DOI: 10.1088/1751-8113/44/38/385402
8 citations
Abstract:

A general regularization/renormalization scheme based on intrinsic properties of quantum fields as Operator Valued Distributions with adequate test functions is presented. The paracompactness property of the Minkowskian or Euclidean manifolds permits a unique definition of fields through integrals over the manifold based on test functions which are partition of unity (PU). These test functions turn out to provide a direct Lorentz invariant scheme to the extension procedure of singular distributions and possess the unique property of being equal to their Taylor remainder of any order. When expressed through Lagrange's formulae this remainder leads to specific procedures of extension in the UV and IR domains. These results, directly obtainable at the physical dimension $D=4$, are found to depend on an arbitrary scale present in the definition of any PU test functions and relevant to the final RG-analysis of physical amplitudes. The method is of general character in that it comprises the well known symmetry preserving procedures of BPHZ, Pauli-Villars substractions at the level of propagators and dispersion relations. Symmetry preservation is indeed verified explicitely in simple QED/QCD gauge-boson contributions and in a Covariant Light-Front Dynamics treatment of the Yukawa model.

Ref HAL: in2p3-00538671_v1
Exporter : BibTex | endNote
Abstract:

The radiative corrections to the Higgs mass are calculated to the first loop order using both the usual sharp cut-off procedure and Taylor-Lagrange renormalization scheme (TLRS). Results appear to differ significantly. The TLRS results allow for a different interpretation of the Higgs renormalized mass. The fine tuning issue is discussed.

Ref HAL: in2p3-00515253_v1
Ref Arxiv: 1006.5282
DOI: 10.1103/PhysRevD.82.025012
Ref. & Cit.: NASA ADS
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6 citations
Abstract:

We show how the recently proposed Taylor-Lagrange renormalization scheme can lead to extensions of singular distributions which are reminiscent of the Pauli-Villars subtraction. However, at variance with the Pauli-Villars regularization scheme, no infinite mass limit is performed in this scheme. As an illustration of this mechanism, we consider the calculation of the self-energy in second order perturbation theory in the Yukawa model, within the covariant formulation of light-front dynamics. We show in particular how rotational invariance is preserved in this scheme.

Comments: 9 pages, 1 figure To be published in Physical Review D

Ref HAL: in2p3-00473563_v1
DOI: 10.1016/j.nuclphysbps.2010.02.027
Exporter : BibTex | endNote
Abstract:

The recently proposed renormalization scheme based on the definition of field operators as operator valued distributions acting on specific test functions is shown to be very convenient in explicit calculations of physical observables within the framework of light-front dynamics. We first recall the main properties of this procedure based on identities relating the test functions to their Taylor remainder of any order expressed in terms of Lagrange's formulae, hence the name given to this scheme. We thus show how it naturally applies to the calculation of state vectors of physical systems in the covariant formulation of light-front dynamics. As an example, we consider the case of the Yukawa model in the simple two-body Fock state truncation.

Ref HAL: in2p3-00417608_v1
Ref Arxiv: 0909.1715
DOI: 10.1103/PhysRevD.80.105012
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
12 citations
Abstract:

The recently proposed renormalization scheme based on the definition of field operators as operator valued distributions acting on specific test functions is shown to be very convenient in explicit calculations of physical observables within the framework of light-front dynamics. We first recall the main properties of this procedure based on identities relating the test functions to their Taylor remainder of any order expressed in terms of Lagrange's formulae, hence the name given to this scheme. We thus show how it naturally applies to the calculation of state vectors of physical systems in the covariant formulation of light-front dynamics. As an example, we consider the case of the Yukawa model in the simple two-body Fock state truncation.

Comments: 26 pages, 6 figures

Ref HAL: hal-00288727_v1
Exporter : BibTex | endNote
Abstract:

The photon propagator is built in the "usual" LC-gauges within the distributional approach with test functions for the gauge fields. It is shown that test functions provide a sound definition, as distributions, of singular terms in (1/n.k)p where n2=0. The relevance of these extensions is exemplified in a test case where an infinite re-summation in powers of 1/n.k leads to known exact results. The effect of residual gauge degrees of freedom on the presence of singular terms in the most general LC-propagator is discussed in the Dirac-Bergmann algorithm.

Ref HAL: hal-00288719_v1
Exporter : BibTex | endNote
Abstract:

We show how Causal Field Theory (CFT) can be transcribed from the conventional Minkowski formulation to the Light-Coneframework and how nonperturbative vacuum effects can be incorporated. The combination of the divergence free CFT with nonperturbative LC-physics opens a road to a mathematically sound renormalization of nonperturbative theories.