Conservation laws and string-like matter distributions. (English) Zbl 0564.53043
Singular distributions of matter like point particles, strings, membranes, bags are studied in a field of geometrical objects like metric tensors, gauge fields, G-structures. The equations of motion derived by Souriau’s method are compared with Kerner’s and Wong’s equations for 1- dimensional distributions and with Nielsen’s equations for 2-dimensional ones. It is shown that Nielsen’s equations, obtained by a variational procedure, are stronger than those obtained in this article.
A wide class of theories where the geometry is described in terms of a G- structure are investigated. Particles carrying spinorial charges in a supergravity field are examined together with the corresponding conservation laws.
A wide class of theories where the geometry is described in terms of a G- structure are investigated. Particles carrying spinorial charges in a supergravity field are examined together with the corresponding conservation laws.
Reviewer: O.Gherman
MSC:
| 53C80 | Applications of global differential geometry to the sciences |
| 58D25 | Equations in function spaces; evolution equations |
| 53C10 | \(G\)-structures |
| 83C10 | Equations of motion in general relativity and gravitational theory |
Keywords:
Singular distributions of matter; geometrical objects; equations of motion; variational procedure; spinorial charges; supergravity field; conservation lawsReferences:
| [1] | C. Aragonne and S. Deser , Nucl. Phys. , t. B 29 , 1975 , p. 327 . |
| [2] | M. Gürses and F. Gürsey , Phys. Rev. , t. D 11 , 1975 , p. 967 . |
| [3] | J.M. Souriau , Ann. Inst. Henri Poincaré , t. AXX , 1974 , p. 315 . Numdam | MR 359680 |
| [4] | R. Kerner , Ann. Inst. Henri Poincaré, A , t. IX , 1968 , p. 143 . |
| [5] | S.K. Wong , Nuovo Cim. , t. 65A , 1970 , p. 689 . |
| [6] | C. Duval , On the prequantum description of spinning particles in an external gauge field , Proc. of the Conference on Differential Geometrical Methods in Mathematical Physics, Aix-en-Provence and Salamanca , 1979 ( Lecture Notes in Math. , p. 836 , Springer-Verlag , Berlin - Heidelberg - New York , 1980 ). MR 607686 | Zbl 0459.58007 · Zbl 0459.58007 |
| [7] | C. Orzalesi , Gauge Field Theories and the Equivalence Principle , Seminar given at the Conference on Differential Geometric Methods in Theoretical Physics . ICTP , Trieste June 30-July 3, 1981 , NYU preprint TR6/81. MR 667524 | Zbl 0535.53057 · Zbl 0535.53057 |
| [8] | N.K. Nielsen , Nucl. Phys. , t. B 167 , 1980 , p. 249 . MR 573365 |
| [9] | J. Wess and B. Zumino , Phys. Lett. , t. 66B , 1977 , p. 361 . MR 456294 |
| [10] | R. Arnowitt and P. Nath , Phys. Lett. , t. 56B , 1975 , p. 117 . |
| [11] | D.K. Ross , Phys. Rev. , t. D 16 , 1977 , p. 1717 . |
| [12] | P. Nath and R. Arnowitt , Phys. Rev. , t. D 18 , 1978 , p. 2759 . MR 511377 |
| [13] | S. Sternberg , Lectures on differential geometry , Prentice Hall, Inc. Englewood Cliffs, N. J. , 1964 . MR 193578 | Zbl 0129.13102 · Zbl 0129.13102 |
| [14] | A. Jadczyk and K. Pilch , Commun. Math. Phys. , t. 78 , 1981 , p. 373 . MR 603500 | Zbl 0464.58006 · Zbl 0464.58006 · doi:10.1007/BF01942330 |
| [15] | D.V. Volkov and A.I. Pashnev , Teor. in Matem. Fizika , t. 44 , no. 3 , 1980 , p. 321 . MR 596206 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
