Dirac Bracket - Inadequacy of The Standard Hamiltonian Procedure

Inadequacy of The Standard Hamiltonian Procedure

The standard development of Hamiltonian mechanics is inadequate in several specific situations:

  1. When the Lagrangian is at most linear in the velocity of at least one coordinate; in which case, the definition of the canonical momentum leads to a constraint. This is the most frequent reason to resort to Dirac brackets. For instance, the Lagrangian (density) for any fermion is of this form.
  2. When there are gauge (or other unphysical) degrees of freedom which need to be fixed.
  3. When there are any other constraints that one wishes to impose in phase space.

Read more about this topic:  Dirac Bracket

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