Astronomy and Astrophysics – Astrophysics
Scientific paper
Apr 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002aps..apr.x4007c&link_type=abstract
American Physical Society, April Meeting, Jointly Sponsored with the High Energy Astrophysics Division (HEAD) of the American As
Astronomy and Astrophysics
Astrophysics
Scientific paper
The canonical transformation of a classical field, e.g. that of the vibration of a continuous rod, has been largely unexplored. The difficulty is attributed to the following: Although the usual form of the Hamiltonium density of such a system has a momentum density, pie, is properly in the form of a density, the field, eta, is not. The potential energy depends on eta at different positions.(According to remarks in standard texts of analytical mechanics) It will now be shown that this problem can be solved.We worked out a new form of Hamiltonian density free of this difficulty and yet is equivalent to the usual form in that it yields the same wave equation. The method is then extended to the field of a real Klen-Gordon equation. It turned out that the canonical variables so obtained has all the required properties of a quantum wave function, i.e. having a non-negative conserved probability density etc. In addition, it is equivalent to the K-G equation and is therefore relativistic. In the meantime, it turns out that the usual method of canonical quantization really does not guarantee the final result to be relativitic even if we start out from a covariant form of Hamiltonan. It must be modified in accordance with the present method.
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