SPACETIME STRUCTURE
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PERSONAL RESEARCH
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Books
D. H. Delphenich (ed.), Selected Papers on Teleparallelism, Neo-classical Press, Spring Valley, OH, 2013.
Published articles
D. H. Delphenich, "Pre-metric electromagnetism as a path to unification," in Unified Field Mechanics, eds. Amoroso, Kaufmann, Rowlands, World Scientific, New Jersey, 2016, arXiv:1512.05183.
D. H. Delphenich, “A more direct representation for complex relativity,” Ann. Phys. (Leipzig) 16 (2007) 615-639.
D. H. Delphenich, “Projective geometry and special relativity,” Ann. Phys. (Leipzig) 15 (2006), 216-246
Invited talk at University of Missouri – Columbia
D. H. Delphenich, “Projective geometry and spacetime structure”
arXiv.org uploads
D. H. Delphenich, "On the equations of diffracted geodesics," arXiv:2008.03113
D. H. Delphenich, "A pre-metric generalization of the Lorentz transformation," arXiv:2002.09500 .
D. H. Delphenich, "On geodesics of gradient-index optical metrics and the optical-mechanical analogy," arXiv:2002.04390 .
D. H. Delphenich, "On the risk of premature unification," arXiv:1811.06068
D. H. Delphenich, "Singular Teleparallelism," arXiv:1809.02663
D. H. Delphenich, "Teleparallelism as anholonomic geometry," arXiv:1808.09318
D. H. Delphenich, "Transverse momentum as a source of gravitoelectromagnetism," arXiv:1711.07953
D. H. Delphenich, "On the local integrability of almost-product structures defined by space-time metrics," arXiv:1607.03839
D. H. Delphenich, “Proper Time Foliations of Lorentz Manifolds,” arXiv:gr-qc/0211066
D. H. Delphenich, “Spacetime G-structures I: Topological Defects,” arXiv:gr-qc/0304016
D. H. Delphenich, “Spacetime G-structures II: geometry of the ground states,” arXiv:gr-qc/0401089
D. H. Delphenich, “Some Mathematical Issues Pertaining to Translational Gauge Theories,” arXiv:gr-qc/0401066
D. H. Delphenich, “Nonlinear connections and 1+3 splittings of spacetime, ” arXiv:gr-qc/0702115
D. H. Delphenich, “Transverse geometry and physical observers,” arXiv:0711.2033
D. H. Delphenich, "The use of the teleparallelism connection in continuum mechanics," arXiv:1305.3477
D. H. Delphenich, "On the electromagnetic constitutive laws that are equivalent to spacetime metrics," arXiv:1409.5107
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TRANSLATIONS
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G. Holzmuller, "On the application of the Jacobi-Hamilton method to the case of attraction according to Weber's electrodynamical laws," Zeit. Math. Phys. 15 (1870), 69-91.
F. Tisserand, "On the motion of planets around the Sun according to Weber's electrodynamical law," C. R. Acad. Sci. Paris 75 (1872), 760-763.
E. Schering, "Gravity in multiply-extended Gaussian and Riemannian spaces," Nachr. Kön. Ges. Wiss. Göttingen 6 (1873), 149-159.
F. Tisserand, "On the motion of planets when one supposes that the attraction is represented by either the electrodynamical law of Weber or that of Gauss," C. R. Acad. Sci. Paris 100 (1890), 313-315.
F. Klein, “On the geometric foundations of the Lorentz group,” Ges. math. Abh., pp. 555-574.
G. Herglotz, “On the mechanics of deformable bodies from the standpoint of relativity theory,” Ann. Phys. (Leipzig) (1911), 493-533.
M. Abraham, "On the theory of gravitation," Rend. Reale Accad. Lincei, cl. sci. fiz., mat. e nat. (5) 20 (1911), 678-682.
A. Einstein, "The speed of light and the statics of the gravitational field," Ann. Phys. (Leipzig) 38 (1912), 355-369.
M. Abraham, "On luminous and gravitational waves," Ann. Phys. (Leipzig) 3 (1912), 211-219.
M. Abraham, "A new theory of gravitation," Ann. Phys. (Leipzig) 4 (1912), 459-481.
G. Nordstrom, "The principle of relativity and gravitation," Phys. Zeit. 13 (1912), 1126-1129.
B. Caldonazzo, "Trajectories of light rays and material points in a gravitational field," Nuovo Cim. (5) 5 (1913), 267-300.
