Supersymmetry and the physical phase space formulation of spinning particles

Gauntlett, Jerome P.; Gomis, J.; Townsend, P.K.

doi:10.1016/0370-2693(90)90294-G

Supersymmetry and the physical phase space formulation of spinning particles

Jerome P. Gauntlett
(
- Cambridge U.
)
,
J. Gomis
(
- Barcelona U.
)
,
P.K. Townsend
(
- Cambridge U.
)

Aug 20, 1990

7 pages

Published in:

Phys.Lett.B 248 (1990) 288-294

Published: 1990

DOI:

10.1016/0370-2693(90)90294-G

Report number:

DAMTP-R-90-16,
UB-ECM-PF-13-90

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Abstract: (Elsevier)

We present an action for the relativistic spin- 1 2 particle, with non-linearly realised Lorentz invariance, in terms of physical phase-space variables only. It is the relativistic counterpart of a standard form of the non-relativistic spin- 1 2 particle action. On quantisation of the non-relativistic particle, galilean supersymmetry is crucial to the recovery of the Levy-Leblond equation as the square root of the Schrödinger equation. The Dirac equation is not obtained in a similar way from quantisation of the relativistic particle because supersymmetry implies positive energy. Instead, the pair of Schrödinger equations for positive and negative energy yield the Foldy-Wouthuysen transform of the Dirac equation.

mechanics: classical
particle: relativistic
spin: 1/2
1/2: spin
supersymmetry: superspace
mechanics: action
wave function
Dirac equation
Levy-Leblond equation
Foldy-Wouthuysen transformation

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