Tevian Dray |
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Oregon State University College of Science Mathematics ProfessorAppointed: 1997 |  |
Mailing AddressKidder Hall 306 Oregon State University Corvallis, Oregon 97331United States | Contact Information |
Qualifications
Ph.D., University of California, Berkeley, Mathematics, 1981.
M.A., University of California, Berkeley, Mathematics, 1977.
B.S., Massachusetts Institute of Technology, Mathematics, 1976.
Expertise and Research Interests
Parametric Manifolds: The usual ``3+1'' decomposition of spacetime into space and time is based on slicing spacetime with spacelike hypersurfaces. An alternative ``1+3'' approach is based on threading spacetime with timelike curves, then using the resulting ``parametric manifold'' of orbits to describe what observers moving along these curves actually see. Substantial progress has been made in giving this approach a rigorous, mathematical foundation.
Rotating Vacuum: One of the wonders of special relativity is that different observers have different notions of space and time. An analogous result holds when one begins to merge quantum field theory with relativity: Different observers have different notions of what a particle is. Thus, a (linearly) accelerating particle detector will respond in the (inertial) vacuum state. However, folklore has it that such a detector will not detect particles in the vacuum state appropriate to its motion. This is true for linear acceleration; this is the basic idea behind Hawking radiation. Surprisingly, it turns out to be false for circular motion. This paradox has been resolved by carefully imposing physical boundary conditions.
Signature Change: One of the fundamental assumptions in relativity is that the universe is a spacetime, i.e. a Lorentzian manifold. But there are surfaces which arise, e.g. in string theory, on which there does not exist a Lorentzian metric. The language of differential forms has been used to carefully describe the propagation of solutionsof the Laplace equation on manifolds exhibiting signature change. Physically, this describes the propagation of the scalar field across a Euclidean region, and has interesting applications to cosmology. Analogous results hold for Einstein's equations. A generalization of this approach permits one to compare spinors across such a surface.
Algebraic Computing: Ever since my first exposure to algebraic computing, I have been fascinated by the possibility of using computers to derive equations which are then solved by hand, rather than the other way around. In relativity, one has need of a particular set of repetitive manipulations, without the baggage of a general system for doing mathematics. A preferred family of symbolic manipulation languages has thus evolved for general relativity, namely SHEEP, CLASSI, and STENSOR. CLASSI is used to develop an algorithmic approach to the equivalence problem for solutions of Einstein's equations by determining theoretic invariants of spacetimes, such as their symmetry groups, thus assisting in their classification.
Octonions: The octonions are a nonassociative, noncommutative generalization of the complex numbers. Intriguing results have been obtained regarding the eigenvalues of 3x3 Hermitian octonionic matrices, notably that they admit 6, rather than 3, real eigenvalues. The octonions also provide an elegant mathematical framework for doing Clifford algebra (gamma matrix) computations, which, among other things, shows why superstring theory only works in certaindimensions. This suggests that the octonions play a fundamental role in describing the physics of elementary particles.
Rotating Vacuum: One of the wonders of special relativity is that different observers have different notions of space and time. An analogous result holds when one begins to merge quantum field theory with relativity: Different observers have different notions of what a particle is. Thus, a (linearly) accelerating particle detector will respond in the (inertial) vacuum state. However, folklore has it that such a detector will not detect particles in the vacuum state appropriate to its motion. This is true for linear acceleration; this is the basic idea behind Hawking radiation. Surprisingly, it turns out to be false for circular motion. This paradox has been resolved by carefully imposing physical boundary conditions.
Signature Change: One of the fundamental assumptions in relativity is that the universe is a spacetime, i.e. a Lorentzian manifold. But there are surfaces which arise, e.g. in string theory, on which there does not exist a Lorentzian metric. The language of differential forms has been used to carefully describe the propagation of solutionsof the Laplace equation on manifolds exhibiting signature change. Physically, this describes the propagation of the scalar field across a Euclidean region, and has interesting applications to cosmology. Analogous results hold for Einstein's equations. A generalization of this approach permits one to compare spinors across such a surface.
