GENERALIZED DERIVATIVE EXPANSION AND ONE-LOOP CORRECTIONS TO THE VACUUM ENERGY OF STATIC BACKGROUND FIELDS

The derivative expansion of the effective action for held theories wit h spontaneous symmetry breaking has a variable expansion parameter whi ch may become locally infinite. To circumvent this difficulty, I propo se an alternative expansion series in which the series expansion is si multaneously developed in order of the number of derivatives of the fi eld and in powers of the deviation of the field from its ground-state value. As an example, I have applied this new method to calculate the quantum correction to the energy of the (1+1)-dimensional soliton in v arious models which have been well investigated previously. The expans ion series are calculated using MATHEMATICA to 14 terms. For the model s in which exact solutions have been found, such as the sine-Gordon so liton, phi(4) soliton, and phi(4) soliton with a fermion loop, the new improved series can be recognized as well-known analytically summable series. The complete results of exact solutions are recovered. More i mportantly, for the cases where exact solutions may not be available, Pade approximants or the Borel summation can be used as an efficient m ethod to provide an excellent approximation, in contrast with cumberso me numerical calculations. The Christ-Lee soliton and the phi(4) bag a re used to illustrate this approximation. We also derive a compact hyb rid formula in closed form to estimate the quantum correction to the s tatic energy of the (1+1)-dimensional field. This new method can be ea sily extended to higher dimensions as well as other important applicat ions such as vacuum tunneling, Skyrmion physics, etc.