著者

JENS HOPPE

出版者

Soryushiron Kenkyu Editorial Office

雑誌

素粒子論研究 (ISSN:03711838)

巻号頁・発行日

vol.80, no.3, pp.145-202, 1989-12-20 (Released:2017-10-02)

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A massless relativistic surface is defined in a Lorentz invariant way by letting its action be proportional to the volume swept out in Minkowski space. The system is described in light cone coordinates and by going to a Hamiltonian formalism one sees that the dynamics depend only on the transverse coordinates X and Y. The Hamiltonian H is invariant under the group of area preserving reparametrizations whose Lie algebra can be shown to correspond in some sense to the Large N-limit of SU(N). Using this one arrives at a SU(N) invariant, large N-two-matrix model with a quartic interaction [X, Y]^2. The problem of N partices with nearest neighbors δ-function interactions is defined by regularizing the 2 body problem and deriving an eigenvalue integral equation that is equivalent to the Schrodinger equation (for bound states). The 3 body problem is discussed extensively and it is argued to be free of irregularities, in contrast with the known results in 3 dimensions. The crucial role of the dimension is displayed in looking at the limit of a short-range potential.