G. Nordstrom, "Inertial and gravitational mass in relativistic mechanics," Ann. Phys. (Leipzig) (4) 40 (1913), 856-878.
G. Nordstrom, "On the possibility of unifying the electromagnetic field and the gravitational field," Phys. Zeit. 15 (1914), 504-506.
F. Kottler, "The principle of relativity and accelerated motion," Ann. Phys. (Leipzig) (4) 44 (1914), 701-748.
F. Kottler, "Falling reference systems from the standpoint of the principle of relativity," Ann. Phys. (Leipzig) (4) 45 (1914), 481-516.
F. Kottler, "Relatively-accelerated motions and the conformal group of Minkowski space," Sitz. Ber. Kais. Akad. Wiss. 125 (1916), 899-919.
F. Kottler, "On Einstein's equivalence hypothesis and gravitation," Ann. Phys. (Leipzig) 50 (1916), 955-972.
A. Einstein, "On Friedrich Kottler's treatise "Uber Einsteins Aquivalenzhypothese und die Gravitation'," Ann. Phys. (Leipzig) 51 (1916), 955-972.
F. Klein, "On Hilbert's first note on the foundation of physics," Nachr. Kgl. Ges. Wiss. Gott. (1917).
T. Levi-Civita, "Einsteinian statics," Rend. Reale Accad. Lincei (5) 26 (1917), 458-470.
T. Levi-Civita, "Einstein's theory and Fermat's principle," Nuovo Cim. 16 (1918), 105-114.
T. Levi-Civita, "Einsteinian ds2 in Newtonian fields. I. Generalities and first approximation," Rend. Reale Accad. Lincei (5) 26 (1917), 307-317.
T. Levi-Civita, "The physical reality of some normal Bianchi spaces," Rend. Reale Accad. Lincei (5) 26 (1917), 519-531.
F. Klein, "On the differential laws for the conservation of impulse and energy in Einstein's theory of gravitation," Nachr. Kgl. Ges. Wiss. Gott. (1918).
F. Klein, "On the integral form of conservation laws and the theory of the spatially-closed world," Nachr. Kon. Ges. Wiss zu Gottingen (1918); Ges. math. Abh., v. I, art. XXXIII.
J. Lense and H. Thirring, "On the influence of the proper rotation of a central body on the motion of the planets and the moon, according to Einstein's theory of gravitation," Zeit. Phys. 19 (1918), 156-163.
H. Thirring, "On the effect of rotating distant masses in Einstein's theory of gravitation," Phys. Zeit. 19 (1918), 33-39.
H. Thirring, "On the formal analogy between the basic electromagnetic equations and Einstein's gravitational equations in the first approximation," Phys. Zeit. 19 (1918), 204-205.
H. Weyl, "Gravitation and Electricity," Sitz. Kon. Preuss. Akad. Wiss. (1918), 465-480.
H. Weyl, "A new extension of the theory of relativity," Ann. Phys. (Leipzig) (4) 59 (1919), 101-133.
A. Gullstrand, " General solution to the static one-body problem in Einstein's theory of gravitation," Arkiv for Matematik Astronomi och Physik 16 (1921), 1-15.
J. Soldner (1801)," On the deflection of a light ray from its rectilinear motion by the attraction of a celestial body that it passes close to," Ann. Phys. (Leipzig) 370 (1921), 593-604.
F. Kottler, "Rotating reference systems in a Minkowski space," Phys. Zeit. 22 (1921), 274-280.
H. Thirring, "Correction to my paper: 'On the effect of rotating distant masses in Einstein's theory of gravitation' ", Phys. Zeit. 22 (1921), 29-30.
A. Einstein, "On a natural extension of the foundations of the general theory of relativity," Sitz. preuss. Akad. Wiss. Math.-Phys. Kl. (1921), 261-264.
J. Le Roux, "Special relativity and the geometry of wave systems," J. math. pures appl. 1 (1922), 205-253.
E. Fermi, "On the phenomena that occur in the neighborhood of a time-line, I, II, III," Atti Acc. Maz. Lincei 31 (1922), 21-23, 51-52, 101-103.
F. Kottler, "Newton's laws and metrics," Sitz. d. Akad. d. Wiss. in Wien 131, Abt. 2a (1922), 1-14.
W. Gordon, “On the propagation of light in the theory of relativity,” Ann. Phys. (Leipzig) 72 (1923), 421-456.
D. Hilbert, "The foundations of physics," Math. Ann. 92 (1924), 1-32.
E. Schrodinger, "Fulfilling the demand of relativity in classical mechanics," Ann. Phys. (Leipzig) 382 (1925), 325-336.
A. Schidlof, "On the interpretation of the masses of the electron and proton in a five-dimensional," C. R. Acad. Sci. Paris 185 (1927), 889-891.
