Zusammenfassung
To treat the front-form Hamiltonian approach to quantum field theory, called light cone quantum field theory, in a mathematically rigorous way, the existence of a well-defined restriction of the corresponding free fields to the hypersurface {x(0)+x(3)=0} in Minkowski space is of an essential necessity. However, even in the situation of a real scalar free field such a restriction does canonically ...
Zusammenfassung
To treat the front-form Hamiltonian approach to quantum field theory, called light cone quantum field theory, in a mathematically rigorous way, the existence of a well-defined restriction of the corresponding free fields to the hypersurface {x(0)+x(3)=0} in Minkowski space is of an essential necessity. However, even in the situation of a real scalar free field such a restriction does canonically not exist; this is called the restriction problem. Furthermore, since the beginning of light cone quantum field theory there is the problem of nonexistence of a well-defined Fock space expansion of a free quantum field in terms of light cone momenta which is called the zero-mode problem. In this paper we present solutions to these long outstanding problems where the study of the zero-mode problem (of the corresponding classical field) will lead us to a solution of the restriction problem. We introduce a new function space of "squeezed" smooth functions which can canonically be embedded into the Schwartz space S(R-3). The restriction of the free field to {x(0)+x(3)=0} is canonically definable on this function space and we show that the covariant field is uniquely determined by this "tame" restriction. (C) 2004 American Institute of Physics.
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