Hamiltonian Vector Fields and the Moment Map

Peter Woit ()
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Peter Woit: Columbia University, Department of Mathematics

Chapter Chapter 15 in Quantum Theory, Groups and Representations, 2017, pp 199-214 from Springer

Abstract: Abstract A basic feature of Hamiltonian mechanics is that, for any function f on phase space M, there are parametrized curves in phase space that solve Hamilton’s equations $$\dot{q}_j=\frac{\partial f}{\partial p_j}\ \ \ \dot{p}_j=-\frac{\partial f}{\partial q_j}$$ and the tangent vectors of these parametrized curves provide a vector field on phase space. Such vector fields are called Hamiltonian vector fields. There is a distinguished choice of f, the Hamiltonian function h, which gives the velocity vector fields for time evolution trajectories in phase space.

Date: 2017
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DOI: 10.1007/978-3-319-64612-1_15

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