The possibility of tachyons as soliton solutions in 3+1 dimensions via k-field models

Tachyons or hypothetical faster-than-light (FTL) particles would fail the principle of causality. Such particles may only be imagined when they have no energy and momentum and, thus, no observable interaction. In this paper, we show that the classical relativistic field theory with non-standard Lagrangian densities ($k$-field models) does not rule out the existence of FTL particle-like solutions (solitons) with zero energy and momentum in $3+1$ dimensions. However, contrary to our expectation, we show that it is possible to have $k$-field models that lead to energetic FTL soliton solutions in $3+1$ dimensions.