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Canonical quantization with constraints

  1. Sep 14, 2008 #1
    let be the Lagrangian [tex] (1/2)m( \dot x ^{2} + \dot y^{2}) - \lambda (x^{2}+y^{2}-R^{2}) [/tex]

    with 'lambda' a Lagrange multiplier , and 'R' is the radius of an sphere.

    basically , this would be the movement of a particle in 2-d with the constraint that the particle must move on an sphere of radius 'R' , my doubt is that i do not know how to quantizy it since [tex] p_{\lambda}=0 [/tex]
  2. jcsd
  3. Sep 14, 2008 #2


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    Have a look at the Wiki page for Dirac brackets and Dirac-Bergman quantization:
    It explains the essence of constrained quantization.

    See also this paper:

    R. Jackiw, "(Constrained) Quantization Without Tears", hep-th/9306075
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