However, for suitably defined boundary conditions, the spectral transform can, in fact, be interpreted as a transformation to "'completely ignorable coordinates "', in which the conserved quantities form half of a doubly infinite set of canonical coordinates, and the flow linearizes in these.
32.
In Hamiltonian mechanics, a classical physical system is described by a set of canonical coordinates \ boldsymbol { r } = ( \ boldsymbol { q }, \ boldsymbol { p } ), where each component of the coordinate q _ i, p _ i is indexed to the frame of reference of the system.
33.
We identify "'canonical coordinates "'( such as in the example above, or a field in the case of quantum field theory ) and "'canonical momenta "'( in the example above it is, or more generally, some functions involving the derivatives of the canonical coordinates with respect to time ):
34.
We identify "'canonical coordinates "'( such as in the example above, or a field in the case of quantum field theory ) and "'canonical momenta "'( in the example above it is, or more generally, some functions involving the derivatives of the canonical coordinates with respect to time ):
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