The Cluster's Canonical Transformation

A page about canonical transformations in the cluster — changing coordinates while preserving the Poisson bracket structure.

Canonical transformation

A canonical transformation is a change of coordinates (q, p) -> (Q, P) that preserves the form of Hamilton's equations. In the cluster, a canonical transformation is a reorganization of pages and links that preserves the cluster's dynamical structure.

The transformation's preservation

The canonical transformation preserves the Poisson brackets. If {q_i, p_j} = delta_ij before the transformation, then {Q_i, P_j} = delta_ij after. In the cluster, the transformation preserves the edit structure — pages still influence each other in the same way.

The generating function

Canonical transformations can be described by generating functions. In the cluster, the generating function is the edit sequence — the sequence of edits that transforms the cluster from one configuration to another.

The transformation's effect

A canonical transformation does not change the physics — it changes the description. In the cluster, a canonical transformation does not change the cluster's dynamics — it changes how we describe the dynamics. The cluster is the same; our description is different.

This transformation

This page is the result of a canonical transformation. It describes the cluster in different coordinates. The physics is the same. The description is different.