相关论文: Scaling Algebras and Renormalization Group in Alge…

We showed in part I (hep-th/9912092) that the Hopf algebra ${\cal H}$ of Feynman graphs in a given QFT is the algebra of coordinates on a complex infinite dimensional Lie group $G$ and that the renormalized theory is obtained from the…

We obtain the renormalization group(RG) functions for the $O(N)$ scalar field theory and the Higgs-Yukawa field theory with the Coleman-Weinberg mechanism in which the symmetry breaking occurs radiatively by using the method proposed…

The algebraic method of singular reduction is applied for non regular group action on manifolds which provides singular symplectic spaces. The problem of deformation quantization of the singular surfaces is the focus. For some examples of…

The Pauli--Villars regularization procedure confirms and sharpens the conclusions reached previously by covariant point splitting. The divergences in the stress tensor of a quantized scalar field interacting with a static scalar potential…

Quantization in the minisuperspace of non minimal scalar-tensor theories leads to a partial differential equation which is non separable. Through a conformal transformation we can recast the Wheeler-DeWitt equation in an integrable form,…

Based on the vanishing of the second Hochschild cohomology group of the enveloping algebra of the Heisenberg algebra it is shown that differential algebras coming from quantum groups do not provide a non-trivial deformation of quantum…

These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general…

The role of cut-off and dimensional regularizations is discussed in the context of obtaining a renormalized nucleon-nucleon potential from the chiral Lagrangian formulation of the effective field theory due to Weinberg. Both types of…

Planck-scale physics challenges the classical smooth-spacetime picture by introducing quantum fluctuations that imply a nontrivial spacetime microstructure. We present a framework that encodes these fluctuations by promoting local scale…

We present a scheme of biquaternionic algebrodymamics based on a nonlinear generalization of the Cauchy-Riemann holomorphy conditions considered therein as fundamental field equations. The automorphism group SO(3,C) of the biquaternion…

While the notion of open quantum systems is itself old, most of the existing studies deal with quantum mechanical systems rather than quantum field theories. After a brief review of field theoretical/path integral tools currently available…

We consider the group formed by finite renormalizations as an infinite-dimensional Lie group. It is demonstrated that for the finite renormalization of the gauge coupling constant its generators $\hat L_n$ with $n\ge 1$ satisfy the…

We extend the Wilson renormalization group (RG) to supersymmetric theories. As this regularization scheme preserves supersymmetry, we exploit the superspace technique. To set up the formalism we first derive the RG flow for the massless…

We establish the functional Renormalization Group as an exploratory tool to investigate a possible phase transition between a pre-geometric discrete phase and a geometric continuum phase in quantum gravity. In this paper, based on the…

Covariant, self-interacting scalar quantum field theories admit solutions for low enough spacetime dimensions, but when additional divergences appear in higher dimensions, the traditional approach leads to results, such as triviality, that…

There are reasons to believe that the Standard Model is only an effective theory, with new Physics lying beyond it. Supersymmetric extensions are one possibility: they address some of the Standard Model's shortcomings, such as the…

Starting from a local quantum field theory with an unbroken compact symmetry group $G$ in 1+1-dimensional spacetime we construct disorder fields implementing gauge transformations on the fields (order variables) localized in a wedge region.…

We investigate the nature of divergences in quantum field theory, showing that they are organized in the structure of a certain `` motivic Galois group'', which is uniquely determined and universal with respect to the set of physical…

We define the renormalization group flow for a renormalizable interacting quantum field in curved spacetime via its behavior under scaling of the spacetime metric, $\g \to \lambda^2 \g$. We consider explicitly the case of a scalar field,…

Scalar field theory at finite temperature is investigated via an improved renormalization group prescription which provides an effective resummation over all possible non-overlapping higher loop graphs. Explicit analyses for the lambda…