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Conceptual Foundations
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The Gaussian Model An
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Preface
Contents
Conceptual Foundations
Philosophical Preliminaries
The Euclidean Lattice
Fields on the Lattice
Classical Field Theory
Definition of the Classical Theory
Fixed Boundary Conditions
Finite-Difference Operators
Space of Field Configurations
Momentum Space
Finite Fourier Transforms
Eigenvalues and Eigenvectors of the Laplacian
Eigenvectors for Fixed Boundary Conditions
Basis Transformations in Configuration Space
External Sources and Green Functions
Sources and Fixed Boundary Conditions
Quantum Field Theory
Definition of the Quantum Theory
Relation with Statistical Mechanics
Gaussian Integration
Factorization of the Correlation Functions
External Sources in the Quantum Theory
Functional Generators on the Lattice
Physical Significance of the Effective Action
Correlation Structure
Structure of the Two-Point Function
Discontinuity of the Configurations
Block Variables and Observables
The Concept of Energy
Connection with the Canonical Formalism
Energy and States of Particles
Relation with Hilbert Spaces
Conclusions and Outlook
Analysis of the Situation
Blocked Temporal Evolution
Problems and Possibilities
Bibliography