International Journal of Modern Physics A

A review of the present experimental status of the rates and the Dalitz-plot slope parameters in CP conserving K→2π and K→3π decays is given. The corresponding isospin amplitudes have been determined by a common fit to the recent experimental data and have been used as an input to a consequent fit based on the constraints from O(p⁴) chiral Lagrangian. It has been found that the constraints of the chiral fit are well satisfied by the experimental data, allowing one to estimate the weak coupling constants and to predict the quadratic amplitudes in K→3π decays and the one-loop strong rescattering phases. The consistency of the obtained weak coupling constants with weak resonance models has also been considered.

I study indirect CP violation for neutral kaons, and extend it to large values of the CP-violating parameter (taken to be real). I show how and at which condition there can exist a continuous set of basis in which the kinetic and mass terms in the Lagrangian can be diagonalized simultaneously. An ambiguity results for the mass spectrum, which then depends on the basis. In particular, for fixed (positive) (mass)² of the CP eigenstates , and for certain ranges of values of the CP-violating parameter, a negative (mass)² can arise in the CP-violating basis. Under certain conditions, even a small perturbation, lifting the ambiguity, can drastically affect the pattern of masses.

These investigations extend in a natural way to indirect CP violation among a set of Higgs-like doublets.

The C-odd commutator , or its equivalent for Higgs multiplets, plays an important role. The condition for its vanishing and its consequences are among the main concerns of this work.

In the orientiworld framework the Standard Model fields are localized on D3-branes sitting on top of an orientifold three-plane. The transverse six-dimensional space is a noncompact orbifold (or a more general conifold). The four-dimensional gravity on D3-branes is reproduced due to the four-dimensional Einstein–Hilbert term induced at the quantum level. The orientifold three-plane plays a crucial role, in particular, without it the D3-brane world-volume theories would be conformal due to the tadpole cancellation. We study nonperturbative gauge dynamics in various supersymmetric orientiworld models based on the Z₃ as well as Z₅ and Z₇ orbifold groups. Our discussions illustrate that there is a rich variety of supersymmetry preserving dynamics in some of these models. On the other hand, we also find some models with dynamical supersymmetry breaking.

Recently the operator algebra and twisted vertex operator equations were given for each sector of all WZW orbifolds, and a set of twisted KZ equations for the WZW permutation orbifolds were worked out as a large example. In this companion paper we report two further large examples of this development. In the first example we solve the twisted vertex operator equations in an Abelian limit to obtain the twisted vertex operators and correlators of a large class of Abelian orbifolds. In the second example, the twisted vertex operator equations are applied to obtain a set of twisted KZ equations for the (outer-automorphic) charge conjugation orbifold on .

The differential cross-sections for scattering of gravitons into photons on bosons and fermions are calculated in linearized quantum gravity. They are found to be strongly peaked in the forward direction and become constant at high energies. Numerically, they are very small as expected for such gravitational interactions.

The demonstration that the electromagnetic fields derived from the Liénard–Wiechert potentials do not satisfy the Maxwell equations is proved to be false. Errors were made in the computation of the derivatives of retarded quantities. The subsequent inference of the necessity of both instantaneous and retarded electromagnetic interactions cannot be made. Different choices of gauge can lead to a variety of forms for the scalar and vector potentials, always with the same retarded fields. Classical electromagnetic theory is complete as usually expressed. One may choose to work in the Lorentz gauge in which all quantities are retarded.