Algebraic Computing: Ever since my first exposure to algebraic computing, I have been fascinated by the possibility of using computers to derive equations which are then solved by hand, rather than the other way around. In relativity, one has need of a particular set of repetitive manipulations, without the baggage of a general system for doing mathematics. A preferred family of symbolic manipulation languages has thus evolved for general relativity, namely SHEEP, CLASSI, and STENSOR. CLASSI is used to develop an algorithmic approach to the equivalence problem for solutions of Einstein's equations by determining theoretic invariants of spacetimes, such as their symmetry groups, thus assisting in their classification.
Octonions: The octonions are a nonassociative, noncommutative generalization of the complex numbers. Intriguing results have been obtained regarding the eigenvalues of 3x3 Hermitian octonionic matrices, notably that they admit 6, rather than 3, real eigenvalues. The octonions also provide an elegant mathematical framework for doing Clifford algebra (gamma matrix) computations, which, among other things, shows why superstring theory only works in certaindimensions. This suggests that the octonions play a fundamental role in describing the physics of elementary particles.
Other Expertise
Academic Experience:
1995, Fulbright Senior Scholar (Adelaide; Australia);
1987, Indo-American Fellow (Madras, Bombay, Bangalore; India);
1986-1987, SERC Postdoctoral Research Fellow (York; United Kingdom);
1982-1983, NATO Postdoctoral Fellow (Berlin;West Germany);
1978-1979, DAAD Stipendiat (Munich; West Germany).
1995, Fulbright Senior Scholar (Adelaide; Australia);
1987, Indo-American Fellow (Madras, Bombay, Bangalore; India);
1986-1987, SERC Postdoctoral Research Fellow (York; United Kingdom);
1982-1983, NATO Postdoctoral Fellow (Berlin;West Germany);
1978-1979, DAAD Stipendiat (Munich; West Germany).
Keywords
COS Keywords:
Algebra, Computer and Information Sciences, Differential Geometry, Geometry, Mathematical Physics, Quantum Physics.Additional Terms:
Algebraic Computing, Differential Geometry, General Relativity, Mathematical Physics, Non-Euclidean Geometry, Octonions, Quantum Field Theory in Curved Space.Languages
(Reading, Writing, Speaking)
Dutch: (Fluent, Fluent, Fluent)
French: (Fluent, Fluent, Fluent)
German: (Fluent, Fluent, Fluent)
Memberships
American Association for the Advancement of Science
American Association of University Professors
American Mathematical Society
American Physical Society
Australasian Society for General Relativity and Gravitation
Indian Association for General Relativity and Gravitation
International Society for General Relativity and Gravitation
London Mathematical Society
Mathematical Association of America
Oregon Academy of Science (OAS)
Southern African Relativity Society
Previous Positions
1995, Fulbright Senior Scholar,
Adelaide University
1991, Senior Member,
Mathematical Sciences Research Institute (MSRI)
1990-1997, Associate Professor,
Oregon State University,
College of Science,
Mathematics
1988-1990, Assistant Professor,
Oregon State University
1986-1987, Research Fellow,
University of York (United Kingdom)
1984, Member,
Institute for Advanced Study,
Mathematics
1984-1985, Wetenschappelijk Medewerker,
Rijksuniversiteit Utrecht (the Netherlands)
Funding Received
- National Science Foundation (NSF): Bridging the Vector Calculus Gap, 2001 to 2002.
- Oregon Collaborative for Excellence in the Preparation of Teachers (OCEPT): Bridging the Vector Calculus Gap, 2000 to 2001.
- OSU Research Council: Algebraic Computing, 1994 to 1995.
- NSF: The Wave Equation Isn't As Simple As You Thought, 1992 to 1995.
- National Science Foundation (NSF): The Wave Equation Isn't As Simple As You Thought, 1992 to 1995.
- OSU Research Council: Algebraic Computing, 1989 to 1990.
- National Science Foundation (NSF): Algebraic Computing in General Relativity, 1988 to 1991.
