Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-02-19
Annalen Phys.9:247-257,2000
Physics
High Energy Physics
High Energy Physics - Theory
15 pages Latex. Invited contrib. to JR99 (Weimar), to be published in Annalen der Physik (Leipzig)
Scientific paper
10.1002/(SICI)1521-3889(200005)9
It is shown how the the introduction of a suitably defined dilatonic auxiliary field, $\Phi$ say, makes it possible for the non-linear Lagrangian for a generic elastic string model, of the kind appropriate for representing superconducting cosmic strings, to be converted into a standardised form as the sum of a kinetic term that is just homogeneously quadratic in the relevant scalar phase gradient (as in a simple linear model) together with a potential energy term, $V$ say, that is specified as a generically non-linear function of $\Phi$. The explicit form of this function is derived for various noteworthy examples, of which the most memorable is that of the transonic string model, as characterised by a given mass scale, $m$ say, for which this potential energy density will be expressible in terms of the zero current limit value $\Phi_{_0}$ of $\Phi$ by $ V= {1\over 2} m \big(\Phi_{_0}^{-2} \Phi^2+ \Phi_{_0}^{2} \Phi^{-2} \big)$.
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