Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-03-29
Physics
High Energy Physics
High Energy Physics - Theory
60 pages, 22 Postscript figures
Scientific paper
The interest in string Hamiltonian system has recently been rekindled due to its application to target-space duality. In this article, we explore another direction it motivates. In Sec.\ 1, conformal symmetry and some algebraic structures of the system that are related to interacting strings are discussed. These lead one naturally to the study of Lorentz surfaces in Sec.\ 2. In contrast to the case of Riemann surfaces, we show in Sec.\ 3 that there are Lorentz surfaces that cannot be conformally deformed into Mandelstam diagrams. Lastly in Sec.\ 4, we discuss speculatively the prospect of Lorentzian conformal field theory. Additionally, to have a view of what quantum picture a string Hamiltonian system may lead to, we discuss independently in the Appendix a formal geometric quantization of the string phase space.
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