Canonical quantization with constraints

[mhill]

let be the Lagrangian $$(1/2)m( \dot x ^{2} + \dot y^{2}) - \lambda (x^{2}+y^{2}-R^{2})$$

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 $$p_{\lambda}=0$$

 

[strangerep]

let be the Lagrangian $$(1/2)m( \dot x ^{2} + \dot y^{2}) - \lambda (x^{2}+y^{2}-R^{2})$$

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 quantize it since $$p_{\lambda}=0$$

Have a look at the Wiki page for Dirac brackets and Dirac-Bergman quantization:
http://en.wikipedia.org/wiki/Dirac_bracket
It explains the essence of constrained quantization.

See also this paper:

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