Light-Front Quantisation as an Initial-Boundary Value Problem

Details Light-Front Quantisation as an Initial-Boundary Value Problem Light-Front Quantisation as an Initial-Boundary Value Problem

1993-11-18

arxiv.org/abs/hep-th/9311108v1

Z.Phys. C62 (1994) 521-532

Physics

High Energy Physics

High Energy Physics - Theory

26 pages (including figure), tex, figure in latex, TPR 93-3

Scientific paper

10.1007/BF01555913

In the light front quantisation scheme initial conditions are usually provided on a single lightlike hyperplane. This, however, is insufficient to yield a unique solution of the field equations. We investigate under which additional conditions the problem of solving the field equations becomes well posed. The consequences for quantisation are studied within a Hamiltonian formulation by using the method of Faddeev and Jackiw for dealing with first-order Lagrangians. For the prototype field theory of massive scalar fields in 1+1 dimensions, we find that initial conditions for fixed light cone time {\sl and} boundary conditions in the spatial variable are sufficient to yield a consistent commutator algebra. Data on a second lightlike hyperplane are not necessary. Hamiltonian and Euler-Lagrange equations of motion become equivalent; the description of the dynamics remains canonical and simple. In this way we justify the approach of discretised light cone quantisation.

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