Saturday, October 3, 2009

Quantum/Classical transition

The nature of the quantum/classical transition is according to my opinion, the most important fundamental question of physics. There are many approaches and many insights that have consequences on the continuing debate on the interpretation of quantum mechanics and its mysterious features such as the collapse of the wave function. Some of the approaches and related topics, not necessarily independent from each other are
  1. The Ehrenfest theorem (My favorite).
  2. The Koopman- von Neumann equation for the classical wave function.
  3. The Wigner function for a quantum formulation in the phase space.  Moyal brackets and Weyl quantization [1]
  4. Feynman Path integrals and decoherence.
  5. The classical spinor formalism. Electrodynamics: a modern geometric approach By William Eric Baylis
  6. The limit to the Thomas-Fermi model by Elliott H. Lieb
  7. The analogy of classical statistical mechanics with quantum mechanics inspired on the Wigner function by  Blokhintsev. Another researcher, A. O. Bolivar pursues this idea further but it seems that he was unaware of the previous work by Blokhintsev. 
  8. Related with the previous approach is also the work by Amir Caldeira and Anthony J. Leggett, who proposed a quantum dissipation model.  
  9. The very intriguing derivation of the Schrodinger equation from classical mechanics with complexified Brownian motion by Edward Nelson.  
  10. The p-mechanics formalism, which exploits the representations of the Heisemberg. This method is also closely related with the Weyl quantization.
  11. Geometric quantization, is another method inspired on the Weyl quantization trying to maintain a coordinate-free procedure based on differential geometry.

[1]  Zachos, C. and Fairlie, D. and Curtright, T., Quantum mechanics in phase space: an overview with selected papers, World Scientific Pub Co Inc, 2005

    1 comment:

    1. Dear Renan,

      Read please my paper on the quantum-classical transition:

      Best regards,