Наукова електронна бібліотека
періодичних видань НАН України
періодичних видань НАН України
Natural and Projectively Invariant Quantizations on Supermanifolds
Репозиторій DSpace/Manakin
- Домашня сторінка
- →
- Фізико-технічні та математичні науки
- →
- Відділення математики
- →
- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
- →
- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
- →
- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7, випуск за цей рік
- →
- Переглянути статтю
JavaScript is disabled for your browser. Some features of this site may not work without it.
Natural and Projectively Invariant Quantizations on Supermanifolds
Інший ID:
2010 Mathematics Subject Classification: 53B05; 53B10; 53D50; 58A50
DOI:10.3842/SIGMA.2011.034
DOI:10.3842/SIGMA.2011.034
Посилання:
Natural and Projectively Invariant Quantizations on Supermanifolds / T. Leuther, F. Radoux // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 16 назв. — англ.
Підтримка:
It is a pleasure to thank P. Mathonet for fruitful discussions. We also thank the referees for
suggestions leading to great improvements of the original paper. Finally, F. Radoux thanks the Belgian FNRS for his research fellowship.
Дата:
2011
Переглядів:
665
Завантажень:
247
Анотація:
The existence of a natural and projectively invariant quantization in the sense of P. Lecomte [Progr. Theoret. Phys. Suppl. (2001), no. 144, 125-132] was proved by M. Bordemann [math.DG/0208171], using the framework of Thomas-Whitehead connections. We extend the problem to the context of supermanifolds and adapt M. Bordemann's method in order to solve it. The obtained quantization appears as the natural globalization of the pgl(n+1|m)-equivariant quantization on Rn|m constructed by P. Mathonet and F. Radoux in [arXiv:1003.3320]. Our quantization is also a prolongation to arbitrary degree symbols of the projectively invariant quantization constructed by J. George in [arXiv:0909.5419] for symbols of degree two.
