aqora

Geometric quantization on homogeneous spaces and the meaning of “inequivalent” quantizations

M.A. Robson

arXiv:hep-th/9406057Physics Letters BSep 1, 19943 citations

On wave functions in geometric quantization

Jędrzej Śniatycki

Springer eBooksApr 6, 20080 citations

Geometric Quantization of a Particle in a Perpendicular Magnetic Field

Marin Drinov Academic Publishing House, Guillermo Capobianco, Walter Reartes

In this paper we develop the quantization of a particle in the plane under the influence of a perpendicular magnetic field using the geometric quantization with half--forms in Hilbert space of holomorphic functions. An original coordinate transformation is applied to convert the problem into a system of harmonic oscillators. Then, it is solved highlighting the relationship between different representations. We emphasize the isomorphism between the holomorphic representation and the Schrödinger representation.In this paper we develop the quantization of a particle in the plane under the influence of a perpendicular magnetic field using the geometric quantization with half--forms in Hilbert space of holomorphic functions. An original coordinate transformation is applied to convert the problem into a system of harmonic oscillators. Then, it is solved highlighting the relationship between different representations. We emphasize the isomorphism between the holomorphic representation and the Schrödinger representation.

Journal of Geometry and Symmetry in PhysicsJan 1, 20160 citations

Geometric quantization and the Bogoliubov transformation

N M J Woodhouse

Abstract This paper treats some simple applications of geometric quantization theory to problems involving the interaction of quantum fields with external classical potentials. The main new result is a representation of the transition amplitudes for a boson field in terms of functional integrals over the classical phase space (the space of solutions of the classical field equations). An analogous representation for fermion fields is also constructed.

Proceedings of the Royal Society of London A Mathematical and Physical SciencesSep 11, 198123 citations

Wave functions in geometric quantization

Antonio Díaz Miranda

International Journal of Theoretical PhysicsOct 1, 19963 citations

Vector coherent state representations, induced representations and geometric quantization: I. Scalar coherent state representations

Stephen D. Bartlett, DAVID J. ROWE, Joe Repka

Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization, (ii) induced unitary representations corresponding to prequantization and (iii) irreducible unitary representations obtained in geometric quantization by choice of a polarization. These representations establish an intimate relation between coherent state theory and geometric quantization in the context of induced representations.Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization, (ii) induced unitary representations corresponding to prequantization and (iii) irreducible unitary representations obtained in geometric quantization by choice of a polarization. These representations establish an intimate relation between coherent state theory and geometric quantization in the context of induced representations.

arXiv:quant-ph/0201129Journal of Physics A Mathematical and GeneralJun 28, 200221 citations

On representation spaces in geometric quantization

Related papers

On representation spaces in geometric quantization

Related papers