E. Wigner, "A remark about Einstein's new formulation of the principal of relativity," Zeit. Phys. 53 (1929), 592-596.
H. Weyl, "Electrons and gravitation. I," Zeit. Phys. 56 (1929), 330-352.
R. Zaycoff, "On a general form of the Dirac equation," Ann. Phys. (Leipzig) 7 (1930), 650-660.
Th. de Donder, "Einsteinian gravity," Ann. de l'Inst. H. Poincare 1 (1930), 77-116.
R. Zaycoff, "On Einstein's theory of teleparallelism," Zeit. Phys. 66 (1930), 572-576; "On Einstein's theory of teleparallelism (Second and final notice)," ibid. 67 (1931), 135-137; "Remarks and additions to my paper 'On Einstein's theory of teleparallelism,' " ibid. 69 (1931), 428-430.
A. Einstein and W. Mayer, “Unified theory of gravitation and electricity,” Sitz. Preuss. Akad. Wiss. (1931), 541-557.
E. Cartan, “The unitary theory of Einstein-Mayer,” Oeuvres complètes.
E. Schroedinger, "The Dirac electron in a gravitational field I," Sitzber. Preuss. Akad. Wiss., Phys-Math. Kl. (1932), 105-128.
W. Pauli, “On the formulation of the laws of Nature with five homogeneous components. Part I: classical theory,” Ann. Phys. (Leipzig) 18 (1933), 305-336; “Part II: the Dirac equation for matter waves,” 337-372.
O. Veblen, “Projective relativity theory,” Ergebnisse der Mathematik, v. 2, Springer, Berlin, 1933.
J. Weyssenhoff, "Inituitive aspects of the theory of relativity. I. Linear coordinates and gik coefficients in the the special theory of relativity," Zeit. Phys. 95 (1935), 391-408.
J. A. Schouten, "Projective relativity," Ann. de l'Inst. Henri Poincare 5 (1935), 51-88.
J. A. Schouten and J. Haantjes, :On the conformally-invariant form of the relativistic equations of motion." Proc. Kon. Akad. Wet. Amsterdam 39 (1936), 1059-1065.
G. Vranceanu, “On an anholonomic unitary theory of physical fields,” J. de Phys. 7 (7) (1936), 514-526.
J. Weyssenhoff, "Inituitive aspects of the theory of relativity. II. Space-time measurements in gravitational fields," Zeit. Phys. 107 (1937), 64-72.
J. Weyssenhoff, "Metric field and gravitational field," Bull. int. Acad. polonaise sci. et de lett. Cl. sci. math. et nat. (1937), 252-259.
K. Yano, “Non-holonomic relativity and the unitary theory of Einstein and Mayer,” Mathematica 14 (1938), 124-132.
J. Haantjes, "The equivalence of uniformly-accelerated observers for electromagnetic phenomena," Proc. Nat. Akad. Sci. 43 (1940), 1288-1299.
L. Rosenfeld, "On the energy-momentum tensor," Mémoires Acad. Roy. de Belgique 18 (1940), 1-30.
O. Costa de Beauregard, The Special Theory of Relativity, Masson and Co., Paris, 1949.
G. Ludwig, Progress in the Projective Theory of Relativity, Friedr. Wieweg and Son, Braunschweig, 1951.
A. Matte, "On some new oscillatory solutions of the equations of gravitation," Can. J. Math. 5 (1953), 1-16.
A. Lichnerowicz, " The relativistic theory of gravitation and electromagnetism, Masson and Co., Paris, 1955.
Book I: General relativity, Book II: Unitary theories.
Y. B. Rumer, Studies in 5-optics, State Publishing Office, Moscow, 1956.
R. Debever, “Super-energy in general relativity,” Bull. Soc. math. Belg. 10 (1958), 112-147.
A. Lichnerowicz, "On gravitational waves and radiation," C. R. Acad. Sci. Paris 246 (1958), 893-897.
L. Bel, "On gravitational radiation," C. R. Acad. Sci. Paris 246 (1958), 1094-1096.
L. Bel, "Algebraic study of a certain type of curvature tensor. Petrov's case 3," C. R. Acad. Sci. Paris 246 (1958), 2097-2099.
