Long distance effects and CP violation inB ±→ρ ± γ

We demonstrate that the long distance contribution toB ^±→ρ ^± γ may have a large effect on the decay rate and through it on the CP violating partial rate asymmetry. The change in the asymmetry can be between a factor of 0.4 and 1.4 with respect to the effect of the short distance contribution alone, depending on the values of the CKM parametersρ andη.     

A new theory of elementary matter part III: A self-consistent field theory of electrodynamics and correspondence with quantum mechanics

This paper exploits the axioms and general mathematical structure of a new theory of elementary matter, thus far developed in two earlier papers (Sachs, 1971b, c). It is shown here, in an explicit fashion, how the exact form of this theory approaches that of quantum mechanics of a many-particle system that interacts electromagnetically. The form of the mathematical expression of quantum mechanics of a many-particle system is found to be a linear approximation for the nonlinear (deterministic) field theory of this author's approach. The latter approximation is valid only when the components of the (asserted) closed system are sufficiently weakly coupled so that it appears as a many-particle system. The physical equivalent of the Pauli exclusion principle is derived in this paper as anexact feature of the theory, which is, in fact, sensitive to its closed and nonlinear features. It is then shown how the Fermi-Dirac statistics in particle physics follows from the present nonlinear theory only in a linear approximation.     

A new theory of elementary matter Part IV: Two-particle systems: The particle-antiparticle pair and hydrogen

The general theory developed thus far (Sachs, 1971b, c, d) is applied to two-particle systems. An exact bound state solution of the nonlinear field equations of this theory for a particle-antiparticle pair is demonstrated. From the Lagrangian formalism, this solution is shown to predict all of the experimental facts that are conventionally interpreted in terms of pair annihilation: (1) the energy-momentum four-vector (and each of the four components, separately) are zero, compared with the energy, 2mc ², of the state when the particle and antiparticle are (asymptotically) free and (2) the dynamical properties of this state of positronium make it appear in experimentation as two distinguishable currents, correlated with a 90° phase difference and polarised in a plane that is perpendicular to the direction of propagation of interaction with other charged matter. The latter features are conventionally interpreted as the two photons which are produced in the annihilation event — however, there are no photons in this theory. The spectral distribution of blackbody radiation is then derived from the properties of an ideal gas of such pairs, in their ground states of null energy-momentum, as observed in a finite cavity.The properties of theclosed electron-proton system are considered and the entire hydrogen spectrum is derived — including the Lamb splitting. The correct lifetimes of the excited hydrogenic states are then derived by considering the radiating hydrogen gas to be immersed in the ideal gas of pairs, that explained blackbody radiation.     

Ultrametric subsets with large Hausdorff dimension

It is shown that for every ε∈(0,1), every compact metric space (X,d) has a compact subset S?X that embeds into an ultrametric space with distortion O(1/ε), and $$\dim_H(S)\geqslant (1-\varepsilon)\dim_H(X),$$ where dim _H (?) denotes Hausdorff dimension. The above O(1/ε) distortion estimate is shown to be sharp via a construction based on sequences of expander graphs.     

Negative-energy spinors and the Fock space of lattice fermions at finite chemical potential

Recently it was suggested that the problem of species doubling with Kogut-Susskind lattice fermions entails, at finite chemical potential, a confusion of particles with antiparticles. What happens instead is that the familiar correspondence of positive-energy spinors to particles, and of negative-energy spinors to antiparticles, ceases to hold for the Kogut-Susskind time derivative. To show this we highlight the role of the spinorial “energy” in the Osterwalder-Schrader reconstruction of the Fock space of non-interacting lattice fermions at zero temperature and nonzero chemical potential. We consider Kogut-Susskind fermions and, for comparison, fermions with an asymmetric one-step time derivative.     

π-Orbital electron–energy contributions to chemical reaction heats,I. Reactions involving only linear molecules containing up to three first–row atoms

Ab initio calculations of various expectation energies have been made for the reactant and product species in six reactions that involve only small linear molecules. The reactions include fission by hydrogen, addition of hydrogen, exchange of triply bonded atoms, fluorination, and oxygen atom transfer. The change in total electronic energy is not invariably the result of changes in inner shell energy and outer shell σ- and π-electron energies simply augmenting each other, but in several cases there is a complex interplay of opposing effects. This approach gives a different insight into the energetic aspects of changes in bonding from that derived from the concept of shared electron pairs in σ and π bonds together with lone pairs in valence shells. Changes in π-electron energy are shown to be important in a reaction in which neither reactant nor product molecules contain π bonds in the usual chemical sense. While in a reaction in which there is a complete change in the nature of the triple bonds, and hence the π bonding, the change in π-electron energy makes a smaller contribution than either the change in inner shell or the outer shell σ-electron energies.