The Vacuum Functional at Large Distances

Abstract

For fields that vary slowly on the scale of the lightest mass the logarithm of the vacuum functional can be expanded as a sum of local functionals, however this does not satisfy the obvious form of the Schrödinger equation. For ${\phi }^4$ theory we construct the appropriate equation that this expansion does satisfy. This reduces the eigenvalue problem for the Hamiltonian to a set of algebraic equations. We suggest two approaches to their solution. The first is equivalent to the usual semi-classical expansion whilst the other is a new scheme that may also be applied to theories that are classically massless but in which mass is generated quantum mechanically.

11 pages, latex

References in corpus (5)

• The Schrödinger Functional - a Renormalizable Probe for Non-Abelian Gauge Theories
• Functional Schroedinger Equation for Fermions in External Gauge Fields
• Quantum Field Theories on Manifolds with Curved Boundaries: Scalar Fields
• Continuum Strong Coupling Expansion of Yang-Mills Theory: Quark Confinement and Infra-Red Slavery
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• Solving the Functional Schroedinger Equation: Yang-Mills String Tension and Surface Critical Scaling
• The O(N) sigma-model Laplacian
• The Schrodinger Representation for Fermions and a Local Expansion of the Schwinger Model
• The Coulomb Branch of Yang-Mills Theory from the Schroedinger Representation
• Finite VEVs from a Large Distance Vacuum Wave Functional
• Second Order Calculations of the O(N) sigma-Model Laplacian
• A Modified Borel Summation Technique
• Virasoro Algebra and O(N) Sigma Model