First-class constraint: Difference between revisions

Revision as of 14:15, 18 January 2016

Revision as of 14:21, 18 January 2016

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What is the Hamiltonian version of this model? Well, first, we have to split '''A''' noncovariantly into a time component {{mvar|φ}} and a spatial part <math>\vec {{vec|''A''}}</math>. Then, the resulting symplectic space has the conjugate variables {{mvar|σ}}, {{math|''π_σ''}} (taking values in the underlying vector space of <math>\bar{\rho}</math>, the dual rep of {{mvar|ρ}}), <math>\vec {{vec|''A''}}</math>, <math>\vec {\pi{vec|''π''}_A}<sub>''A''</mathsub>, ''φ'' and ''π_φ''. forFor each spatial point, we have the constraints, ''π_φ''=0 and the [[Gaussian constraint]]

:<math>\vec{D}\cdot\vec{\pi}_A-\rho'(\pi_\sigma,\sigma)=0</math>

where since {{mvar|ρ}} is an [[intertwiner]]