A connection between quantum Hilbert-space and classical phase-space operators

2000 ◽  
Vol 33 (35) ◽  
pp. 6129-6158 ◽  
Author(s):  
D Campos ◽  
J D Urbina ◽  
C Viviescas
Keyword(s):  
Hilbert Space ◽  
Phase Space ◽  
Classical Phase Space

scholarly journals QUANTUM MECHANICS IN INFINITE SYMPLECTIC VOLUME

2004 ◽  
Vol 19 (05) ◽  
pp. 349-355
Author(s):  
JOSÉ M. ISIDRO
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Phase Space ◽  
Projective Space ◽  
Bergman Metric ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Classical Phase Space ◽  
Dimensional Projective Space

We quantise complex, infinite-dimensional projective space CP(ℋ). We apply the result to quantise a complex, finite-dimensional, classical phase space [Formula: see text] whose symplectic volume is infinite, by holomorphically embedding it into CP(ℋ). The embedding is univocally determined by requiring it to be an isometry between the Bergman metric on [Formula: see text] and the Fubini–Study metric on CP(ℋ). Then the Hilbert-space bundle over [Formula: see text] is the pullback, by the embedding, of the Hilbert-space bundle over CP(ℋ).

Classical nonlinearity and quantum decay: The effect of classical phase-space structures

2001 ◽  
Vol 64 (5) ◽  
Author(s):  
Yosef Ashkenazy ◽  
Luca Bonci ◽  
Jacob Levitan ◽  
Roberto Roncaglia
Keyword(s):  
Phase Space ◽  
Space Structures ◽  
Classical Phase Space

scholarly journals NONCOMMUTATIVE METAFLUID DYNAMICS

2006 ◽  
Vol 21 (03) ◽  
pp. 505-516 ◽  
Author(s):  
A. C. R. MENDES ◽  
C. NEVES ◽  
W. OLIVEIRA ◽  
F. I. TAKAKURA
Keyword(s):  
Phase Space ◽  
Nonlinear Equations ◽  
Equations Of Motion ◽  
Additional Term ◽  
Dissipative Force ◽  
Covariant Form ◽  
Covariant Quantization ◽  
Noncommutative Spaces ◽  
Classical Phase Space

In this paper we define a noncommutative (NC) metafluid dynamics.1,2 We applied the Dirac's quantization to the metafluid dynamics on NC spaces. First class constraints were found which are the same obtained in Ref. 4. The gauge covariant quantization of the nonlinear equations of fields on noncommutative spaces were studied. We have found the extended Hamiltonian which leads to equations of motion in the gauge covariant form. In addition, we show that a particular transformation3 on the usual classical phase space (CPS) leads to the same results as of the ⋆-deformation with ν = 0. Besides, we have shown that an additional term is introduced into the dissipative force due to the NC geometry. This is an interesting feature due to the NC nature induced into model.

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