dimensional scalar theory in Minkowski space–time. It is argued that the appropriate choice of the subtraction point is more important in Minkowski than in Euclidean space–time. The parameters of the cutoff theory, defined by a subtraction point in the quasi-particle domain, are complex due to the mass-shell contributions and the renormalization group flow becomes much more involved than its Euclidean counterpart.

A Supersymmetric Hierarchical Model for Weakly Disordered 3d Semimetals

In this paper, we study a hierarchical supersymmetric model for a class of gapless, three-dimensional, weakly disordered quantum systems, displaying pointlike Fermi surface and conical intersections of the energy bands in the absence of disorder. We use rigorous renormalization group methods and supersymmetry to compute the correlation functions of the system. We prove algebraic decay of the two-point correlation function, compatible with delocalization. A main technical ingredient is the multiscale analysis of massless bosonic Gaussian integrations with purely imaginary covariances, performed via iterative stationary phase expansions.

Large-x resummation of off-diagonal deep-inelastic parton scattering from d-dimensional refactorization

The off-diagonal parton-scattering channels g + γ* and q + ϕ* in deep-inelastic scattering are power-suppressed near threshold x → 1. We address the next-to-leading power (NLP) resummation of large double logarithms of 1 − x to all orders in the strong coupling, which are present even in the off-diagonal DGLAP splitting kernels. The appearance of divergent convolutions prevents the application of factorization methods known from leading power resummation. Employing d-dimensional consistency relations from requiring 1/ϵ pole cancellations in dimensional regularization between momentum regions, we show that the resummation of the off-diagonal parton-scattering channels at the leading logarithmic order can be bootstrapped from the recently conjectured exponentiation of NLP soft-quark Sudakov logarithms. In particular, we derive a result for the DGLAP kernel in terms of the series of Bernoulli numbers found previously by Vogt directly from algebraic all-order expressions. We identify the off-diagonal DGLAP splitting functions and soft-quark Sudakov logarithms as inherent two-scale quantities in the large-x limit. We use a refactorization of these scales and renormalization group methods inspired by soft-collinear effective theory to derive the conjectured soft-quark Sudakov exponentiation formula.

Solitons in the Peyrard–Bishop model of DNA and the Renormalization Group method

We investigate solitons in the Peyrard–Bishop model of a DNA molecule using Renormalization Group methods which provide a systematic way for perturbation analysis. Small amplitude expansion is carried out in both the continuous and discrete limits. We review exact solutions for the continuous model. Further, we discuss the reliability of the solitonic solutions and argue that the envelope should propagate with a group velocity, contrary to previous proposals.

Influence of exact Lorentz-violating mechanism on the critical exponents for massive q-deformed λϕ4 scalar field theory

We probe the influence of Lorentz-violating mechanism, treated exactly, on the radiative quantum corrections to critical exponents for massive [Formula: see text]-deformed O([Formula: see text]) [Formula: see text] scalar field theories. We attain that task by employing three distinct and independent field-theoretic renormalization group methods. Firstly, we compute the critical exponents up to the finite next-to-leading order for then generalizing the results for any loop level. We show that the [Formula: see text]-deformed critical exponents are insensible to the Lorentz symmetry breaking mechanism thus agreeing with the universality hypothesis.