Spinor symmetries and underlying properties
J. M. Hoff da Silva, R. T. Cavalcanti, D. Beghetto, and R. da Rocha
TL;DR
This paper investigates the symmetries of spinor spaces with spin 1/2 representations, revealing a Lie group structure and connecting Dirac dynamics to fluid-like behavior in spinor space.
Contribution
It demonstrates that spinor symmetries form a Lie group and links massless Dirac dynamics to incompressible fluid behavior within spinor space.
Findings
Spinor symmetries form a Lie group.
Dirac dynamics relate to fluid behavior in spinor space.
Massless spinors exhibit incompressible fluid dynamics.
Abstract
By exploring a spinor space whose elements carry a spin 1/2 representation of the Lorentz group and satisfy the the Fierz-Pauli-Kofink identities we show that certain symmetries operations form a Lie group. Moreover, we discuss the reflex of the Dirac dynamics in the spinor space. In particular, we show that the usual dynamics for massless spinors in the spacetime is related to an incompressible fluid behavior in the spinor space.
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