General concept of quantization

Berezin, F. A.

doi:10.1007/bf01609397

Cited by 783 publications

(776 citation statements)

References 3 publications

Supporting

Mentioning

757

Contrasting

Unclassified

Order By: Relevance

“…We define a noncommutative field theory using the Berezin product [18] and its generalization to deformation quantization [19,20] and construct static solutions of the theory.…”

Section: Jhep03(2002)011mentioning

confidence: 99%

“…In this section we briefly review Berezin's approach [18] to the quantization of Kähler manifolds using generalized coherent states and its generalization to deformation quantization [19,20]. 3 Let us recall the problem of quantization of a Poisson manifold M. Let A be the Lie algebra of smooth functions on M with the Poisson bracket…”

Section: Quantization Of Kähler Manifoldsmentioning

confidence: 99%

“…Berezin's approach to geometric quantization [18] is based on the use of generalized coherent states (see [24] for a review on coherent states) and will be well-suited to the study of noncommutative solitons. His construction is also local, and therefore best suited for manifolds for which there is an open dense subset which can be covered with a single chart.…”

Section: Jhep03(2002)011mentioning

confidence: 99%

“…Berezin was only able to prove that his quantization procedure satisfies the correspondence principle (2.2) under very restrictive assumptions on the geometry of M [18]. This quantization works for the case when M is a homogeneous Kähler manifold and L is a homogeneous bundle (later it was generalized to generalized flag varieties [28]).…”

Section: Jhep03(2002)011mentioning

confidence: 99%

See 3 more Smart Citations

Noncommutative solitons on Kahler manifolds

Spradlin¹,

Volovich²

2002

J. High Energy Phys.

View full text Add to dashboard Cite

We construct a new class of scalar noncommutative multi-solitons on an arbitrary Kähler manifold by using Berezin's geometric approach to quantization and its generalization to deformation quantization. We analyze the stability condition which arises from the leading 1/ correction to the soliton energy and for homogeneous Kähler manifolds obtain that the stable solitons are given in terms of generalized coherent states. We apply this general formalism to a number of examples, which include the sphere, hyperbolic plane, torus and general symmetric bounded domains. As a general feature we notice that on homogeneous manifolds of positive curvature, solitons tend to attract each other, while if the curvature is negative they will repel each other. Applications of these results are discussed.

show abstract

“…We define a noncommutative field theory using the Berezin product [18] and its generalization to deformation quantization [19,20] and construct static solutions of the theory.…”

Section: Jhep03(2002)011mentioning

confidence: 99%

Section: Quantization Of Kähler Manifoldsmentioning

confidence: 99%

Section: Jhep03(2002)011mentioning

confidence: 99%

Section: Jhep03(2002)011mentioning

confidence: 99%

See 2 more Smart Citations

Noncommutative solitons on Kahler manifolds

Spradlin¹,

Volovich²

2002

J. High Energy Phys.

View full text Add to dashboard Cite

show abstract

“…So far several fuzzy spaces have been constructed since the introduction of the seminal example, the fuzzy 2-sphere [5,6,7] and various field theories have been studied within this approach both analytically [8,9] and numerically [10,11,12,13]. In particular, fuzzy complex projective spaces, flag manifolds and toric varieties have been constructed [14,15,16] and provide a wide generalization of previous examples.…”

Section: Introductionmentioning

confidence: 99%