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Twistor formulation of a massive particle with rigidity
A massive rigid particle model in dimensions is reformulated in terms
of twistors. Beginning with a first-order Lagrangian, we establish a twistor
representation of the Lagrangian for a massive particle with rigidity. The
twistorial Lagrangian derived in this way remains invariant under a local transformation of the twistor and other relevant variables.
Considering this fact, we carry out a partial gauge-fixing so as to make our
analysis simple and clear. We develop the canonical Hamiltonian formalism based
on the gauge-fixed Lagrangian and perform the canonical quantization procedure
of the Hamiltonian system. Also, we obtain an arbitrary-rank massive spinor
field in dimensions via the Penrose transform of a twistor function
defined in the quantization procedure. Then we prove, in a twistorial fashion,
that the spin quantum number of a massive particle with rigidity can take only
non-negative integer values, which result is in agreement with the one shown
earlier by Plyushchay. Interestingly, the mass of the spinor field is
determined depending on the spin quantum number.Comment: 50 pages, Section 6 is revised, A reference added, minor corrections,
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