Euclidean Configuration Space Renormalization, Residues and Dilation Anomaly1
نویسندگان
چکیده
Configuration (x-)space renormalization of euclidean Feynman amplitudes in a massless quantum field theory is reduced to the study of local extensions of associate homogeneous distributions. Primitively divergent graphs are renormalized, in particular, by subtracting the residue of an analytically regularized expression. Examples are given of computing residues that involve zeta values. The renormalized Green functions are again associate homogeneous distributions of the same degree that transform under indecomposable representations of the dilation group. Invited lecture by I. Todorov at the 9. International Workshop Lie Theory and Its Applications in Physics (LT-9), Varna, Bulgaria, June 2011, and at the International Workshop ”Supersymmetries and Quantum Symmetries” (SQS’2011), Dubna, Russia, July 2011.
منابع مشابه
Euclidean Configuration Space Renormalization, Residues and Dilation Anomaly
Configuration (x-)space renormalization of euclidean Feynman amplitudes in a massless quantum field theory is reduced to the study of local extensions of associate homogeneous distributions. Primitively divergent graphs are renormalized, in particular, by subtracting the residue of an analytically regularized expression. Examples are given of computing residues that involve zeta values. The ren...
متن کاملTime-Dependent Real-Space Renormalization Group Method
In this paper, using the tight-binding model, we extend the real-space renormalization group method to time-dependent Hamiltonians. We drive the time-dependent recursion relations for the renormalized tight-binding Hamiltonian by decimating selective sites of lattice iteratively. The formalism is then used for the calculation of the local density of electronic states for a one dimensional quant...
متن کاملCohomological analysis of the Epstein-Glaser renormalization
A cohomological analysis of the renormalization freedom is performed in the Epstein-Glaser scheme on a flat Euclidean space. We study the deviation from commutativity between the renormalization and the action of all linear partial differential operators. It defines a natural Hochschild 1–cocycle and the renormalization ambiguity exactly corresponds to the cohomological class of this renormaliz...
متن کاملAxioms for Renormalization in Euclidean Quantum Field Theory
A set of axioms which fix Euclidean renormalizations up to a finite renormalization is proposed. There exists a one to one correspondence between Euclidean renormalizations and renormalizations in Minkowski space-time satisfying Hepp's axioms. No restrictions on masses are imposed.
متن کاملEuclidean spanners in high dimensions
A classical result in metric geometry asserts that any n-point metric admits a linear-size spanner of dilation O(log n) [PS89]. More generally, for any c > 1, any metric space admits a spanner of size O(n), and dilation at most c. This bound is tight assuming the well-known girth conjecture of Erdős [Erd63]. We show that for a metric induced by a set of n points in high-dimensional Euclidean sp...
متن کامل