Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-08-18
Physics
High Energy Physics
High Energy Physics - Theory
8 pages
Scientific paper
It has been argued that, underlying any given quantum-mechanical model, there exists at least one deterministic system that reproduces, after prequantisation, the given quantum dynamics. For a quantum mechanics with a complex d-dimensional Hilbert space, the Lie group SU(d) represents classical canonical transformations on the projective space CP^{d-1} of quantum states. Let R stand for the Ricci flow of the manifold SU(d-1) down to one point, and let P denote the projection from the Hopf bundle onto its base CP^{d-1}. Then the underlying deterministic model we propose here is the Lie group SU(d), acted on by the operation PR. Finally we comment on some possible consequences that our model may have on a quantum theory of gravity.
de Cordoba Pedro Fernandez
Isidro Jose M.
Santander J. L. G.
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