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What is relativistic canonical transformation? I need every piece of information about it. Does anyone know a reference or an article about relativistic canonical transformation? For example, in classical mechanics, under one and only one condition, you can say that a transformation is canonical and that is:

$J\cdot M\cdot J^T= M$
where $J$ and $M$ are two matrices which are represented in Goldstein (3rd Edition) - Page 342

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In classical mechanics a transformation is canonical if it preserves the form of Hamilton equations. When you are talking about canonical transformation in SR you should mention what hamiltonian formalism you are using. There is a formalism that just takes the SR expression for the energy in terms of velocities, which is not explicitly invariant. Also, there is a formalism which is explicitly invariant, but uses constrained hamiltonian mechanics. While the first one in completely analogous to the classic one, the second one may not be the cause of your question. So please clarify your setting. – Peter Kravchuk May 15 '13 at 17:08
thanks for your respond please explain about second one. – kaveh karbakhsh May 16 '13 at 7:49

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