New improved derivative expansion for field theories with spontaneous symmetry breaking

摘要

Derivative expansion of the effective action for field theories with spontaneous symmetry breaking may be badly divergent. I propose a new expansion series in which the series expansion are simultaneous developed in order of the number of derivatives of the field and in power of the deviation of the field from its ground state value. As examples, I have applied this new method to calculate the quantum correction to the energy of the 1+1 dimension soliton in various models. For the models in which exact solutions have been found, such as the Sine-Gordon soliton, (phi)(sup 4) soliton, and (phi)(sup 4) soliton with fermion loop, the improved series can be recognized as well-known analytically summable series. The results of the exact solutions are completely recovered. More importantly, for the cases where exact solutions may not be available, Pade approximant or the Borel summation can be used to give good approximation.