Publications
- David Hartley, Robin W. Tucker, Philip Tuckey, Tevian Dray, Tensor Distributions on Signature-Changing Spacetimes, Gen. Rel. Grav., 32, 491-504, 2000
- Kevin Thompson, Tevian Dray, Taxicab Angles and Trigonometry, Pi Mu Epsilon Journal, 11, 87-96, 2000
- Corinne A. Manogue, Tevian Dray, Octonionic Möbius Transformations, Modern Physics Letters A, 14, 1243-1255, 1999
- Jim Fischer, Tevian Dray, A New Look at the Ashtekar-Magnon Energy Condition, Gen. Rel. Grav., 31, 511-526, 1999
- Corinne A. Manogue, Tevian Dray, Dimensional Reduction, Modern Physics Letters, 14, 93-97, 1999
- Tevian Dray, Corinne A. Manogue, The Exceptional Jordan Eigenvalue Problem, International Journal of Theoretical Physics, 38, 2901-2916, 1999
- Tevian Dray, Corinne A. Manogue, The Octonionic Eigenvalue Problem, Advances in Applied Clifford Algebras, 8, 341-364, 1998
- Tevian Dray, Corinne A. Manogue, Finding Octonionic Eigenvectors Using Mathematica, Comput. Phys. Comm., 115, 536-547, 1998
- Tevian Dray, C. A. Hurst, Corinne A. Manogue, Topology Change: The Regulated Trousers and Tin Woodman Models, Comm. Math. Theoret. Phys., 1, 24-49, 1998
- Tevian Dray, Tensor Distributions in the Presence of Degenerate Metrics, International Journal of Mod. Phys. D, 6, 717-740, 1997
- Tevian Dray, George Ellis, Charles Hellaby, Corinne A. Manogue, Gravity and Signature Change, Gen. Rel. Grav., 29, 591-597, 1997
- Jörg Schray, Tevian Dray, Corinne A. Manogue, Robin W. Tucker, and Charles Wang, The Construction of Spinor Fields on Manifolds with Smooth Degenerate Metrics, Journal of Mathematical Physics, 37, 3882-3896, 1996
- Tevian Dray, Charles Hellaby, Comment on `Smooth and Discontinuous Signature Type Change in General Relativity', Gen. Rel. Grav., 28, 1401-1408, 1996
- Paul C. W. Davies, Tevian Dray, Corinne A. Manogue, The Rotating Quantum Vacuum, Phys. Rev. D, 53, 4382-4387, 1996
- Tevian Dray, Einstein's Equations in the Presence of Signature Change, Journal of Mathematical Physics, 37, 5627-5636, 1996
- Charles Hellaby, Tevian Dray, Reply Comment: Comparison of Approaches to Classical Signature Change, Phys. Rev. D, 52, 7333-7339, 1995
- Tevian Dray, Corinne A. Manogue, Robin W. Tucker, Boundary Conditions for the Scalar Field in the Presence of Signature Change, Classical and Quantum Gravity, 12, 2767-2777, 1995
- Stuart Boersma, Tevian Dray, Slicing, Threading & Parametric Manifolds, Gen. Rel. Grav., 27, 319-339, 1995
- Stuart Boersma, Tevian Dray, Parametric Manifolds II: Intrinsic Approach, Journal of Mathematical Physics, 36, 1394-1403, 1995
- Stuart Boersma, Tevian Dray, Parametric Manifolds I: Extrinsic Approach, Journal of Mathematical Physics, 36, 1378-1393, 1995
- Tevian Dray, Charles Hellaby, The Patchwork Divergence Theorem, Journal of Mathematical Physics, 35, 5922-5929, 1994
- Charles Hellaby, Tevian Dray, Failure of Standard Conservation Laws at a Classical Change of Signature, Phys. Rev. D, 49, 5096-5104, 1994
- Dieter Brill, Tevian Dray, Spell it Nordström, Gen. Rel. Grav., 25, 435-436, 1993
- Tevian Dray, Corinne A. Manogue, Robin W. Tucker, The Scalar Field Equation in the Presence of Signature Change, Phys. Rev. D, 48, 2587-2590, 1993
