Gauge Invariant Magnetism

Manifestly Gauge Invariant Exact

We construct a manifestly gauge invariant Exact Renormalization Group for SU(N) Yang-Mills theory, in a form suitable for calculations without gauge fixing at any order of perturbation theory. The effective cutoff is incorporated via a manifestly realised spontaneously broken SU(N |N) gauge invariance. Diagrammatic methods are developed which allow the calculations to proceed without specifying...

Manifestly Gauge Invariant QCD

Building on recent work in SU(N) Yang-Mills theory, we construct a manifestly gauge invariant exact renormalization group for QCD. A gauge invariant cutoff is constructed by embedding the physical gauge theory in a spontaneously broken SU(N |N) gauge theory, regularized by covariant higher derivatives. Intriguingly, the construction is most efficient if the number of flavours is a multiple of t...

Gauge-Invariant Noncompact Lattice Simulations

Three techniques for performing gauge-invariant, noncompact lattice simulations of nonabelian gauge theories are discussed. In the first method, the action is not itself gauge invariant, but a kind of lattice gauge invariance is restored by random compact gauge transformations during the successive sweeps of the simulation. This method has been applied to pure SU(2) gauge theory on a 12 lattice...

On Gauge Invariant Wilsonian Flows

We investigate non-Abelian gauge theories within a Wilsonian Renormalisation Group approach. Our main question is: How close can one get to a gauge invariant flow, despite the fact that a Wilsonian coarse-graining seems to be incompatible with gauge invariance? We discuss the possible options in the case of quantum fluctuations, and argue that for thermal fluctuations a fully gauge invariant im...

A Gauge Invariant Flow Equation