Abstract
We will discuss in this chapter two applications of the theory to physically interesting cases, dealing with dynamics of particles with spin 1/2 in a magnetic field, i.e.
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Notes
- 1.
The hyperhamiltonian framework for this equation has been considered elsewhere [60, 61] in the simplified setting of no electric field.
- 2.
This will depend only on time, as it also follows from the fact we are considering the momentum representation for the particle, i.e. its position is completely undetermined.
- 3.
Notice that these are field PDEs rather than ODEs, so that hyperhamiltonian dynamics can deal only with finite dimensional reductions of them. This remark would call for the extension of hyperhamiltonian dynamics to a hyperhamiltonian field theory; a task which lies beyond the limits of the present discussion.
- 4.
Again, the Majorana-Weyl equation would be written in simple hyperhamiltonian form.
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Gaeta, G., Rodríguez, M.A. (2017). Physical Applications. In: Lectures on Hyperhamiltonian Dynamics and Physical Applications. Mathematical Physics Studies. Springer, Cham. https://doi.org/10.1007/978-3-319-54358-1_7
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DOI: https://doi.org/10.1007/978-3-319-54358-1_7
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