No abstract available

[en] We discuss the correct criteria for determining whether or not a gauge hierarchy exists. We apply these criteria to the O(3) model, both at the tree level and at the one-loop level, and find conditions under which an arbitrary gauge hierarchy can occur. We find that if a large gauge hierarchy can occur, its existence depends on the choice of renormalization point. We compare our results with other approaches to this question. (orig.)

[en] Shift operators are constructed in product form for the Lie algebra O(p,q). Their normalization is found and they are used to construct discrete series representations of the algebra. Certain other representations are also constructed for the case q = 1

[en] A discussion of the constraints on superfield covariant derivatives in global and local O(1) and O(2) supersymmetry is presented. (Auth.)

No abstract available

[en] In this paper, we explore the relationship between integrability and the discrete holomorphicity of a class of complex lattice observables in the context of the Potts dense loop model and the O(n) dilute loop model. It is shown that the conditions for integrability, namely, the inversion and Yang–Baxter relations, can be derived from the condition of holomorphicity of the observables. Furthermore, the Z-invariance of the models is shown to result in the invariance of the observables on the boundary of a sublattice under reshuffling of the rhombuses of its planar rhombic embedding. (paper)

[en] The quantum-mechanical properties of the recently developed supergravity theory are studied. The supergravity theory is first analyzed canonically to isolate the dynamical variables of the model. The action is split into space-plus-time form, and the differential constraints are exhibited. The theory is then formally quantized in terms of the implicitly reduced set of unconstrained dynamical variables. Once a formal quantized procedure is established (either canonical or the manifestly covariant path-integral method), the question of divergences is addressed. With the results from the quantization of other gauge field theories as a guide, it is assumed that, once an appropriate locally supersymmetric regularization scheme is found, the local divergences will themselves be locally supersymmetric. On the basis of this assumption, possible locally supersymmetric counterterms are sought; it is found that, to the one and two loop orders for both pure and extended supergravity, the divergent local counterterms are proportional to field equations. They can therefore be removed by a higher-derivative field redefinition. At three loops it is found, both for pure and O(2) extended supergravity models, that there exists a nonvanishing (on shell) counterterm that would not allow the field redefinition to render the theory predictive. Thus, supergravity is nonrenormalizable at three loops. A possible way to find a renormalizable theory by means of restrictive symmetry groups is suggested. Alternatively, one might abandon renormalizability in favor of asymptotic safety, since with present methods a renormalizable theory of quantum gravity is still lacking

No abstract available

[en] We derive model-independent bounds on production and detection non-standard neutrino interactions (NSI). We find that the constraints for NSI parameters are around O(10^-2) to O(10^-1). Furthermore, we review and update the constraints on matter NSI. We conclude that the bounds on production and detection NSI are generally one order of magnitude stronger than their matter counterparts.

[en] The group 0(3) LAMBDA (T₂ x anti T₂) in which the generators additional to those of 0(3) form a reducible tensor representation of 0(3), [T(¹/₂ +- ¹/₂), anti T(¹/₂ +- ¹/₂)] is considered. The states correspond to Stark or parabolic states of the hydrogen atom. 36 references