Kanon

Field theory is a branch of physics. The two most important applications of field theory are

- Quantum field theory (Particle physics)
- Critical phenomena (Continuous phase transitions)

The FREEWARE software tool "kanon" automates the process of determining the critical and canonical dimensions of field theoretic models (that is, the dimensions of coupling constants, fields and coordinates). It is useful for constructing and checking new models. A "model" in this context is the matrix of the Exponents occurring in the Hamiltonian or Lagrangian.

The calculation of canonical dimensions is a matter of Linear Algebra, but the automatisation of the process illustrates the following points:

- To calculate canonical dimensions requires at least as many terms in the Hamiltonian/Lagrangian as there are coordinates and fields (the "model order").
- Below the critical dimension, the canonical dimensions are not unique. They depend on which terms will be fixed in the renormalization procedure and to which terms a coupling constant (with some wave vector dimension) will be assigned. It suffices to have one coupling constant for the first "model order" terms. For every additional term another coupling constant is required.
- There is a Geometric interpretation for the dimensional Analysis: The terms Hamiltonian or Lagrangian define a hyperplane in an exponent space. The normal vector to this hyperplane (the canonical dimensions) together with the critical dimension are a good signature for a critical model.