1992
DOI: 10.1007/bf02096666
|View full text |Cite
|
Sign up to set email alerts
|

Coherent states and geometric quantization

Abstract: Based on the concept of generalized coherent states, a theory of mechanical systems is formulated in a way which naturally exhibits the mutual relation of classical and quantum aspects of physical phenomena.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1

Citation Types

1
77
0

Year Published

1994
1994
2013
2013

Publication Types

Select...
5
2

Relationship

0
7

Authors

Journals

citations
Cited by 69 publications
(78 citation statements)
references
References 20 publications
1
77
0
Order By: Relevance
“…(More precisely, Kontsevich's formula is an expansion of a certain Feynman integral at a saddle point, see Cattaneo and Felder [60].) Connections between Feynman path integrals, coherent states, and the Berezin quantization are discussed in Kochetov and Yarunin [152], Odzijewicz [189], Horowski, Kryszen and Odzijewicz [130], Klauder [149], Chapter V in Berezin and Shubin [33], Marinov [168], Charles [61], and Bodmann [41]. For a discussion of Feynman path integrals in the context of geometric quantization, see Gawedzki [98], Wiegmann [258], and Chapter 9 in the book of Woodhouse [263].…”
Section: Some Other Quantization Methodsmentioning
confidence: 99%
See 2 more Smart Citations
“…(More precisely, Kontsevich's formula is an expansion of a certain Feynman integral at a saddle point, see Cattaneo and Felder [60].) Connections between Feynman path integrals, coherent states, and the Berezin quantization are discussed in Kochetov and Yarunin [152], Odzijewicz [189], Horowski, Kryszen and Odzijewicz [130], Klauder [149], Chapter V in Berezin and Shubin [33], Marinov [168], Charles [61], and Bodmann [41]. For a discussion of Feynman path integrals in the context of geometric quantization, see Gawedzki [98], Wiegmann [258], and Chapter 9 in the book of Woodhouse [263].…”
Section: Some Other Quantization Methodsmentioning
confidence: 99%
“…Thus, in some sense, the quantizers ∆ y above and their associated reproducing kernel Hilbert spaces may be regarded as generalizations of the coherent states to the situation when there is no group action present. For more information on coherent states and their applications in quantization, see for instance Klauder [149], Odzijewicz [189], Unterberger [251], Ali and Goldin [10], Antoine and Ali [6], Ali [4], Bartlett, Rowe and Repka [220], and the survey by Ali, Antoine, Gazeau and Mueller [7], as well as the recent book [8], and the references therein. An interesting characterization of the cut locus of a compact homogeneous Kähler manifold in terms of orthogonality of coherent states has recently been given by Berceanu [30].…”
mentioning
confidence: 99%
See 1 more Smart Citation
“…Recently reproducing kernels of Bergman type have been used to define the quantization of classical states in holomorphic models of quantum field theory (see [11], [7] or [8]). Earlier they have been appeard in studies of wave and Dirac equations (see [2]).…”
Section: Introductionmentioning
confidence: 99%
“…spaces of sections of trivial bundles over the open domains in C™. In holomorphic models of quantum field theory however ( [11] and [8]) the holomorphic sections of non-trivial line bundles over the Káhler manifold have been appeard and reproducing kernels for such spaces have been used. The purpose of this paper is to introduce reproducing kernels in the case of an arbitrary holomorphic vector bundle and to prove basic properties of these kernels.…”
Section: Introductionmentioning
confidence: 99%