We construct the complete SU(2) parity-violating (PV) π,N,∆ interaction Lagrangian with one derivative, and calculate the chiral corrections to the PV Yukawa NNπ coupling constant hπ through O(1/Λχ) in the leading order of heavy baryon expansion. We discuss the relationship between the renormalized hπ, the measured value of hπ, and the corresponding quantity calculated microscopically from the ...

The purpose of this paper is to introduce and study the notion of a vector-valued π-invariant mean associated to a unitary representation π of a locally compact groupG on S, a self-adjoint linear subspace containing I of B(Hπ). We obtain, among other results, an extension theorem for π-invariant completely positive maps and π-invariant means which characterizes amenability of G. We also study v...

We introduce the notion of rational Hopf algebras that we think are able to describe the superselection symmetries of two dimensional rational quantum field theories. As an example we show that a six dimensional rational Hopf algebra H can reproduce the fusion rules, the conformal weights, the quantum dimensions and the representation of the modular group of the chiral Ising model. H plays the ...

A wavelet, in the generalized sense, is a vector in the Hilbert space, Hπ , of a unitary representation, π, of a locally compact group, G, with the property that the wavelet transform it defines is an isometry of Hπ into L2(G). We study the image of this transform and how that image varies as the wavelet varies. We obtain a version of the Peter-Weyl Theorem for the class of groups for which the...

Two new strongly AEE active (I/I0 ≈ 94) tetraphenylsilole-containing cyclosiloxanes with cyan emissions (λem = 500 nm) and ∼100% solid state fluorescence quantum yields are reported. The intra- and intermolecular C-Hπ interactions in the crystal play a major role in the observed high solid state fluorescence quantum yields.

Let U(M) be the unitary group of a finite, injective von Neumann algebra M . We observe that any subrepresentation of a group representation into U(M) is amenable in the sense of Bekka; this yields short proofs of two known results—one by Robertson, one by Haagerup—concerning group representations into U(M). A unitary representation π of a group Γ on a Hilbert space Hπ is amenable if there exis...

We briefly describe a model for soft diffraction. The model description of ISR, Spp̄S and Tevatron data, and the predictions of the total, elastic, single and double diffractive cross sections at the LHC can be found in the original paper. Here we address issues raised at Diffraction 2000, in particular concerning the nature of the resulting Pomeron trajectory. †Based on a talk by M.G. Ryskin at...

In [1] we introduced the concept of restricted representations for an inverse semigroup S and studied the restricted forms of some important Banach algebras on S. In this paper, we continue our study by considering the relation between the restricted positive definite functions and retricted representations. In particular, we prove restricted versions of the Godement’s characterization of the p...

Let χ denote the space of all gai sequences and Λ the space of all analytic sequences. First we show that the set E = { s(k) : k = 1, 2, 3, · · · } is a determining set for χM . The set of all finite matrices transforming χM into FKspace Y denoted by (χM : Y ) . We characterize the classes (χM : Y ) when Y = (c0)π , cπ, χM , `π, `s,Λπ, hπ. In summary we have the following table: ↗ (c0)π cπ χM `...

this is true for indicator functions, since ∫ 1Adπ = π(A) = ∫ A hπ,μdμ by definition of the Radon-Nikodym derivative. Then by linearity of the integral, the claim is also true for simple functions. Then we can show the claim for non-negative measurable functions, by approximating by simple functions. Indeed, if f ≥ 0 is measurable, then there exists a sequence of simple functions 0 ≤ sn ↑ f suc...