Berezin quantization and unitary representations of Lie groups

  title={Berezin quantization and unitary representations of Lie groups},
  author={D. Bar-Moshe and M. S. Marinov},
In 1974, Berezin proposed a quantum theory for dynamical systems having a Kähler manifold as their phase space. The system states were represented by holomorphic functions on the manifold. For any homogeneous Kähler manifold, the Lie algebra of its group of motions may be represented either by holomorphic differential operators (“quantum theory”), or by functions on the manifold with Poisson brackets, generated by the Kähler structure (“classical theory”). The Kähler potentials and the… CONTINUE READING
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Publications referenced by this paper.
Showing 1-10 of 37 references

General concept of quantization

  • F. A. Berezin
  • Comm. Math. Phys. 40
  • 1975
Highly Influential
18 Excerpts

Groupes et algèbres de Lie

  • N. Bourbaki
  • chaps. 4-6
  • 1981
Highly Influential
10 Excerpts

Quantum Kinematics and Dynamics (W

  • J. Schwinger
  • A. Benjamin, New York,
  • 1970
Highly Influential
3 Excerpts

Foundations of Differential Geometry

  • S. Kobayashi, K. Nomizu
  • vol. 2
  • 1969
Highly Influential
11 Excerpts

Geometric Quantization on Kählerian Systems

  • D. Bar-Moshe
  • PhD Thesis
  • 1993
2 Excerpts

Quantum Field Theory and Topology (J

  • A. S. Schwarz
  • 1993
1 Excerpt


  • B. DeWitt
  • 2nd edition
  • 1992
1 Excerpt

On reproducing kernels and quantization of states

  • A. Odzijewicz
  • Comm. Math. Phys. 114
  • 1988

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