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Radiation fields of a uniformly accelerating point source in the framework of Stueckelberg’s manifestly covariant relativistic dynamics
1.A far from inclusive list includes Refs. 15–17, 20, 23, 26, 36, 37, 43, 45, and 48.
2.The exact form of the hypercone depends on the choice of (4,1) or (3,2) metric of the field.
3.Applies to any odd dimensional space-time.
4.In the nonrelativistic limit, the mass distribution converges to a single point; one may choose the parameter to have this Galilean target mass value (Ref. 18). We shall assume that has this value in the following.
5.Recall that is the dimensionality of the overall system.
6.Strictly speaking, it is which would be the spatial distance, and not .
7.For example, in Phillips’s book (Ref. 38), it is shown that most of the contribution to a solution of the wave equation emerges along a characteristic surface, i.e., the null cone.
8.Or even in higher dimensional Maxwell electrodynamics, e.g., see Refs. 21, 25, 30, and 34.
9.Indeed, the very separation to radiation zone in odd dimensional space-times is far less obvious, if it is at all possible.
10.Aharonovich, I. and Horwitz, L. P. , “Green-Functions for wave propagation on a five-dimensional manifold and the associated gauge fields generated by a uniformly moving point source,” J. Math. Phys. 47, 122902 (2006).
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12.Arshansky, R. and Horwitz, L. P. , “The quantum relativistic two-body bound state. ii. the induced representation of sl(2,c),” J. Math. Phys. 30, 380 (1989).
14.Bailey, D. H. , Yozo, H. , Li, X. S. , and Thompson, B. , ARPREC, An arbitrary precision computation package, Lawrence Berkeley National Laboratory, Paper LBNL-53651, 2002.
15.Bondi, H. and Gold, T. , “The field of a uniformly accelerated charge, with special reference to the problem of gravitational acceleration,” Proc. R. Soc. London, Series A 229, 416 (1955).
18.Burakovsky, L. , Horwitz, L. P. , and Schieve, W. C. , “New relativistic high-temperature Bose-Einstein condensation,” Phys. Rev. D 54, 4029 (1996);
18.T. Jordan, personal communication.
22.Gel’fand, I. M. and Shilov, G. E. , Generalized Functions, Properties and Operations, volume 1 of Generalized Functions (Academic, New York, 1964) (translated from Russian).
24.Gough, Brian J. , GNU Scientific Library Reference Manual, 3rd ed. (Network Theory, 2009).
28.Horwitz, L. P. and Piron, C. , “Relativistic dynamics,” Helv. Phys. Acta 46, 316 (1973);
28.Fock, V. , “Proper time in classical and quantum mechanics,” Phys. Z. Sowjetunion 12, 404 (1937);
29.Jackson, J. D. , Classical Electrodynamics, 3rd ed. (Wiley, New York, 1998).
30.Kazinski, P. O. , Lyakhovich, S. L. , and Sharapov, A. A. , “Radiation reaction and renormalization in classical electrodynamics of a point particle in any dimension,” Phys. Rev. D 66, 025017 (2002);
31.Land, M. C. and Horwitz, L. P. , “Green’s functions for off-shell electromagnetism and spacelike correlations,” Found. Phys. 21, 299 (1991).
32.Land, M. C. , Shnerb, N. , and Horwitz, L. P. , “On Feynman’s approach to the foundations of gauge theory,” J. Math. Phys. 36, 3263 (1995).
33.Lindner, F. , Schatzel, M. G. , Walther, H. , Baltuska, A. , Goulielmakis, E. , Krausz, F. , Milosevic, D. B. , Bauer, D. , Becker, W. , and Paulus, G. G. , “Attosecond double-slit experiment,” Phys. Rev. Lett. 95, 040401 (2005);
33.see also Palacios, A. , Rescigno, T. N. , and McCurdy, C. W. , “Two-electron time-delay interference in atomic double ionization by attosecond pulses,” Phys. Rev. Lett. 103, 253001 (2009).
38.Peter, D. , Lax. Hyperbolic Partial Differential Equations (American Physical Society, College Park, MD, 2006), Chap. 7.
40.Riesz, M. , “Intégrales de Riemann-Liouville et potentiels,” Acta Sci. Math. 9, 1 (1938).
42.Rindler, W. , Introduction to Special Relativity, 2nd ed. (Oxford University Press, Oxford, 1991).
43.Rohrlich, F. , Classical Charged Particles (Wiley, New York, 1990).
44.Saad, D. , Horwitz, L. P. , and Arshansky, R. I. , “Off-shell electromagnetism in manifestly covariant relativistic quantum mechanics,” Found. Phys. 19, 1125 (1989);
44.Barut, A. O. and Bohm, A. , “Reduction of a class of O(4, 2) representations with respect to SO(4, 1) and SO (3, 2),” J. Math. Phys. 11, 2938 (1970);
44.Barut, A. O. , “Derivation of mass spectrum and magnetic moments from current conservation in relativistic O(3, 2) and O(4, 2) theories,” Phys. Rev. 167, 1527 (1968);
44.Barut, A. O. , Cordero, P. and Ghirardi, G. C. , “A unified theory of leptons,” International Atomic Energy Agency, ICTP, Miramare-Trieste, 1968;
44.Barut, A. O. and Raczka, R. , Theory of Group Representations (World Scientific, Singapore, 1986);
44.related studies of relativistic systems can be found in selected papers of Thirring, W. E. (AMS, Providence, 1998).
45.Singal, A. K. , “The equivalence principle and an electric charge in a gravitational field II. A uniformly accelerated charge does not radiate,” Gen. Relativ. Gravit. 29, 1371 (1997).
46.Stueckelberg, E. C. G. , Helv. Phys. Acta 14, 372 (1941).
47.Stueckelberg, E. C. G. , Helv. Phys. Acta 15, 23 (1942).
48.Vallisneri, M. , “Relativity and acceleration. Ph.D. thesis, Università Degli Studi di Parma, 2000.
49.Zozulya, V. , “Regularization of the divergent integrals. I. General consideration,” Electronic Journal of Boundary Elements 4, 49 (2006).
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