- Tevian Dray, Ravi Kulkarni, Corinne A. Manogue, Scalar Field Quantization in Stationary, Non-Static Spacetimes, Gen. Rel. Grav., 24, 1255-1266, 1992
- Marcelo E. Araujo, Tevian Dray, James E. F. Skea, Finding Isometry Groups in Theory and Practice, Gen. Rel. Grav., 24, 477-500, 1992
- Tevian Dray, Corinne A. Manogue, Robin W. Tucker, Particle Production from Signature Change, Gen. Rel. Grav., 23, 967-971, 1991
- Tevian Dray, Bouncing Shells, Classical and Quantum Gravity, 7, L131-L134, 1990
- Tevian Dray, The Twin Paradox Revisited, American Journal of Phys., 58, 822-825, 1990
- Steven G. Harris, Tevian Dray, The Causal Boundary of the Trousers Space, Classical and Quantum Gravity, 7, 149-161, 1990
- Tevian Dray, Pankaj Joshi, Glueing Reissner-Nordstrøm Spacetimes Together Along Charged Shells of Matter, Classical and Quantum Gravity, 7, 41-49, 1990
- Tevian Dray, T. Padmanabhan, Conserved Quantities from Piecewise Killing Vectors, Gen. Rel. Grav., 21, 741-745, 1989
- Tevian Dray, Ravi Kulkarni, Joseph Samuel, Duality and Conformal Structure, Journal of Mathematical Physics, 30, 1306-1309, 1989
- Tevian Dray, Corinne A. Manogue, Bogolubov Transformations and Completeness, Gen. Rel. Grav., 20, 957-965, 1988
- Corinne A Manogue, Tevian Dray, Ed Copeland, The Trousers Problem Revisited, Pramana - Journal of Physics, 30, 279-292, 1988
- C J S Clarke, Tevian Dray, Junction Conditions for Null Hypersurfaces, Classical and Quantum Gravity, 4, 265-275, 1987
- Tevian Dray, Gerard 't Hooft, The Gravitational Effect of Colliding Planar Shells of Matter, Classical and Quantum Gravity, 3, 825-840, 1986
- Tevian Dray, A Unified Treatment of Wigner D Functions, Spin-Weighted Spherical Harmonics, and Monopole Harmonics, Journal of Mathematical Physics, 27, 781-792, 1986
- Tevian Dray, Gerard 't Hooft, The Effect of Spherical Shells of Matter on the Schwarzschild Black Hole, Commun. Math. Phys., 99, 613-625, 1985
- Tevian Dray, Gerard 't Hooft, The Gravitational Shock Wave of a Massless Particle, Nuclear Physics B, 253, 173-188, 1985
- Tevian Dray, Momentum Flux at Null Infinity, Classical and Quantum Gravity, 2, L7-L10, 1985
- Tevian Dray, The Relationship Between Monopole Harmonics and Spin-Weighted Spherical Harmonics, Journal of Mathematical Physics, 26, 1030-1033, 1985
- Tevian Dray, Michael Streubel, Angular Momentum at Null Infinity, Classical and Quantum Gravity, 1, 15-26, 1984
- Tevian Dray and, Jürgen Renn, Space-Times with a Stable Adiabatic Vacuum, Gen. Rel. Grav., 16, 453-458, 1984
- Tevian Dray, Jürgen Renn, The Normal-Form (In)Dependence of the Adiabatic Particle Definitions, Gen. Rel. Grav., 16, 325-332, 1984
- Tevian Dray, Jürgen Renn, and Donald C. Salisbury, Particle Creation with Finite Energy Density, Lett. Math. Phys., 7, 145-153, 1983
- Tevian Dray, On the Asymptotic Flatness of the C-Metrics at Spatial Infinity, Gen. Rel. Grav., 14, 109-112, 1982
- Abhay Ashtekar, Tevian Dray, On the Existence of Solutions to Einstein's Equation with Non-Zero Bondi News, Commun. Math. Phys., 79, 581-589, 1981
- Tevian Dray, Martin Walker, On the Regularity of Ernst's Generalized C-Metric, Lett. Math. Phys., 4, 15-18, 1980
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