Abstract
The choice of representation is determined by the choice of polarization. The polarization spanned by the Hamiltonian vector fields of the position functions gives rise to the Schrödinger representation. The momentum representation corresponds to the polarization spanned by the Hamiltonian vector fields of the momentum variables. The Blattner-Kostant-Sternberg kernel between these representations reduces to the Fourier transform. In this chapter, we describe the Bargmann-Fock representation defined by the polarization spanned by the Hamiltonian vector fields of complex coordinates on the phase space as well as the harmonic oscillator energy representation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1980 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Śniatycki, J. (1980). Other Representations. In: Geometric Quantization and Quantum Mechanics. Applied Mathematical Sciences, vol 30. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6066-0_8
Download citation
DOI: https://doi.org/10.1007/978-1-4612-6066-0_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90469-6
Online ISBN: 978-1-4612-6066-0
eBook Packages: Springer Book Archive