Summary
The finite particle propagator can be constructed by a path integral method provided the infinitesimal propagator is known. Hitherto, however, it has not been possible to specify the relativistic infinitesimal propagator except in anad hoc way. From consideration of the nature of mass, in a Machian cosmological sense, it is shown in the present paper that the infinitesimal propagator can be derived in relativistic quantum mechanics by a method similar to that used in the nonrelativistic path integral.
Riassunto
Si può costruire il propagatore finito delle particelle per mezzo di un metodo di integrale di percorso purché sia noto il propagatore infinitesimo. Sinora però non è stato possibile specificare il propagatore inflnitesimo relativistico eccetto chead hoc. Da considerazioni sulla natura della massa, nel senso cosmologico machiano, si mostra in questo articolo che si può dedurre il propagatore infinitesimo nella meccanica quantistica relativistica con un metodo simile a quello usato nell’integrale di percorso non relativistico.
Реэюме
Конечный пропагатор частиц может быть сконструирован с помошью метода интегрирования по путям, при условии, что иэвестен бесконечно малый пропагатор. До сих пор однако не было воэможно определить релятивистский бесконечно малый пропагатор, эа исключением специального способа. Иэ рассмотрения природы массы, в космологическом смысле Макиана, в настояшей работе покаэывается, что бесконечно малый пропагатор может быть выведен в релятивистской квантовой механике с помошью метода, аналогичного методу в нерелятивистском случае, испольэуюшему интегрирование по путям.
Similar content being viewed by others
References
F. Hoyle andJ. V. Narlikar:Ann. of Phys.,54, 207 (1969).
F. Hoyle andJ. V. Narlikar:Ann. of Phys.,62, 44 (1971).
F. Hoyle andJ. V. Narlikar:Proc. Roy. Soc., A282, 191 (1964).
F. Hoyle andJ. V. Narlikar:Proc. Roy. Soc., A294, 138 (1966).
F. Hoyle andJ. V. Narlikar:Gamow Memorial Volume.
S. W. Hawking:Proc. Roy. Soc., A285, 313 (1965).
In their bookQuantum Mechanies and Path Integrals Feynmann andHibbs give a problem (p. 34) in which the propagator in one space-one time dimension is built up from paths of this kind. The resulting propagator satisfies the two-dimensional Dirac equation.
Author information
Authors and Affiliations
Additional information
On a visit to the Department of Physics and Astronomy, University of Maryland, College Park, Md., under contract No. NGL 21-002-033.
Rights and permissions
About this article
Cite this article
Hoyle, F., Narlikar, J.V. On the relation of the infinitesimal particle propagator to the nature of mass. Nuov Cim A 7, 242–261 (1972). https://doi.org/10.1007/BF02728689
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02728689