Continuum Limit of the Green Function in Scaled Affine <inline-formula><math display="inline"><semantics><msubsup><mi>φ</mi><mn>4</mn><mn>4</mn></msubsup></semantics></math></inline-formula> Quantum Euclidean Covariant Relativistic Field Theory

Abstract

Through path integral Monte Carlo computer experiments, we prove that the affine quantization of the φ44-scaled Euclidean covariant relativistic scalar field theory is a valid quantum field theory with a well-defined continuum limit of the one- and two-point functions. Affine quantization leads to a completely satisfactory quantization of field theories in situations involving scaled behavior, leading to an unexpected term, ℏ2/φ2, which arises only in the quantum aspects.

Keywords

• field theory
• affine quantization
• continuum limit
• green function