A Alternate Constructive Approach to the Phi 4(3) Quantum Field Theory, and a Possible Destructive Approach to PHI4(4)
Abstract
I study the construction of (phi)('4) quantum field theories by means of lattice approximations. It is easy to prove the existence of the continuum limit (by subsequences); the key question is whether this limit is something other than a (generalized) free field. I use correlation inequalities, infrared bounds and field equations to investigate this question. For spacetime dimension d less than four, I give a simple proof that the continuum limit theory is indeed nontrivial; it relies, however, on a conjectured correlation in inequality closely related to the (GAMMA)(,6) conjecture of Glimm and Jaffe. Moreover, the Euclidean invariance of the continuum theory is an open question within the present approach. For spacetime dimension d greater than or equal to four, I arguebut do not provethat the continuum limit is inevitably a (generalized) free field, irrespective of the choice of charge renormalization. The argument is based on old ideas of Landau and Pomeranchuk, improved through the use of correlation inequalities applied to the exact field equations.
 Publication:

Ph.D. Thesis
 Pub Date:
 1981
 Bibcode:
 1981PhDT.......143S
 Keywords:

 Physics: Elementary Particles and High Energy