---

Prog. Theor. Phys. Vol. 70 No. 1 (1983) pp. 18-35

Lagrangian Mechanics of Massless Particles with Spin

Takeshi Shirafuji

Physics Department, Saitama University, Urawa, Saitama 338

(Received February 10, 1983)

Abstract:

Lagrangian mechanics of massless particles with spin is studied, based on the interpretation that spin corresponds to displacement in complex directions. Starting with the action integral which ensures the masslessness of particles, two possibilities to introduce spin are investigated. In both cases, the equations of motion cannot fix the world line of massless spinning particles uniquely, due to a “gauge” invariance property of the action integral. The space-time coordinates are not the most suitable for describing massless spinning particles, but it is convenient to take a pair of spinor variables, i.e., a twistor, as the basic dynamical variables to which the canonical quantization procedure can be applied. In one of the two cases, where massless particles are considered to move in superspace with N spinor coordinates, it is found that massless particles form a spin (or helicity) multiplet with the helicity running from -N/4 to +N/4.

URL : http://ptp.ipap.jp/link?PTP/70/18/
DOI : 10.1143/PTP.70.18

[ Full Text PDF : FREE ACCESS (842K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

---

References:

1. C. Fronsdal, Phys. Rev. D 18 (1978), 2624[APS].
   J. Fang and C. Fronsdal, Phys. Rev. D 18 (1978), 3630[APS].
   F. A. Berends, J. W. von Holton, P. van Nieuwenhuizen and B. de Wit, Phys. Lett. B 83 (1979), 188[CrossRef]; Nucl. Phys. B 154 (1979), 261[CrossRef].
   B. de Wit and D. Z. Freedman, Phys. Rev. D 21 (1980), 358[APS].
2. C. Fronsdal, in Supergravity, ed. P. van Nieuwenhuizen and D. Z. Freedman (North-Holland, Amsterdam, 1979), p. 245.
   C. Aragon and S. Deser, Phys. Lett. B 86 (1979), 161[CrossRef].
   B. de Wit and D. Z. Freedman, cited in Ref. 1).
   F. A. Berends, J. W. van Holten, B. de Wit and P. van Nieuwenhuizen, J. of Phys. A 13 (1980), 1643[CrossRef].
3. R. Penrose, J. Math. Phys. 8 (1967), 345[CrossRef]; in Quantum Gravity, ed. C. J. Isham, R. Penrose and D. W. Sciama (Oxford Univ. Press, Oxford, 1975), p. 268; Rep. Math. Phys. 12 (1977), 65; in Quantum Gravity 2, ed. C. J. Isham, R. Penrose and D. W. Sciama (Oxford Univ. Press, Oxford, 1981), p. 578.
   R. Penrose and M. A. H. MacCallum, Phys. Rep. C 6 (1973), 241[CrossRef].
4. R. Penrose, J. Math. Phys. 10 (1969), 38[CrossRef].
5. R. Penrose, Int. J. Theor. Phys. 1 (1968), 61.
6. R. Penrose, Gen. Relat. Gravit. 7 (1976), 31.
   R. S. Ward, Phys. Lett. A 61 (1977), 81[CrossRef]; Proc. R. Soc. (London) A 363 (1978), 289.
7. C. Møller, Commun. Dublin Inst. Adv. Studies A No. 5 (1949).
8. R. Penrose and M. A. H. MacCallum, cited in Ref. 3).
9. E. T. Newman and J. Winicour, J. Math. Phys. 15 (1974), 1113[CrossRef].
10. A. Salam and J. Strathdee, Nucl. Phys. B 76 (1974), 477[CrossRef].
11. A. Ferber, Nucl. Phys. B 132 (1978), 55[CrossRef].
12. R. Casalbuoni, Nuovo Cim. A 33 (1976), 389.
13. S. Coleman and J. Mandula, Phys. Rev. 159 (1967), 1251[APS].
14. J. Wess and B. Zumino, Nucl. Phys. B 70 (1974), 39[CrossRef].
15. M. G. Eastwood, R. Penrose and R. O. Wells, Commun. Math. Phys. 78 (1981), 305[CrossRef]; earlier references are cited therein.

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 80 No. 1 (1988) pp. 1-6 :

   Superparticles and Division Algebras

   Tadahiko Kimura and Ichiro Oda

2. Progress of Theoretical Physics Vol. 80 No. 3 (1988) pp. 367-372 :

   Superparticles and Division Algebras

   Ichiro Oda, Tadahiko Kimura and Atsushi Nakamura

3. Progress of Theoretical Physics Vol. 124 No. 6 (2010) pp. 969-994 :

   Spinor and Twistor Formulations of Tensionless Bosonic Strings in Four Dimensions

   Shinichi Deguchi, Takeshi Egami and Jun-ichi Note

---

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.