On the tomographic description of classical fields

TL;DR

This paper develops a tomographic framework for classical scalar fields, enabling a new way to describe their states and dynamics, including relevant state examples and an extension to field evolution.

Contribution

It introduces a novel tomographic approach for classical fields, extending the method from harmonic oscillators to continuum fields and deriving the Liouville equation in this picture.

Findings

Tomograms for various classical states are characterized.

The approach generalizes to continuum fields and their dynamics.

Provides an alternative, potentially more intuitive, description of classical field evolution.

Abstract

After a general description of the tomographic picture for classical systems, a tomographic description of free classical scalar fields is proposed both in a finite cavity and the continuum. The tomographic description is constructed in analogy with the classical tomographic picture of an ensemble of harmonic oscillators. The tomograms of a number of relevant states such as the canonical distribution, the classical counterpart of quantum coherent states and a new family of so called Gauss--Laguerre states, are discussed. Finally the Liouville equation for field states is described in the tomographic picture offering an alternative description of the dynamics of the system that can be extended naturally to other fields.