I'm currently coding a lattice QCD project and ran into an issue with my understanding.

A link variable connecting two points could be in the $\mu$ or $\nu$ direction, for example, $U\mu(x)$ goes from bottom left to bottom right on the diagram and $U\nu(x)$ goes bottom left to top left, but what do these directions actually mean? Are both of these directions somehow along the same 1-D axis x? Or is $\mu$ is in the direction of the specified axis and $\nu$ is in the direction of time? (Both of these ideas do not work since you cannot go in two perpendicular directions on a 1-D line and $\mu$ and $\nu$ both apply to link variables with time; $U\mu(t)$ and $U\nu(t)$ exist)

It would also be great to know what 2-D slice of the 4-D lattice the diagram represents and the relative coordinates of the sites shown.

Diagram taken from https://fse.studenttheses.ub.rug.nl/20342/1/BRP_Thesis_Piter_Annema.pdf page 12

I'm currently coding a lattice QCD project and ran into an issue with my understanding.

A link variable connecting two points could be in the $\mu$ or $\nu$ direction, for example, $U_\mu(x)$ goes from bottom left to bottom right on the diagram and $U_\nu(x)$ goes bottom left to top left, but what do these directions actually mean? Are both of these directions somehow along the same 1-D axis $x$? Or is $\mu$ is in the direction of the specified axis and $\nu$ is in the direction of time? (Both of these ideas do not work since you cannot go in two perpendicular directions on a 1-D line and $\mu$ and $\nu$ both apply to link variables with time; $U_\mu(t)$ and $U_\nu(t)$ exist)

It would also be great to know what 2-D slice of the 4-D lattice the diagram represents and the relative coordinates of the sites shown.

Diagram taken from https://fse.studenttheses.ub.rug.nl/20342/1/BRP_Thesis_Piter_Annema.pdf page 12

I'm currently coding a lattice QCD project and ran into an issue with my understanding.

A link variable connecting two points could be in the µ or v direction, for example, Uµ(x) goes from bottom left to bottom right on the diagram and Uv(x) goes bottom left to top left, but what do these directions actually mean? Are both of these directions somehow along the same 1-D axis x? Or is µ is in the direction of the specified axis and v is in the direction of time? (Both of these ideas do not work since you cannot go in two perpendicular directions on a 1-D line and µ and v both apply to link variables with time; Uµ(t) and Uv(t) exist)

It would also be great to know what 2-D slice of the 4-D lattice the diagram represents and the relative coordinates of the sites shown.

Diagram taken from https://fse.studenttheses.ub.rug.nl/20342/1/BRP_Thesis_Piter_Annema.pdf page 12

I'm currently coding a lattice QCD project and ran into an issue with my understanding.

A link variable connecting two points could be in the $\mu$ or $\nu$ direction, for example, $U\mu(x)$ goes from bottom left to bottom right on the diagram and $U\nu(x)$ goes bottom left to top left, but what do these directions actually mean? Are both of these directions somehow along the same 1-D axis x? Or is $\mu$ is in the direction of the specified axis and $\nu$ is in the direction of time? (Both of these ideas do not work since you cannot go in two perpendicular directions on a 1-D line and $\mu$ and $\nu$ both apply to link variables with time; $U\mu(t)$ and $U\nu(t)$ exist)

It would also be great to know what 2-D slice of the 4-D lattice the diagram represents and the relative coordinates of the sites shown.

Diagram taken from https://fse.studenttheses.ub.rug.nl/20342/1/BRP_Thesis_Piter_Annema.pdf page 12