PhySyHCAl
A Physics System based on Hierarchical Computer Algebra

The following examples attempt to illustrate typical applications of the framework.

Quark propagator (Wilson-type action)

The following code calculates the inverse quark propagator of a Wilson-type action with improved Gauge action at one loop in a general covariant gauge. It generates an optimized C++ program to numerically evaluate the amplitude for an arbitrary momentum-point.

Show code (C++, 58 lines)

 

Domain-wall quark propagator with finite and infinite fifth dimension

The following code calculates the propagator of domain-wall fermions with finite or infinite fifth dimension. It expands on the the caching system, IR-subtraction, and calculation of derivatives with respect to external momenta.

Show code (C++, 76 lines)

 

Quark propagator and quark-gluon vertex (RHQ)

The following code calculates the one-loop quark propagator and quark-gluon vertex of the RHQ action. It expands on the usage of field rotations and on-shell states.

Show code (C++, 134 lines)

 

Quark propagator (Dimensional Regularization)

The following code calculates the inverse quark propagator at one-loop in dimensional regularization in a general covariant gauge.

Show code (C++, 84 lines)

 

Quark-gluon vertex (Dimensional Regularization)

The following code calculates the quark-gluon vertex at one-loop in dimensional regularization in a general covariant gauge. It expands on the usage of the caching system.

Show code (C++, 215 lines)

 

Tuning of RHQ action

The following Python script can be used to tune the RHQ action at one loop for an arbitrary mass. Minimal modifications are necessary to tune the respective versions of RHQ. The python code expands on many concepts such as the IR-subtraction of the lattice integrand. Future versions of this page will provide a much more detailed explanation. A similar code can also be used to match and improve lattice operators.

Show code (Python, 186 lines)

 

 

Soon to come