Challenges in Hadron Physics

In this talk, I address some open problems in hadron physics and stress their importance for a better understanding of QCD in the confinement regime.Comment: Outlook talk at MESON 2004, Krakow, Poland, June 4-8, 2004, typos correcte

Reply on the ``Comment on `Loss-error compensation in quantum- state measurements' ''

The authors of the Comment [G. M. D'Ariano and C. Macchiavello to be published in Phys. Rev. A, quant-ph/9701009] tried to reestablish a 0.5 efficiency bound for loss compensation in optical homodyne tomography. In our reply we demonstrate that neither does such a rigorous bound exist nor is the bound required for ruling out the state reconstruction of an individual system [G. M. D'Ariano and H. P. Yuen, Phys. Rev. Lett. 76, 2832 (1996)].Comment: LaTex, 2 pages, 1 Figure; to be published in Physical Review

Perfect 3-Dimensional Lattice Actions for 4-Dimensional Quantum Field Theories at Finite Temperature

We propose a two-step procedure to study the order of phase transitions at finite temperature in electroweak theory and in simplified models thereof. In a first step a coarse grained free energy is computed by perturbative methods. It is obtained in the form of a 3-dimensional perfect lattice action by a block spin transformation. It has finite temperature dependent coefficients. In this way the UV-problem and the infrared problem is separated in a clean way. In the second step the effective 3-dimensional lattice theory is treated in a nonperturbative way, either by the Feynman-Bogoliubov method (solution of a gap equation), by real space renormalization group methods, or by computer simulations. In this paper we outline the principles for $\varphi ^4$-theory and scalar electrodynamics. The Ba{\l}aban-Jaffe block spin transformation for the gauge field is used. It is known how to extend this transformation to the nonabelian case, but this will not be discussed here.Comment: path to figures (in added uu-file) revised, no other changes 33 pages, 3 figures, late

On everywhere divergence of the strong Φ\Phi-means of Walsh-Fourier series

Almost everywhere strong exponential summability of Fourier series in Walsh and trigonometric systems established by Rodin in 1990. We prove, that if the growth of a function $\Phi(t):[0,\infty)\to[0,\infty)$ is bigger than the exponent, then the strong $\Phi$-summability of a Walsh-Fourier series can fail everywhere. The analogous theorem for trigonometric system was proved before by one of the author of this paper.Comment: 8 page