Abstract:
The Generalized Chiral Perturbation Theory enlarges the framework of the standard $\chi$PT, relaxing certain assumptions which do not necessarily follow from QCD or from experiment, and which are crucial for the usual formulation of the low energy expansion. In this way, experimental tests of the foundations of the standard $\chi$PT become possible. Emphasis is put on physical aspects rather than on formal developements of G$\chi$PT.

Abstract:
The electromagnetic corrections to the low energy scattering amplitude involving charged pions only are investigated at leading and next-to-leading orders in the two-flavour chiral expansion. As an application, the corresponding variation in the strong $2S-2P$ level shift is evaluated. The relative variation is of the order of 5%.

Abstract:
Autophagy, the pathway whereby cell components are degraded by lysosomes, is involved in the cell response to environmental stresses, such as nutrient deprivation, hypoxia or exposition to chemotherapeutic agents. Under these conditions, which are reminiscent of certain phases of tumor development, autophagy either promotes cell survival or induces cell death. This strengthens the possibility that autophagy could be an important target in cancer therapy, as has been proposed. Here, we describe the regulation of survival and death by autophagy and apoptosis, especially in cultured breast cancer cells. In particular, we discuss whether autophagy represents an apoptosis-independent process and/or if they share common pathways. We believe that understanding in detail the molecular mechanisms that underlie the relationships between autophagy and apoptosis in breast cancer cells could improve the available treatments for this disease.

Abstract:
It is shown that in vector-like gauge theories, such as QCD, and in the limit of a large number of colours Nc, the ordering pattern of narrow vector and axial-vector states at low energies is correlated with the size of the possible local order parameters of chiral symmetry breaking. This has implications on the underlying dynamics of spontaneous chiral symmetry breaking in QCD, and also on possible values of the parameter S for oblique electroweak corrections, the analogue of the QCD low energy constant L10.

Abstract:
A model for planar phenomena introduced by Jackiw and Pi and described by a Lagrangian including a Chern-Simons term is considered. The associated equations of motion, among which a 2+1 gauged nonlinear Schr\"odinger equation, are rewritten into a gauge independent form involving the modulus of the matter field. Application of a Painlev\'e analysis, as adapted to partial differential equations by Weiss, Tabor and Carnevale, shows up resonance values that are all integer. However, compatibility conditions need be considered which cannot be satisfied consistently in general. Such a result suggests that the examined equations are not integrable, but provides tools for the investigation of the integrability of different reductions. This in particular puts forward the familiar integrable Liouville and 1+1 nonlinear Schr\"odinger equations.

Abstract:
We evaluate theoretical uncertainties to the method of Pais and Treiman to measure the $\pi\pi$ phase shifts in $K_{e4}$ decays. We find that they are very small, below $1\%$.

Abstract:
A method of indirect measurement of the light quark running mass $\hat{m} = (m_d + m_u)/2$ is elaborated in detail. It is based on measuring 1\%-level azimuthal angular asymmetries in the decay $\tau \rightarrow \nu_\tau + 3\pi$. The latter are then used in QCD sum rules to obtain experimental lower bounds for $\hat{m}$. For a sample of $2.5 \times 10^5$ $\tau \rightarrow \nu_\tau + 3\pi$ decays free of background, the resulting statistical error in the bound for $\hat{m}$ is estimated to be 1 MeV, i.e., comparable to the systematic error due to the use of QCD sum rules. Contribution to the Third Workshop on the $\tau$ Charm Factory 1-6 June 1993, Marbella, Spain.

Abstract:
The cross section for $\gamma\gamma\to\pi^0\pi^0$ and the pion polarizabilities are computed, within generalized chiral perturbation theory, in the full one loop approximation, {\it i.e.} up to and including order $O({p^5})$. The result depends on the parameter ${\alpha}_{\pi\pi}$ defining the tree level $\pi - \pi$ scattering amplitude and on an additional low energy constant. The latter is shown to be related by an exact sum-rule to the $e^+ e^-$ data. The parameter ${\alpha}_{\pi\pi}$ is related to the quark mass ratio $r = m_s /{\hat m}$ via the expansion of pseudoscalar meson masses. The generalized one loop $\gamma\gamma\to\pi^0\pi^0$ amplitude agrees with the experimental data in the threshold region provided $r= {m_s}/{\hat m}\lapprox 10$. Higher order corrections are estimated comparing our calculation with the dispersive approach.

Abstract:
It is shown that the K -> pi pi matrix elements of the four-quark operator Q_7, generated by the electroweak penguin-like diagrams of the Standard Model, can be calculated to first non-trivial order in the chiral expansion and in the 1/Nc expansion. Although the resulting B factors B_7^(1/2) and B_7^(3/2) are found to depend only logarithmically on the matching scale, mu, their actual numerical values turn out to be rather sensitive to the precise choice of mu in the GeV region. We compare our results to recent numerical evaluations from lattice-QCD and to other model estimates.