Related papers: A note on regularization and renormalization
In this paper I argue that infinities in the classical computation theory such as the unsolvability of the Halting Problem can be addressed in the same way as Feynman divergences in Quantum Field Theory, and that meaningful versions of…
We give a new construction of symbols of the differential operators on the sections of a quantum line bundle $L$ over a Kaehler manifold $M$ using the natural contravariant connection on $L$. These symbols are the functions on the tangent…
Generalizing the algebra of motion-invariant differential operators on a symmetric space we study invariant operators on equivariant vector bundles. We show that the eigenequation is equivalent to the corresponding eigenequation with…
The necessity of renormalization arises from the infinite integrals which are caused by the discrepancy between the orders of differential and integral operators in the four dimensional QFTs. Therefore in view of the fact that finiteness…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
In this work we give a deformation theoretical approach to the problem of quantization. First the notion of a deformation of a noncommutative ringed space over a commutative locally ringed space is introduced within a language coming from…
We formulate the standard real-space renormalization group method in a way which takes into account the correlation between blocks. This is achieved in a dynamical way by means of operators which reflect the influence on a given block of…
Satisfiability is a classic problem in computational complexity theory, in which one wishes to determine whether an assignment of values to a collection of Boolean variables exists in which all of a collection of clauses composed of logical…
For a finite group $D$, we study categorical factorisation homology on oriented surfaces equipped with principal $D$-bundles, which `integrates' a (linear) balanced braided category $\mathcal{A}$ with $D$-action over those surfaces. For…
We study the dynamics of the renormalization operator for multimodal maps. In particular, we prove the exponential convergence of this operator for infinitely renormalizable maps with same bounded combinatorial type.
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…
We define and explore the notion of linear weightings for vector bundles, extending the recent work by Loizides and Meinrenken. We construct weighted normal bundles and deformation spaces in the category of vector bundles. We explain how a…
We present a categorical formulation of the Hamiltonian renormalisation programme for quantum field theories, establishing a systematic bridge between functional and lattice renormalisation. To this end, we introduce two categories, $Seq$…
We present the notion of a filtered bundle as a generalisation of a graded bundle. In particular, we weaken the necessity of the transformation laws for local coordinates to exactly respect the weight of the coordinates by allowing more…
This paper is the first of two papers constructing a calculus of pseudodifferential operators suitable for doing analysis on Q-rank 1 locally symmetric spaces and Riemannian manifolds generalizing these. This generalization is the interior…
In this note a general approach is suggested for comparison of operators. This is done by means of the Fourier transform of a measure. This approach is applied to comparison of approximation properties of various summability methods of the…
It is shown how nucleon-nucleon potentials can be defined in N dimensions, using dimensional regularization to continue amplitudes. This provides an easy way to separate out contact ($\delta$-function) terms arising from renormalization. An…
Results on derivations and automorphisms of some quantum and classical Poisson algebras, as well as characterizations of manifolds by the Lie structure of such algebras, are revisited and extended. We prove in particular somehow unexpected…
The renormalization group method is a successive integration over the fluctuations which are ordered according to their length scale, a parameter in the external space. A different procedure is described, where the fluctuations are treated…
We present a general analysis of the field theoretical properties which guarantee the recovery, at the renormalized level, of symmetries broken by regularization. We also discuss the anomalous case.