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A Classical and Spinorial Description of the Relativistic Spinning Particle | | Trevor Rempel
; Laurent Freidel
; | | Date: |
2 Dec 2016 | | Abstract: | In a previous work we showed that spin can be envisioned as living in a phase
space that is dual to the standard phase space of position and momentum. In
this work we demonstrate that the second class constraints inherent in this
"Dual Phase Space" picture can be solved by introducing a spinorial
parameterization of the spinning degrees of freedom. This allows for a purely
first class formulation that generalizes the usual relativistic description of
spinless particles and provides several insights into the nature of spin and
its relationship with spacetime and locality. In particular, we find that the
spin motion acts as a Lorentz contraction on the four-velocity and that, in
addition to proper time, spinning particles posses a second gauge invariant
observable which we call proper angle. Heuristically, this proper angle
represents the amount of Zitterbewegung necessary for a spin transition to
occur. Additionally, we show that the spin velocity satisfies a causality
constraint, and even more stringently, that it is constant along classical
trajectories. This leads to the notion of "half-quantum" states which violate
the classical equations of motion, and yet do not experience an exponential
suppression in the path integral. Finally we give a full analysis of the
Poisson bracket structure of this new parametrization. | | Source: | arXiv, 1612.0551 | | Services: | Forum | Review | PDF | Favorites | |
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