168 research outputs found
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 K\"ahler 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 K\"ahler 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 K\"ahler 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/94-11Comment: 22 pages, latex, PAR/LPTHE/94-1
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.Comment: 7 pages, LaTex file, 2 references adde
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.Comment: 14 pages, Latex fil
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.Comment: 25 pages, Latex file, extended version of Am. J. Phys. 69 (2001) 32
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.Comment: 11 pages, latex, PAR/LPTHE/94-0
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 K\"ahler ; in the non-exact Einstein-Weyl
case with a Bianchi metric of the type or , 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, K\"ahler Bianchi case.Comment: Latex file, 12 pages, a minor modification, accepted for publication
in Class. Quant. Gra
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