Ref HAL: hal-00288714_v1
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Abstract:

Les champs quantiques sont construits comme des operateurs a valeurs de distributions sur des fonctions test partitions de l'unite. Cette construction conduit a un nouveau type de regularisation preservant la causalite et les symetries.L'application au modele a couplage lineaire boson-fermions (dit de Yukawa) est explicitee"

Ref HAL: hal-00117160_v1
Ref Arxiv: hep-th/0610048
DOI: 10.1142/S0217732308026510
Ref. & Cit.: NASA ADS
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2 citations
Abstract:

We give a simple derivation of the Higgs mechanism in an abelian light front field theory. It is based on a finite volume quantization with antiperiodic scalar fields and a periodic gauge field. An infinite set of degenerate vacua in the form of coherent states of the scalar field that minimize the light front energy, is constructed. The corresponding effective Hamiltonian descibes a massive vector field whose third component is generated by the would-be Goldstone boson. This mechanism, understood here quantum mechanically in the form analogous to the space-like quantization, is derived without gauge fixing as well as in the unitary and the light cone gauge.

Comments: 8 pages

Ref HAL: hal-00011228_v2
Ref Arxiv: math-ph/0510052
DOI: 10.1016/j.nuclphysbps.2006.08.008
Ref. & Cit.: NASA ADS
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13 citations
Abstract:

Following Epstein-Glaser's work we show how a QFT formulation based on operator valued distributions (OPVD) with adequate test functions treats original singularities of propagators on the diagonal in a mathematically rigourous way.Thereby UV and/or IR divergences are avoided at any stage, only a finite renormalization finally occurs at a point related to the arbitrary scale present in the test functions.Some well known UV cases are examplified.The power of the IR treatment is shown for the free massive scalar field theory developed in the (conventionally hopeless) mass perturbation expansion.It is argued that the approach should prove most useful for non pertubative methods where the usual determination of counterterms is elusive

Comments: 6 pages 2 columns per page

Ref HAL: hal-00002930_v2
Ref Arxiv: math-ph/0409068
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
Abstract:

The treatment of fields as operator valued distributions (OPVD) is recalled with the emphasis on the importance of causality following the work of Epstein and Glaser. Gauge invariant theories demand the extension of the usual translation operation on OPVD, thereby leading to a generalized $QED$ formulation. At D=2 the solvability of the Schwinger model is totally preserved. At D=4 the paracompactness property of the Euclidean manifold permits using test functions which are decomposition of unity and thereby provides a natural justification and extension of the non perturbative heat kernel method (Fujikawa) for abelian anomalies. On the Minkowski manifold the specific role of causality in the restauration of gauge invariance (and mass generation for $QED_{2}$) is examplified in a simple way.

Comments: soumis le 22/09/2004

Ref HAL: hal-00317518_v1
Ref Arxiv: math-ph/0409068
DOI: 10.1007/s00601-004-0085-8
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
4 citations
Abstract:

The treatment of fields as operator valued distributions (OPVD) is recalled with the emphasis on the importance of causality following the work of Epstein and Glaser. Gauge invariant theories demand the extension of the usual translation operation on OPVD, thereby leading to a generalized $QED$ formulation. At D=2 the solvability of the Schwinger model is totally preserved. At D=4 the paracompactness property of the Euclidean manifold permits using test functions which are decomposition of unity and thereby provides a natural justification and extension of the non perturbative heat kernel method (Fujikawa) for abelian anomalies. On the Minkowski manifold the specific role of causality in the restauration of gauge invariance (and mass generation for $QED_{2}$) is examplified in a simple way.

Ref HAL: hal-00317589_v1
Ref Arxiv: hep-th/0202081
DOI: 10.1103/PhysRevD.65.125014
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
13 citations
Abstract:

The dynamics of the phase transition of the continuum $\Phi ^{4}_{1+1}$-theory in Light Cone Quantization is reexamined taking into account fluctuations of the order parameter $< \Phi >$ in the form of dynamical zero mode operators (DZMO) which appear in a natural way via the Haag expansion of the field $\Phi (x)$ of the interacting theory. The inclusion of the DZM-sector changes significantly the value of the critical coupling, bringing it in agreement within 2% with the most recent Monte-Carlo and high temperature/strong coupling estimates. The critical slowing down of the DZMO governs the low momentum behavior of the dispersion relation through invariance of this DZMO under conformal transformations preserving the local light cone structure. The critical exponent $\eta$ characterising the scaling behaviour at $k^2 \to 0$ comes out in agreement with the known value 0.25 of the Ising universality class. $\eta$ is made of two contributions: one, analytic $(75 %$) and another (25%) which can be evaluated only numerically with an estimated error of 3%. The $\beta$-function is then found from the non-perturbative expression of the physical mass. It is non-analytic in the coupling constant with a critical exponent $\omega=2$. However, at D=2, $\omega$ is not parametrisation independent with respect to the space of coupling constants due to this strong non-analytic behaviour.

Ref HAL: hal-00268372_v1
Ref Arxiv: hep-th/0111186
DOI: 10.1016/S0920-5632(02)01330-0
Ref. & Cit.: NASA ADS
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1 citation
Abstract:

Critical behaviour of the 2D scalar field theory in the LC framework is reviewed. The notion of dynamical zero modes is introduced and shown to lead to a non trivial covariant dispersion relation only for Continuous LC Quantization (CLCQ). The critical exponent $\eta$ is found to be governed by the behaviour of the infinite volume limit under conformal transformations properties preserving the local LC structure. The $\beta$-function is calculated exactly and found non-analytic, with a critical exponent $\omega=2$, in agreement with the conformal field theory analysis of Calabrese et al.

Comments: 6 pages, 1 figure