Construction of the Noncommutative Complex Ball

Abstract

We describe the construction of the noncommutative complex ball whose commutative analog is the Hermitian symmetric space $D=SU(m,1)/U(m)$, with the method of coherent state quantization. In the commutative limit we obtain the standard manifold. We consider also a quantum field theory model on the noncommutative manifold.

26 pages, section 4 and section 5 have been rewritten. Typos corrected. Title changed. Accepted for publication by Journal of Mathematical Physics. arXiv admin note: text overlap with arXiv:1005.5723

References in corpus (3)

• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Self-dual noncommutative ϕ^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory
• Quantum Field Theory on quantized Bergman domain