L. Bel, "Definition of an energy density and a generalized state of total radiation," C. R. Acad. Sci. Paris 246 (1958), 3015-3018.
Y. Thiry, "Penta-dimensional theory of gravitation and electromagnetism," Sem. Janet Mec. anal. et mec. celeste 2 (1958-59), 1-15.
A. Lichnerowicz, “Electromagnetic and gravitational waves in general relativity,” Ann. di Mat. pura e appl. (1959), 1-95.
R. Debever, “Gravitational radiation,” Cahiers de Physique 8 (1964), 303-349.
K. Bichteler, "Exterior differential calculus for spinor forms and its application to the general pure gravitational radiation field," Zeit. Phys. 178 (1964), 488-500.
A book I put together from my translations of key papers on teleparallelism from 1928 to 1935:
Selected Papers on Teleparallelism, ed., D. H. Delphenich
Table of Contents
Introduction
1. The unification of gravitation and electromagnetism
2. The geometry of parallelizable manifolds
3. The field equations
4. The topology of parallelizability
5. Teleparallelism and the Dirac equation
6. Singular teleparallelism
The translations:
1. A. Einstein, "Riemannian geometry, while maintaining the notion of teleparallelism," Sitzber. Preuss. Akad. Wiss. 17
(1928), 217-221.
2. A. Einstein, "A new possibility for a unified field theory of gravitation and electromagnetism," Sitzber. Preuss. Akad.
Wiss. 17 (1928), 224-227.
3. R. Weitzenbock, "Differential invariants in Einstein's theory of teleparallelism," Sitzber. Preuss. Akad. Wiss. 17 (1928),
466-474.
4. E. Bortolotti, "Stars of congruences and absolute parallelism: geometric basis for a recent theory of Einstein,"
Rend. Reale Acc. dei Lincei 9 (1929), 530-538.
5. R. Zaycoff, "On the foundations of a new field theory of A. Einstein," Zeit. Phys. 53 (1929), 719-728.
6. H. Reichenbach, "On the classification of the new Einstein Ansatz on gravitation and electricity," Zeit. Phys. 53 (1929),
683-689.
7. A. Einstein, "On unified field theory," Sitzber. Preuss. Akad. Wiss. 18 (1929), 2-7.
8. R. Zaycoff, "On the foundations of a new field theory of A. Einstein (second part)," Zeit. Phys. 54 (1929), 590-593.
9. R. Zaycoff, "On the foundations of a new field theory of A. Einstein (third part)," Zeit. Phys. 54 (1929), 738-740.
10. R. Zaycoff, "On the most recent formulation of Einstein's unified field theory," Zeit. Phys. 56 (1929), 717-726.
11. R. Zaycoff, "Derivation of the Whattaker-Dirac wave equations from Einstein's unified field theory," Zeit. Phys. 56
(1929), 862-864.
12. A. Einstein, "Unified field theory and Hamilton's principle," Sitzber. Preuss. Akad. Wiss. 18 (1929), 156-159.
13. A. Einstein, "On the unified field theory that is based upon the RIemann metric and absolute parallelism," Math. Ann.
102 (1929), 685-697.
14. E. Cartan, "Historical survey of the notion of absolute parallelism," Math. Ann. 102 (1929),698-706.
15. R. Zaycoff, "Teleparallelism and wave mechanics I," Zeit. Phys. 58 (1929), 833-840.
16. R. Zaycoff, "Teleparallelism and wave mechanics II," Zeit. Phys. 59 (1929), 110-113.
17. A. Einstein, "Unitary theory of the physical field," Ann. de l'Inst. Henri Poincare 1 (1930), 1-24.
18. A. Einstein,"The compatibility of the field equations in unified field theory," Sitzber. Preuss. Akad. Wiss. 19 (1930),
18-23.
19. A. Einstein and W. Mayer, "Two rigorous solutions to the field equations of unified field theory," 19 (1930),110-120.
20. G. C. McVittie, "Solutions with axial symmetry of Einstein's equations of teleparallelism," Edinburgh Math. Soc. Proc.
(2) 2 (1930), 140-150.
21. A. Einstein, "On the theory of spaces with a Riemann metric and teleparallelism," Sitzber. Preuss. Akad. Wiss. 19
(1930), 401-402.
22. E. Cartan, "Absolute parallelism and unitary field theory," Rev. Metaphys. Morale 38 (1931), 13-28.
23. E. Steifel, "Direction fields and teleparallelism in n-dimensional manifolds," Comm. Math. Helv. 25 (1935), 305-353.