Cosmetic surgery in L–space homology spheres

Let K be a nontrivial knot in S^3, and let r and r′ be two distinct rational numbers of same sign. We prove that there is no orientation-preserving homeomorphism between the manifolds S_r^3(K) and S_r′^3(K). We further generalize this uniqueness result to knots in arbitrary L–space homology spheres

The Noncommutative Standard Model and Polarization in Charged Gauge Boson Production at the LHC

We study the pair production of charged gauge bosons at the LHC in a noncommutative extension of the standard model. We use angular distributions in the decays of the gauge bosons to partially reconstruct polarized cross sections. We use this, together with CP considerations, to construct more sensitive observables that allow to separate space-time from space-space noncommutativities.Comment: 13 pages, 8 figures; minor cosmetic change; clarifying remarks on our Feynman rules, add explicit calculation of Ward identities to appendi

Complex Moduli of Physical Quanta

Classical mechanics can be formulated using a symplectic structure on classical phase space, while quantum mechanics requires a complex-differentiable structure on that same space. Complex-differentiable structures on a given real manifold are often not unique. This letter is devoted to analysing the dependence of the notion of a quantum on the complex-differentiable structure chosen on classical phase space.Comment: Some minor cosmetic changes made and new refs. adde

Combinatorial quantisation of Euclidean gravity in three dimensions

In the Chern-Simons formulation of Einstein gravity in 2+1 dimensions the phase space of gravity is the moduli space of flat G-connections, where G is a typically non-compact Lie group which depends on the signature of space-time and the cosmological constant. For Euclidean signature and vanishing cosmological constant, G is the three-dimensional Euclidean group. For this case the Poisson structure of the moduli space is given explicitly in terms of a classical r-matrix. It is shown that the quantum R-matrix of the quantum double D(SU(2)) provides a quantisation of that Poisson structure.Comment: cosmetic chang

Dual Supersymmetry Algebras from Partial Supersymmetry Breaking

The partial breaking of supersymmetry in flat space can be accomplished using any one of three dual representations for the massive N=1 spin-3/2 multiplet. Each of the representations can be ``unHiggsed'', which gives rise to a set of dual N=2 supergravities and supersymmetry algebras.Comment: 12 pages, 1 figure, cosmetic change

Nonlinear Dirac operator and quaternionic analysis

Properties of the Cauchy-Riemann-Fueter equation for maps between quaternionic manifolds are studied. Spaces of solutions in case of maps from a K3-surface to the cotangent bundle of a complex projective space are computed. A relationship between harmonic spinors of a generalized nonlinear Dirac operator and solutions of the Cauchy-Riemann-Fueter equation are established.Comment: Cosmetic changes onl

The Rigged Hilbert Space of the Free Hamiltonian

We explicitly construct the Rigged Hilbert Space (RHS) of the free Hamiltonian $H_0$. The construction of the RHS of $H_0$ provides yet another opportunity to see that when continuous spectrum is present, the solutions of the Schrodinger equation lie in a RHS rather than just in a Hilbert space.Comment: 18 pages. Invited, refereed contribution to the Jaca proceedings; v2: minor, cosmetic change

B -> tau nu: Opening up the Charged Higgs Parameter Space with R-parity Violation

The theoretically clean channel B+ -> tau+ nu shows a close to 3sigma discrepancy between the Standard Model prediction and the data. This in turn puts a strong constraint on the parameter space of a two-Higgs doublet model, including R-parity conserving supersymmetry. The constraint is so strong that it almost smells of fine-tuning. We show how the parameter space opens up with the introduction of suitable R-parity violating interactions, and release the tension between data and theory.Comment: 9 pages, LaTeX, minor cosmetic changes, version accepted for Physics Letters