Analytic solutions for marginal deformations in open string field theory

We develop a calculable analytic approach to marginal deformations in open string field theory using wedge states with operator insertions. For marginal operators with regular operator products, we construct analytic solutions to all orders in the deformation parameter. In particular, we construct an exact time-dependent solution that describes D-brane decay and incorporates all α′ corrections. For marginal operators with singular operator products, we construct solutions by regularizing the singularity and adding counterterms. We explicitly carry out the procedure to third order in the deformation parameter.