Full text
| |
| Author(s): |
Tiago Carlos Adorno de Freitas
Total Authors: 1
|
| Document type: | Doctoral Thesis |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Instituto de Física (IF/SBI) |
| Defense date: | 2013-01-14 |
| Examining board members: |
Dmitri Maximovitch Guitman;
Josif Frenkel;
José Abdalla Helayël Neto;
Jorge Jose Leite Noronha Junior;
Jeferson de Lima Tomazelli
|
| Advisor: | Dmitri Maximovitch Guitman |
| Abstract | |
The present PhD thesis refers to problems in field theory and quantum mechanics in noncommutative (NC) space. We study some well known physical systems in theoretical physics, such as the Maxwell theory in the presence of external sources, the Pauli equation, the Dirac equation with external fields and the relativistic Hydrogen atom. First we study the U(1)* gauge theory and extend the Seiberg-Witten map to include an external current and formulate classical field equations in NC space. Solutions in the vacuum and in an external magnetic field for a static charge of finite size a is determined. We find that a static charge in NC space, besides being an electric monopole, behaves as a magnetic dipole and the external magnetic field modifies the Coulomb law at large distances, as well as some electromagnetic form factors. In this direction we analyse the arbitrariness in the Seiberg-Witten map and show that, at least to the order studied here, this is equivalent to adding a homogeneous solution to the charge conservation condition. Demanding that the NC magnetic moment be less than the existing error in the measurement of leptons magnetic moment we obtain an upper bound for the NC parameter and its associated fundamental length l. In addition we consider the energy levels of a hydrogen-like atom in the framework of a -modified, due to space noncommutativity, Dirac equation with a Coulomb field. It is shown that the noncommutativity completely breaks the degeneracy of the 2S1/2; 2P1/2 and 2P3/2 levels, allowing for new transition channels. At last, but not least, we construct a nonrelativistic wave equation for spin 1/2 particles through the nonrelativistic limit of the NC Dirac equation. We present a pseudoclassical model (à-la Berezin-Marinov) whose quantization coincides with the nonrelativistic wave equations. By extracting the interaction between a nonrelativistic spin and the magnetic field, from the obtained Pauli equation in NC space, we construct a generalization of the Heisenberg model for two coupled spins in NC space. In such model, it is calculated the transition probability amplitude between two orthogonal EPR (Einstein-Podolsky-Rosen) states submitted in the presence of an oscilatory magnetic field and we shown that some of such transitions, which are forbidden in NC space are possible due to space noncommutativity. (AU) | |