arXiv subjects

Guy Bonneau

Publications and source records attributed to Guy Bonneau.

13 recordsLinked to original sources

arXiv2006

Extended QED with CPT violation : clarifying some controversies

We rediscuss the controversy on a possible Chern-Simons like term generated through radiative corrections in QED with a CPT violating term. We analyse some consequences of the division of the Lagrangian density between "free part" and "interaction part". We also emphasize the fact that any absence of an {\sl a priori} divergence should be explained by some symmetry or some non-renormalisation theorem and show that the so-called "unambiguous result" based upon "maximal SO(3) residual symmetry " does not offer a solution.

hep-th↗

arXiv2001

Lorentz and CPT violations in QED : a short comment on recent controversies

We rediscuss the recent controversy on a possible Chern-Simons like term generated through radiative corrections in QED with a CPT violating term. We emphasize the fact that any absence of an {\sl a priori} divergence should be explained by some symmetry or some non-renormalisation theorem : otherwise, no prediction can be made on the corresponding quantity.

hep-th↗

arXiv2001

Self-adjoint extensions of operators and the teaching of quantum mechanics

For the example of the infinitely deep well potential, we point out some paradoxes which are solved by a careful analysis of what is a truly self-adjoint operator. We then describe the self-adjoint extensions and their spectra for the momentum and the Hamiltonian operators in different physical situations. Some consequences are worked out, which could lead to experimental checks.

quant-ph↗

arXiv2000

Cohomogeneity-one Einstein-Weyl structures : a local approach

We analyse in a systematic way the (non-)compact n-dimensional Einstein Weyl spaces equipped with a cohomogeneity-one metric. With no compactness hypothesis, we prove that, as soon as the (n-1)-dimensional space is an homogeneous reductive Riemannian space with an unimodular group of left-acting isometries G 1)a non-exact Einstein-Weyl stucture may exist only if the (n-1)-dimensional homogeneous space G/H contains a non trivial subgroup H' that commutes with the isotropy subgroup H, 2) the extra isometry due to this Killing vector corresponds to the right-action of one of the generators of the algebra of the subgroup H'. We also prove that the subclass with a one-dimensional subgroup H' corresponds to n-dimensional Riemannian locally conformally Kähler metrics, the (n-2)-dimensional space G/(HxH') being an arbitrary compact symmetric Kähler coset space.

gr-qc↗

arXiv2000

Regularisation : many recipes, but a unique principle : Ward identities and Normalisation conditions. The case of CPT violation in QED

We analyse the recent controversy on a possible Chern-Simons like term generated through radiative corrections in QED with a CPT violating term : we prove that, if the theory is correctly defined through Ward identities and normalisation conditions, no Chern-Simons term appears, without any ambiguity. This is related to the fact that such a term is a kind of minor modification of the gauge fixing term, and then no renormalised. The past year literature on that subject is discussed, and we insist on the fact that any absence of an {\sl a priori} divergence should be explained by some symmetry or some non-renormalisation theorem.

hep-th↗

arXiv1999

Non linear $σ$ models : renormalisability versus geometry

After some recalls on the standard (non)-linear $σ$ model, we discuss the interest of B.R.S. symmetry in non-linear $σ$ models renormalisation. We also emphasise the importance of a correct definition of a theory through physical constraints rather than as given by a particular Lagrangian and discuss some ways to enlarge the notion of renormalisability.

hep-th↗

arXiv1998

Compact Einstein-Weyl four-dimensional manifolds

We look for four dimensional Einstein-Weyl spaces equipped with a regular Bianchi metric. Using the explicit 4-parameters expression of the distance obtained in a previous work for non-conformally-Einstein Einstein-Weyl structures, we show that only four 1-parameter families of regular metrics exist on orientable manifolds : they are all of Bianchi $IX$ type and conformally Kähler ; moreover, in agreement with general results, they have a positive definite conformal scalar curvature. In a Gauduchon's gauge, they are compact and we obtain their topological invariants. Finally, we compare our results to the general analyses of Madsen, Pedersen, Poon and Swann : our simpler parametrisation allows us to correct some of their assertions.

