SecondOrder Corrections to the Gaussian Effective Potential for Lambda PHI(4) and Other Theories.
Abstract
We formulate a systematic, nonperturbative expansion for the effective potential of lambdaphi ^4 theory. At first order it gives the Gaussian effective potential (GEP), which itself contains the 1 loop and leadingorder 1over N results. Here, we compute the secondorder terms and hence obtain the postGaussian effective potential (PGEP) in 1, 2, 3, and 4 spacetime dimensions. The renormalization procedure, including the calculation of the physical mass, is discussed in detail. The results in lower dimensions agree well with the GEP when the comparison is made for the same values of the bare parameters. In 4 dimensions the divergent integrals are calculated using coordinatespace methods combined with dimensional regularization. (Difficulties with other regularizations are briefly discussed). The PGEP for the "precarious" lambdaphi ^4 theory is obtained in manifestly finite form. Remarkably, the final result takes the same mathematical form as the GEP, with only some numerical coefficients being changed. Indeed, when parametrized in terms of the physical mass and the renormalized coupling constant, only a single coefficient is changed, from 1 to 11/(N + 3) ^2. The "autonomous" version of the 4dimensional theory refuses to work in this approach: one obtains indeed an autonomouslike theory, but it is unbounded below for a certain range of the parameters. The influence of fermions on scalar systems is also investigated in the postGaussian approximation. For the simple case of an Yukawatype coupling with no scalar selfinteraction terms the results turn out to be the same as in the Gaussian approximation.
 Publication:

Ph.D. Thesis
 Pub Date:
 1990
 Bibcode:
 1990PhDT.......252S
 Keywords:

 Physics: Elementary Particles and High Energy