TL;DR
This paper extends Dirac's approach to membranes in four-dimensional spacetime, resulting in a Lorentz-invariant equation that predicts a hierarchy of masses without tachyons.
Contribution
It introduces a novel Dirac-like equation for membranes, providing a new theoretical framework for understanding extended objects in quantum field theory.
Findings
Predicts an infinite hierarchy of positive and negative masses.
Ensures Lorentz invariance of the membrane equation.
No tachyonic solutions are present.
Abstract
Dirac's idea of taking the square root of constraints is applied to the case of extended objects concentrating on membranes in D=4 space-time dimensions. The resulting equation is Lorentz invariant and predicts an infinite hierarchy of positive and negative masses (tension). There are no tachyonic solutions.
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