gr-qc↗

arXiv1998

Einstein-Weyl structures and Bianchi metrics

We analyse in a systematic way the (non-)compact four dimensional Einstein-Weyl spaces equipped with a Bianchi metric. We show that Einstein-Weyl structures with a Class A Bianchi metric have a conformal scalar curvature of constant sign on the manifold. Moreover, we prove that most of them are conformally Einstein or conformally Kähler ; in the non-exact Einstein-Weyl case with a Bianchi metric of the type $VII_0, VIII$ or $IX$, we show that the distance may be taken in a diagonal form and we obtain its explicit 4-parameters expression. This extends our previous analysis, limited to the diagonal, Kähler Bianchi $IX$ case.

gr-qc↗

arXiv1997

Einstein-Weyl structures corresponding to diagonal Kähler Bianchi IX metrics

We analyse in a systematic way the four dimensionnal Einstein-Weyl spaces equipped with a diagonal Kähler Bianchi IX metric. In particular, we show that the subclass of Einstein-Weyl structures with a constant conformal scalar curvature is the one with a conformally scalar flat - but not necessarily scalar flat - metric ; we exhibit its 3-parameter distance and Weyl one-form. This extends previous analysis of Pedersen, Swann and Madsen , limited to the scalar flat, antiself-dual case. We also check that, in agreement with a theorem of Derdzinski, the most general conformally Einstein metric in the family of biaxial Kähler Bianchi IX metrics is an extremal metric of Calabi, conformal to Carter's metric, thanks to Chave and Valent's results.

hep-th↗

arXiv1994

On a possible breaking of global N=2 supersymmetry in non-linear $\si$ models on compact Kähler target spaces

We analyse with the algebraic, regularisation independent, cohomological B.R.S. methods, the renormalisability of torsionless N=2 supersymmetric non-linear $\si$ models built on compact Kähler spaces. Surprisingly enough with respect to the common wisdom, we obtain an anomaly candidate, when the Hodge number $h^{3,0}$ of the target space manifold is different from zero : this occurs in particular in the Calabi-Yau case. On the contrary, in the compact homogeneous Kähler case, the anomaly candidate disappears.

hep-th↗

arXiv1994

B.R.S. renormalisation of some on-shell closed algebras of symmetry transformations : the example of supersymmetric non-linear sigma models : the N=1 case

In order to study in a regularisation free manner the renormalisability of d=2 supersymmetric non-linear $\si$ models, one has to use the algebraic BRS methods ; moreover, in the absence of an off-shell formulation, one has often to deal with open algebras. We then recall in a pedagogical and non technical manner the standard methods used to handle these questions and illustrate them on N=1 supersymmetric non-linear $\si$ model in component fields, giving the first rigorous proof of their renormalisability. In the special case of compact homogeneous manifolds (non-linear $\si$ model on a coset space G/H), we obtain the supersymmetric extension of the analysis done some years ago in the bosonic case. A further publication will be devoted to extended supersymmetry.

hep-th↗

arXiv1994

B.R.S. renormalisation of some on-shell closed algebras of symmetry transformations : N=2 and 4 supersymmetric non-linear sigma models

We analyse with the algebraic, regularisation independant, cohomological B.R.S. methods, the renormalisability of torsionless N=2 and N= 4 supersymmetric non-linear $\si$ models built on Kähler spaces. Surprisingly enough with respect to the common wisdom, in the case of N=2 supersymmetry, we obtain an anomaly candidate, at least in the compact Kähler Ricci-flat case. If its coefficient does differ from zero, such anomaly would imply the breaking of global N=2 supersymmetry and get into trouble some schemes of superstring compactification as such non-linear $\si$ models offer candidates for the superstring vacuum state. In the compact homogeneous Kähler case, as expected, the anomaly candidate disappears. The same phenomena occurs when one enforces N=4 supersymmetry : in that case, we obtain the first rigorous proof of the expected all-orders renormalisability -`` in the space of metrics"- of the corresponding non-linear $\si$ models. PAR/LPTHE/94-11

hep-th↗

arXiv1994

Anomalies in N=2 supersymmetric non-linear sigma models on compact Kahler Ricci-flat target spaces

We analyse with the algebraic, regularisation independent, cohomological B.R.S. methods, the renormalisability of torsionless N=2 supersymmetric non-linear sigma models built on Kahler spaces. Surprisingly enough with respect to the common wisdom, we obtain an anomaly candidate, at least in the compact Ricci-flat case. In the compact homogeneous Kahler case, as expected, the anomaly candidate disappears.

hep-th↗