Complex Covariance

According to some generalized correspondence principle the classical limit of a non-Hermitian quantum theory describing quantum degrees of freedom is expected to be the well known classical mechanics of classical degrees of freedom in the complex phase space, i.e., some phase space spanned by complex-valued space and momentum coordinates. As special relativity was developed by Einstein merely for real-valued space-time and four-momentum, we will try to understand how special relativity and covariance can be extended to complex-valued space-time and four-momentum. Our considerations will lead us not only to some unconventional derivation of Lorentz transformations for complex-valued velocities, but also to the non-Hermitian Klein-Gordon and Dirac equations, which are to lay the foundations of a non-Hermitian quantum theory

Complex Covariance

According to some generalized correspondence principle the classical limit of a non-Hermitian quantum theory describing quantum degrees of freedom is expected to be the well known classical mechanics of classical degrees of freedom in the complex phase space, i.e., some phase space spanned by complex-valued space and momentum coordinates. As special relativity was developed by Einstein merely for real-valued space-time and four-momentum, we will try to understand how special relativity and covariance can be extended to complex-valued space-time and four-momentum. Our considerations will lead us not only to some unconventional derivation of Lorentz transformations for complex-valued velocities, but also to the non-Hermitian Klein-Gordon and Dirac equations, which are to lay the foundations of a non-Hermitian quantum theory

Pion and Kaon Masses and Pion Form Factors from Dynamical Chiral-Symmetry Breaking with Light Constituent Quarks

Light constituent quark masses and the corresponding dynamical quark masses are determined by data, the quark-level linear sigma model, and infrared QCD. This allows to define effective nonstrange and strange current quark masses, which reproduce the experimental pion and kaon masses very accurately, by simple additivity. In contrast, the usual nonstrange and strange current quarks employed by the Particle Data Group and Chiral Perturbation Theory do not allow a straightforward quantitative explanation of the pion and kaon masses.Comment: 4 pages, AIP style, contribution to conference ``Quark Confinement and the Hadron Spectrum VII'', Azores, Portugal, 2-7 September 200

Complex Meson Spectroscopy

We do meson spectroscopy by studying the behavior of S-matrix poles in the complex-energy plane, as a function of the coupling strength for triplet-P-zero quark-pair creation. Thereto, a general formula for non-exotic hadron-hadron scattering involving arbitrary quark confinement is used, which can be applied to all flavors. We find two distinct types of poles, which we call "confinement" and "continuum" poles, respectively. Together, they suffice to understand the experimental meson spectrum.Comment: talk "http://www.cbpf.br/~hadron05/talks/quinta/plenarias/beveren/start.htm", prepared for the XI International Conference on Hadron Spectroscopy (Hadron05). 10 pages, 15 figure

On the Dynamical Generation of Quark-Level-Linear-Sigma-Model-like Theories beyond one Loop

A self-consistent strategy to complete the dynamical generation of Quark-Level-Linear-Sigma-Model-like Lagrangean theories beyond one loop as proposed in more detail in our manuscript arXiv:0802.1540 [hep-ph] is shortly outlined.Comment: 4 pages, 4 figures; manuscript to be published in the proceedings of the workshop "Scalar Mesons and Related Topics" (Scadron70), February 11-16,2008, at the IST, Lisbon, Portugal, honoring M.D. Scadron's 70th birthday on February 12, 200