An Explicit Large Versus Small Field Multiscale Cluster Expansion

An Explicit Large Versus Small Field Multiscale Cluster Expansion

We introduce a new type of cluster expansion which generalizes a previous formula of Brydges and Kennedy. The method is especially suited for performing a phase-space multiscale expansion in a just renormalizable theory, and allows the writing of explicit non-perturbative formulas for the Schwinger functions. The procedure is quite model independent, but for simplicity we chose the infrared φ 4...

Large Mass Expansion versus Small Momentum Expansion of Feynman Diagrams

The method of the large mass expansion (LME) has the technical advantage that two-loop integrals occur only as bubbles with large masses. In many cases only one large mass occurs. In such cases these integrals are expressible in terms of Γfunctions, i.e. they can be handled completely analytically avoiding even recursions and therefore this approach may find a wide field of application. We cons...

Explicit Polynomial Expansion

An Efficient Implementation of Phase Field Method with Explicit Time Integration

The phase field method integrates the Griffith theory and damage mechanics approach to predict crack initiation, propagation, and branching within one framework. No crack tracking topology is needed, and complex crack shapes can be captures without user intervention. In this paper, a detailed description of how the phase field method is implemented with explicit dynamics into LS-DYNA is provide...

A Large Distance Expansion for Quantum Field Theory

Using analyticity of the vacuum wave-functional under complex scalings, the vacuum of a quantum field theory may be reconstructed from a derivative expansion valid for slowly varying fields. This enables the eigenvalue problem for the Hamiltonian to be reduced to algebraic equations. Applied to Yang-Mills theory this expansion leads to a confining force between quarks. Invited talk at the Secon...