sun_diffusion.action module¶

Physical actions as functions of field configurations.

class sun_diffusion.action.SUNToyAction(beta)¶

Bases: Action

Toy action on a single \({\rm SU}(N)\) matrix defined by

\[S(U) = -\frac{\beta}{N}{\rm Re}{\rm Tr}(U)\]

__call__(U)¶

Computes the action as a function of group elements U.

class sun_diffusion.action.SUNToyPolynomialAction(beta, coeffs=[1.0, 0.0, 0.0])¶

Bases: Action

Toy polynomial action over a single \({\rm SU}(N)\) matrix.

The action is defined as in Eqn. (18) of 2008.05456.

\[S(U) = -\frac{\beta}{N}{\rm Re}{\rm Tr}\left[\sum_{n} c_n U^n\right],\]

where \(U^n\) denotes repeated matrix multiplication.

Parameters:

__call__(U)¶

Computes the action as a function of group elements U.

value_eigs(thetas)¶

Evaluates the action in terms of the matrix eigenangles thetas.

In the angular representation, the action is given by

\[S(\theta) = -\frac{\beta}{N} \sum_n c_n \sum_j\cos(n \theta_j)\]

force_eigs(thetas)¶

Evaluates the force as a function of the matrix eigenangles thetas.

In the angular representation, the force is given by

\[F(\theta) = -\frac{\beta}{N} \sum_n n c_n \sin(n\theta)\]

class sun_diffusion.action.SUNPrincipalChiralAction(beta)¶

Bases: Action

Action for the \({\rm SU}(N) \times {\rm SU}(N)\) Principle Chiral model on the lattice.

The action is defined as

\[S[U] = -\beta N \sum_x \sum_\mu {\rm Re}{\rm Tr}\left[ U^\dagger(x) U(x + \hat{\mu}) \right]\]

This theory enjoys two noteworthy symmetries: