Prof. Andrzej Trautman

email: andrzej.trautman@fuw.edu.pl www: http://trautman.fuw.edu.pl/home.html www.fuw.edu.pl/~amt/amt.html phone: (+48 22) 55 32 295 room: H138

 

Research interests

My early work was devoted to gravitational waves and radiation. In 1960 Ivor Robinson and I found a class of exact solutions of Einstein's equations with diverging, shear free geodetic rays; some of them represent a rather special kind of 'spherical' gravitational waves.
Later, I worked on the Einstein-Cartan theory of gravitation with spin and torsion; I first learned about that theory in England from T. W. B. Kibble and D. W. Sciama. A visit to C. N. Yang at Stony Brook (1976-77) stimulated a period of my interest in gauge theories and their geometric, bundle-theoretic aspects. During the 1980s, I stayed many times at SISSA and ICTP in Trieste; contacts with Paolo Budinich there resulted in work on pure spinors; we wrote together The Spinorial Chessboard. With Ludwik Dabrowski (Trieste), Michel Cahen and Simone Gutt (Brussels)  and Thomas Friedrich (Berlin) we studied spin and pin structures on Riemannian manifolds.
 

Selected interviews

• A. Trautman, D. Salisbury. Memories of my early career in relativity physics. EPJ H 44, 391–413 (2019). https://doi.org/10.1140/epjh/e2019-100044-5

• A. Trautman, T. Rożek - Prof. Trautman - to on udowodnił istnienie fal grawitacyjnych, Interview in Polish

Selected publications

• I. Robinson, A. Trautman - Some spherical gravitational waves in general relativity, Proc. Roy. Soc.London A265, 463--473 (1962)
• A. Trautman - Analytic solutions of Lorentz-invariant linear equations, Proc. Roy. Soc. London A270, 326--328 (1962)
• A. Trautman - On the propagation of information by waves, pp. 459--463 in: Recent Developments in General Relativity, a volume in honour of L. Infeld, Pergamon Press and PWN, London and Warsaw (1962)
• A. Trautman - Conservation laws in general relativity, pp. 169--198 in: Gravitation, ed. by L. Witten, J. Wiley, New York (1962)
• A. Trautman - Sur la theorie newtonienne de la gravitation, CR Acad. Sci. Paris 257, 617--620 (1963)
• A. Trautman - Comparison of Newtonian and relativistic theories of gravitation, pp. 413--425 in: Perspectives in Geometry and Relativity, Essays in honor of V. Hlavaty, ed. by B. Hoffmann, Indiana Univ. Press, Bloomington (1966)
• A. Trautman - Noether equations and conservation laws, Commun Math. Phys. 6, 248--261 (1967)
• A. Trautman - Fibre bundles associated with space-time, Rep. Math. Phys. (Torun) 1, 29--34 (1970)
• A. Trautman - Invariance of Lagrangian systems, pp. 85--99 in: General Relativity, Papers in honour of J. L. Synge, ed. by L. O'Raifeartaigh, Clarendon Press, Oxford (1972)
• A. Trautman - On the structure of the Einstein-Cartan equations, Symp. Math. 12, 139--162 (1973)
• A. Trautman - Spin and torsion may avert gravitational singularities, Nature 242, 7--8 (1973)
• A. Trautman - Solutions of the Maxwell and Yang--Mills equations associated with Hopf fibrings, Intern. J. Theor. Phys. 16, 561--565 (1977)
• A. Trautman - The geometry of gauge fields, Czech. J. Phys. B29, 107--116 (1979)
• A. Trautman - Fibre bundles, gauge fields, and gravitation, pp. 287--308 in: General Relativity and Gravitation, vol. I, ed. by A. Held, Plenum, New York (1980)
• J. Tafel, A. Trautman - Can poles change color?, J. Math. Phys. 24, 1087--1092 (1983)
• A. Trautman - Differential Geometry for Physicists, Bibliopolis, Napoli (1984)
• A. Trautman - Optical structures in relativistic theories, Asterisque, numero hors serie, 401--420 (1985)
• I. Robinson, A. Trautman - A generalization of the Mariot theorem on congruences of null geodesics, Proc. Roy. Soc. London A405, 41--48 (1986)
• L. Dkabrowski, A. Trautman - Spinor structures on spheres and projective spaces, J. Math. Phys. 27, 2022--2028 (1986)
• P. Budinich, A. Trautman - The Spinorial Chessboard, Trieste Notes in Physics, Springer, Berlin (1988)
• W. Kopczynski, A. Trautman - Spacetime and Gravitation, PWN and J. Wiley, Warszawa and Chichester (1992)
• W. Kopczynski, A. Trautman - Simple spinors and real structures, J. Math. Phys. 33, 550--559 (1992)
• A. Trautman - Spinors and the Dirac operator on hypersurfaces. I. General theory, J. Math. Phys. 33, 4011--4019 (1992)
• M. Cahen, S. Gutt, A. Trautman - Spin structures on real projective quadrics, J. Geom. Phys. 10, 127--154 (1993)
• I. Robinson, A. Trautman - The conformal geometry of complex quadrics and the fractional-linear form of Mobius transformations, J. Math. Phys. 34, 5391--5406 (1993)
• A. Trautman,  K. Trautman - Generalized pure spinors, J. Geom. Phys. 15, 1--22 (1994)
• A. Trautman, M. Cahen, S. Gutt - Pin structures and the modified Dirac operator, J. Geom. Phys. 17, 283--297 (1995)
• A. Trautman - The Dirac operator on hypersurfaces, Acta Phys. Polon. B 26, 1283--1310 (1995)
• A. Trautman - Clifford and the `square root' ideas, Contemporary Mathematics 203, 3--24 (1997)
• A. Trautman, P. Nurowski, E. Schucking - Relativistic gravitational fields with close Newtonian analogs, pp. 329--337 in: On Einstein's Path, A. Harvey (ed), Springer-Verlag, New York (1999)
• Th. Friedrich, A. Trautman - Spin spaces, Lipschitz groups, and spinor bundles, Ann. Glob. Anal. Geom. 18, 221--240 (2000)
• A. Trautman - Robinson manifolds and Cauchy--Riemann spaces, Class. Quantum Grav. 19, R1--R10 (2002)
• P. Nurowski, A. Trautman - Robinson manifolds as the Lorentzian analogs of Hermite manifolds, Diff. Geom. Appl. 17, 175--195 (2002)
• A. Trautman - Lectures on general relativity (a ``Golden Oldie''), GRG Journal 34, 721--762 (2002)
• A. Trautman - Clifford algebras and their representations, pp. 518--530 in: Encyclopedia of Mathematical Physics (vol. 1), edited by J.-P. Francoise, G. L. Naber and Tsou S. T., Oxford: Elsevier (2006)
• A. Trautman - Einstein--Cartan theory, pp. 189--195 in: Encyclopedia of Mathematical Physics (vol. 2), edited by J.-P. Francoise, G. L. Naber and Tsou S. T., Oxford: Elsevier (2006)
• A. Trautman - On eight kinds of spinors, Acta Phys. Polon. B 36, 121--130 (2005)
• A. Trautman - Connections and the Dirac operator on spinor bundles, J. Geom. Phys. 58, 238--252 (2008)
• T. Sauer, A. Trautman - Myron Mathisson: what little we know of his life, Acta Phys. Polon. B Proc. Suppl. 1, 7--26 (2008)

Selected talks

• Sur les lois de conservation dans les espaces de Riemann - GR2 Conf., Royaumont, 1959
• Exact degenerate solutions of Einstein's equations - GR3 Conf., Jablonna, 1962
• Theory of gravitation - Conf. in honour of P.A.M. Dirac, Trieste, 1972.
• The Einstein--Cartan theory of gravitation - Conf. Ondes et Radiations Gravitationnelles, Paris, 1973
• Energy, gravitation and cosmology - Third General Conference of the European Physical Society, Bucharest, 1975
• On groups of gauge transformations - Conf. on Geometrical and Topological Methods in Gauge Theories, Montreal, 1979
• Yang-Mills theory and gravitation: A comparison - Conf. on Geometric Techniques in Gauge Theories, Scheveningen, 1981
• Einstein and the geometrization of physics - Conf. Aspetti Matematici della Teoria della Relativita, Accademia Nazionale dei Lincei, Roma, 1983
• A simple proof of the Robinson theorem - Conf. Journees Relativistes, Torino, 1983.
• Cauchy--Riemann structures in optical geometry - Fourth Marcel Grossmann Meeting on General Relativity, Roma, 1985
• Spinor structures on homogeneous Riemannian spaces - Conf. Spinors in Physics and Geometry, Trieste 1986
• Optical geometry - Conf. New Theories in Physics, Kazimierz, 1988
• Geometric aspects of spinors - Third International Conference on Clifford Algebras and their Applications in Mathematical Physics, Deinze, 1992
• Pin structures and the Dirac operator on real projective spaces and quadrics - Conf. on Clifford Algebras and Their Applications in Mathematical Physics, Aachen, 1996
• Pythagorean spinors and Penrose twistors - Conf. The Geometric Universe: Science, Geometry and the Work of Roger Penrose, Oxford, 1998
• Double covers of pseudo-orthogonal groups - Conf. Clifford Analysis and Its Applications, Prague, 2000
• Two approaches to spinor fields on manifolds - Peter Gabriel Bergmann Memorial Symposium, Syracuse (N.Y.), 2003