General Lagrangian of Non-Covariant Self-dual Gauge Field

TL;DR

This paper develops a general non-covariant Lagrangian framework for self-dual gauge theories, demonstrating Lorentz invariance of the resulting equations and extending the approach to higher dimensions including 10D.

Contribution

It introduces a unified formulation of non-covariant self-dual gauge theories applicable in various spacetime decompositions and dimensions, with detailed proofs of self-duality and Lorentz invariance.

Findings

General non-covariant Lagrangian formulated for self-dual gauge fields

Proved self-duality property of the Lagrangian

Field equations exhibit 6D Lorentz invariance

Abstract

We present the general formulation of non-covariant Lagrangian of self-dual gauge theory. After specifying the parameters therein the previous Lagrangian in the decomposition of spacetime into $6=D_1+D_2$ and $6=D_1+D_2+D_3$ can be obtained. The self-dual property of the general Lagrangian is proved in detail. We furthermore show that the new non-covariant actions give field equations with 6d Lorentz invariance. The method can be straightforward extended to any dimension and we also give a short discussion about the 10D self-dual gauge theory.