Nontrivial Continuum Limit of a ϕ4\phi^4 in Four-dimensions Model With Negative Coupling Constant

Feb, 1985
31 pages
Published in:
  • Nucl.Phys.B 257 (1985) 474-504
  • Published: 1985
Report number:
  • HUTMP-84-172

Citations per year

19851994200320122021012345
Abstract: (Elsevier)
We present a rigorous, non-perturbative construction of a non-trivial euclidean π 4 4 field theory with negative coupling constant, as a scaling limit of stable lattice theories. In the present paper the usual propagator is replaced by a hierarchical one for pedagogical reasons. The resulting model has similar renormalization problems as the standard π 4 4 theory. Our non-perturbative construction has the standard renormalized perturbation expansion as an asymptotic expansion, and is asymptotically free. The analysis can be extended to the conventional model with the use of a rigorous block-spin formulation to yield a non-trivial continuum theory with similar properties, but possibly violating reflection positivity in a non-perturbative way.
  • field theory: scalar
  • FIELD THEORY: EUCLIDEAN
  • NONPERTURBATIVE
  • LATTICE FIELD THEORY: CONTINUUM LIMIT
  • COUPLING CONSTANT
  • RENORMALIZATION: REGULARIZATION
  • RENORMALIZATION GROUP
  • TRANSFORMATION: BLOCK SPIN
  • BLOCK SPIN: TRANSFORMATION
  • SCALING