First-class constraint: Difference between revisions

Revision as of 01:52, 14 November 2012

Revision as of 23:58, 15 December 2012

Line 22:

These will only be defined [[chart (topology)|chartwise]] in general. Suppose that everywhere on the constrained set, the ''n'' derivatives of the ''n'' functions are all [[linearly independent]] and also that the [[Poisson bracket]]s

:<math>\{f_i,f_j\}</math>

:{ ''f''_''i'', ''f''_''j'' }

and

:<math>\{f_i,H\}</math>

:{ ''f''_''i'', ''H'' }

all vanish on the constrained subspace. This means we can write

Line 34:

for some smooth functions

:<math>c_{ij}</math>

:''c''_''ij''^''k''

(there is a theorem showing this) and