12 - An Excursion: Constrained Dynamics
from Part III - Canonical Field Theories with Gravity
Published online by Cambridge University Press: 01 March 2026
Summary
In preparation for the ADM formulation of General Relativity, we quickly scan Dirac's theory of constrained systems. How to deal with dynamics when the number of variables is larger than the true degrees of freedom is at issue. Starting from a familiar classical mechanics with Lagrange multipliers, we classify constraints into the first class and the second class. The former is particularly relevant for field theories with gauge redundancies, as is the case with General Relativity. Again, the Maxwell theory is invoked as a prototype, with the Gauss constraint given a unique meaning as the generator of the gauge redundancy.
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- Gravitation for Theorists , pp. 235 - 254Publisher: Cambridge University PressPrint publication year: 2026
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