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This article is cited in 13 scientific papers (total in 13 papers)
Lagrangian model of a massless particle on spacelike curves
A. P. Nersesyanab a Yerevan State University
b Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics
Abstract:
We consider a model of a massless particle in a $D$-dimensional space with the Lagrangian proportional to the $N$th extrinsic curvature of the world line. We present the Hamiltonian formulation of the system and show that its trajectories are spacelike curves satisfying the conditions $k_{N+a}=k_{N-a}$ and $k_{2N}=0$, $a=1,\dots,N-1$, where $N\leq\bigl[(D-2)/2\bigr]$. The first $N$ curvatures take arbitrary values, which is a manifestation of $N+1$ gauge degrees of freedom; the corresponding gauge symmetry forms an algebra of the $W$ type. This model describes $D$-dimensional massless particles, whose helicity matrix has $N$ coinciding nonzero weights, while the remaining $\bigl[(D-2)/2\bigr]-N$ weights are zero. We show that the model can be extended to spaces with nonzero constant curvature. It is the only system with the Lagrangian dependent on the world-line extrinsic curvatures that yields irreducible representations of the Poincaré group.
Received: 28.07.2000
Citation:
A. P. Nersesyan, “Lagrangian model of a massless particle on spacelike curves”, TMF, 126:2 (2001), 179–195; Theoret. and Math. Phys., 126:2 (2001), 147–160
Linking options:
https://www.mathnet.ru/eng/tmf423https://doi.org/10.4213/tmf423 https://www.mathnet.ru/eng/tmf/v126/i2/p179
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