Dr. Marian Apostol (IFIN-HH), Curved Space, Covariance, Motion and Quantization

Wednesday 12 Dec 2007, 11:00 → 12:00 Europe/Bucharest

Weak forces and non-inertial motion are equivalent with the free motion in curved spaces. The "principle of equivalence" is applied to non-inertial motion. It may lead to a new stream of investigation in the field theory. Examples are given for translations and rotations and the Hamilton-Jacobi equation of classical free motion in curved spaces is reviewed. Motion depends on observer, and covariance may ensure a "universal subjectivity" (or "inter-subjectivity"). Motion as a coordinate transform, following Einstein's views, is analyzed. Its limits are emphasized. Classical motion is solved, with curved-space corrections arising from forces and non-inertial motion. The analogy with gravitation is everywhere discussed, but a larger vision is emphasized, regarding the equivalence of the non-inertial motion and curved spaecs. It is shown that quantization introduces a deep change. The quantum motion in curved space consists essentially of quantum transitions. The fields theory provides the suitable framework. Examples are given of such transitions for a scalar field and for photons. 1. Weak forces and non-inertial motion; 2.Curved space, free motion; 3. Translations and rotations; 4. Hamilton-Jacobi in curved space; 5. Quantization, Klein-Gordon, Dirac, etc; 6. Quantum transitions; 7. Scalar fields and photons