Is it always possible to define/find conjugate variables? And if yes how one can find it?

Asked Sep 16 '16 at 19:41

Active Sep 16 '16 at 20:05

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My question is in the context of both classical and quantum mechancis and field theory. Generally, how can one define/find the (canonically) conjugate of some variable/operator/field?

Examples include classical Ising spins $s_i=\pm1$, classical spin variables or quantum spin operators, fermion and boson creation and annihilation operators.

A follow up question would be: is it always possible to define Lagrangian if we are given the Hamiltonina, or vice versa?

Any reference would also be appreciated.

edited Sep 16 '16 at 20:05

Qmechanic

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asked Sep 16 '16 at 19:41

Hamed

This question (v2) seems very broad. A full answer is basically a university course in constrained dynamics and quantization of Hamiltonian and Lagrangian systems. Related: http://physics.stackexchange.com/q/105912/2451 , http://physics.stackexchange.com/q/230934/2451 , http://physics.stackexchange.com/q/30606/2451 and links therein. – Qmechanic Sep 16 '16 at 20:01
There is a nice book "Quanitzation of Gauge Systems" by Henneaux and Teitelboim. It treats also classical case. – Blazej Sep 16 '16 at 20:56

Is it always possible to define/find conjugate variables? And if yes how one can find it?

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