String field theoryะ Time evolution and T-duality

Abstract

The time evolution operator of quantum field theory (Schrödinger functional) can be written in terms of particles moving on S(^1)/Z(_2-). By deriving the 'gluing property’ which joins two propagators across fixed time surfaces, we show that the Feynman diagram expansion of the free Schrödinger functional is determined once we know the field propagator. We generalise the gluing property to a new method of sewing string field propagators and construct the string field Schrödinger functional in terms of strings moving on S(^1)/Z(_2-). Timelike T-duality in string theory then appears as a large/small time symmetry of string field theory with an exchange of boundary states and string backgrounds. All of our arguments apply equally to the open and closed string. The addition of interactions to quantum field theory bring no complication to our arguments, but modifications are required when the interaction is non-local. As application of these methods we construct the interacting string field vacuum wave functional using knowledge of the vacuum expectation values it must generate.