No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Particle symmetry and antisymmetry in approximately relativistic Lagrangians
1.H. W. Woodcock and P. Havas, Phys. Rev. D 6, 3422 (1972). Referred to here both as part I and as WH, the latter to avoid confusion with interaction terms denoted by I.
2.Invariance under the proper orthochronous subgroup of the full inhomogeneous Lorentz group (called the Poincaré group) is the physically important invariance group and it is this subgroup which is meant here.
3.P. Havas, in Problems in the Foundations of Physics, edited by M. Bunge (Springer, Berlin, 1971), p. 31; errata are in footnote 37 of WH.
4.A. D. Fokker, Z. Physik 58, 386 (1929).
5.H. W. Woodcock, Phys. Rev. D 17, 1539 (1978), referred to as II; errata to I are in II. Errata to II precede these footnotes.
6.W. N. Herman and P. Havas, Phys. Rev. D 17, 1985 (1978), referred to as III.
7.Equations (WH75c), (II25a′), and (III49d).
8.Reference 1, immediately below Eq. (WH62). In II, it adds: “at most a constant to the action principle,” immediately below Eq. (II24), while in III, it is: “omitting the irrelevant integrated term,” below Eq. (IIIA14).
9.H. W. Woodcock, Temple University thesis, 1972 (unpublished), Appendix B. This alternative calculation of the ARL was done not by by which is a monotonic variable change only to order
10.W. N. Herman, Temple University thesis, 1976 (unpublished), Appendix B. 1.
11.The notations of WH, II, and III were slightly different, adapted to their purposes. Here we use mainly the notations of II, where, e.g., the coupling constants used in WH have been absorbed into
12.The notation of III is chosen for it is slightly different in WH and II.
13.Nonstatic limits are also possible and were discussed in WH.
14.K. G. Dedrick and E. L. Chu, Arch. Ration. Mech. Anal. 16, 385 (1964).
15.Reference 1, p. 3431, immediately below Eq. (WH62).
16.K. Nordtvedt, Astrophys. J. 297, 390 (1985).
17.Equation is found in Ref. 5 in the “Notes added in proof; the term there is omitted here and the names of the functions have been simplified, e.g., replaces etc.
18.In four‐dimensional form, and or expresses reversal of time. Since only or of the four Poincaré invariants are odd in and [Eqs. (11)], only ’s that are odd in the pair of variables and are non‐time‐reversal invariant.
19.Equations (II56) and (II57).
20.J. Martin and J. L. Sanz, J. Math. Phys. 19, 780 (1978).
21.For an alternative canonical approach, see M. Pauri and G. M. Prosperi, J. Math. Phys. 17, 1468 (1976).
22.D. G. Currie, T. F. Jordan, and E. C. G. Sudarshan, Rev. Mod. Phys. 35, 350 (1963).
23.See, e.g., I. M. Gel’fand and G. E. Shilov, Generalized Functions (Academic, New York, 1964), Vol. 1, p. 21.
24.J. Stachel and P. Havas, Phys. Rev. D 12, 1598 (1976).
25.The method of Ref. 24 yields our form when instead of the choice of particular solution given in their Eq. (A17), one chooses (in their notation with ) together with in place of their Eq. (69). [Note that the factor of in their Eq. (69) should be a ]. Finally, letting yields our result.
26.F. Coester and P. Havas, Phys. Rev. D 14, 2556 (1976).
27.To obtain our form via the derivation in Ref. 26, simply replace their definitions (106) of the arbitrary functions X and Y by and use these in their Eqs. (85), (87), and (104) together with
28.R. W. Childers, Phys. Rev. D 36, 606, 3813 (1987).
Article metrics loading...
Full text loading...