Cut routines
Here is an overview of the cutting routines supported by the code.
Gluon fields can be computed from the logarithm or approximation to the logarithm of the SU(NC)-valued parallel transport matrices. By default the code uses the normal lattice approximation but can also use the logarithmic definition although for NC > 3, this becomes slow and unstable as series expansions are used to compute this thing.
Gluon fields are not uniquely defined unless the gauge is fixed, once it is though we can define our gauge fields from the parallel transport matrices,
The momentum-space gluon fields are matrices as are their Fourier transforms,
The Landau gauge condition in configuration space is
In momentum space this becomes
I define the lattice momentum in the usual manner,
Where n_\mu is an integer Fourier mode,
The factor of e^{iaq_\mu/2} comes from the gauge fields being well approximated by lying halfway between the lattice sites.
The code supports three different types of momentum cuts:
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Psq cut -> adds all possible q^2 orbits up to a maximum value q_max^2
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Hypercubic cut -> includes all momenta up to ( |q_max|, |q_max|, |q_max| ... )
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Cylinder cut -> includes only off-axis momenta that lie on the body diagonals of the momentum-space lattice, e.g. in 4d a vector ( 4 , 0 , 0 , 0 ) would not lie in it but ( 2 , 2 , 2 , 2 ) would. They both lie on the same q^2 orbit but the one on the body diagonal has smaller rotational lattice artifacts. This is because rotational artifacts are of the order q_\mu^{2n} where n > 1.