| Full text | |
| Author(s): |
Assirati, J. L. M.
;
Gitman, D. M.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | EUROPEAN PHYSICAL JOURNAL C; v. 77, n. 7 JUL 17 2017. |
| Web of Science Citations: | 2 |
| Abstract | |
We present covariant quantization rules for non-singular finite-dimensional classical theories with flat and curved configuration spaces. In the beginning, we construct a family of covariant quantizations in flat spaces and Cartesian coordinates. This family is parametrized by a function omega(theta), theta is an element of (1, 0), which describes an ambiguity of the quantization. We generalize this construction presenting covariant quantizations of theories with flat configuration spaces but already with arbitrary curvilinear coordinates. Then we construct a so-called minimal family of covariant quantizations for theories with curved configuration spaces. This family of quantizations is parametrized by the same function omega(theta). Finally, we describe a more wide family of covariant quantizations in curved spaces. This family is already parametrized by two functions, the previous one omega(theta) and by an additional function Theta(chi, xi). The above mentioned minimal family is a part at Theta = 1 of the wide family of quantizations. We study constructed quantizations in detail, proving their consistency and covariance. As a physical application, we consider a quantization of a non-relativistic particle moving in a curved space, discussing the problem of a quantum potential. Applying the covariant quantizations in flat spaces to an old problem of constructing quantum Hamiltonian in polar coordinates, we directly obtain a correct result. (AU) | |
| FAPESP's process: | 16/03319-6 - Non perturbative methods in quantum theory and QFT and their application to actual physical problems |
| Grantee: | Dmitri Maximovitch Guitman |
| Support Opportunities: | Research Projects - Thematic Grants |