Verification and Invalidation of the Theory of Symplectic Manifold with Contact Degeneracies as Applied to the Classical Field Theory

TL;DR

This paper critically examines the SMCD theory's predictions regarding electromagnetic field fronts, comparing it with classical wave analysis, and finds that the SMCD theory's predictions are not supported by established methods.

Contribution

The paper provides a verification and invalidation of the SMCD theory's application to electromagnetic field fronts using classical wave analysis.

Findings

SMCD theory's predictions do not align with classical wave analysis results.

Comparison shows inconsistency between SMCD and established methods.

Supports the validity of classical wave methods over SMCD in this context.

Abstract

A theory of Symplectic Manifold with Contact Degeneracies (SMCD) was developed in [Zot'ev,2007]. The symplectic geometry employs an anti-symmetric tensor (closed differential form) such as a field tensor used in the classical field theory. The SMCD theory studies degeneracies of such form. In [Zot'ev,2011] the SMCD theory was applied to study a front of an electromagnetic pulsed field propagating into a region with no field. Here, the result of [Zot'ev,2011] is compared with the problem solution obtained using the well-known method presented in Whitham, G.B., Linear and nonlinear waves, 1974. It is shown that the SMCD theory prediction is not supported by the result obtained with the Whitham method.