Chris J. L. Doran

Last updated

Chris J. L. Doran is a physicist, Director of Studies in Natural Sciences for Sidney Sussex College, Cambridge. He founded Geomerics, and is its Chief Operating Officer.

Contents

Doran obtained his Ph.D. in 1994 on the topic of Geometric Algebra and its Application to Mathematical Physics. He was an EPSRC Advanced Fellow from 1999 to 2004. In 2004, he became Enterprise Fellow of the Royal Society of Edinburgh.

Doran has been credited, together with Anthony N. Lasenby, Joan Lasenby and Steve Gull, [1] [2] for raising the interest of the physics community to the mathematical language and methods of geometric algebra and geometric calculus. These had been rediscovered and refined by David Hestenes, who built on the fundamental work of William Kingdon Clifford and Hermann Grassmann. [3] In 1998, together with Lasenby and Gull, he proposed the gauge theory gravity. [4]

Doran derived a coordinate system for a rotating (Kerr) black hole suited to freely-falling observers, analogous to Gullstrand–Painlevé coordinates for the non-rotating case (Schwarzschild spacetime). This is useful for solving the Dirac equation on a Kerr background. [5]

He took a break from academics in 2005, and he subsequently founded the software company Geomerics, making use of his knowledge of mathematics. His research interests relate to applied mathematics and theoretical physics, in particular quantum theory, gravitation, geometric algebra and computational geometry.

Doran has authored more than 50 scientific papers. [6]

Publications

Books
Selected articles and book chapters

Related Research Articles

<span class="mw-page-title-main">Differential geometry</span> Branch of mathematics dealing with functions and geometric structures on differentiable manifolds

Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky. The simplest examples of smooth spaces are the plane and space curves and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries.

In mathematics, a geometric algebra is an extension of elementary algebra to work with geometrical objects such as vectors. Geometric algebra is built out of two fundamental operations, addition and the geometric product. Multiplication of vectors results in higher-dimensional objects called multivectors. Compared to other formalisms for manipulating geometric objects, geometric algebra is noteworthy for supporting vector division and addition of objects of different dimensions.

In physics and astronomy, a frame of reference is an abstract coordinate system whose origin, orientation, and scale are specified by a set of reference points―geometric points whose position is identified both mathematically and physically.

<span class="mw-page-title-main">Mathematical physics</span> Application of mathematical methods to problems in physics

Mathematical physics refers to the development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics, known as physical mathematics.

<span class="mw-page-title-main">William Kingdon Clifford</span> British mathematician and philosopher (1845–1879)

William Kingdon Clifford was a British mathematician and philosopher. Building on the work of Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of the Clifford algebra named in his honour. The operations of geometric algebra have the effect of mirroring, rotating, translating, and mapping the geometric objects that are being modelled to new positions. Clifford algebras in general and geometric algebra in particular have been of ever increasing importance to mathematical physics, geometry, and computing. Clifford was the first to suggest that gravitation might be a manifestation of an underlying geometry. In his philosophical writings he coined the expression mind-stuff.

<span class="mw-page-title-main">David Hestenes</span> American physicist and science educator

David Orlin Hestenes is a theoretical physicist and science educator. He is best known as chief architect of geometric algebra as a unified language for mathematics and physics, and as founder of Modelling Instruction, a research-based program to reform K–12 Science, Technology, Engineering, and Mathematics (STEM) education.

<span class="mw-page-title-main">Quantum field theory in curved spacetime</span> Extension of quantum field theory to curved spacetime

In theoretical physics, quantum field theory in curved spacetime (QFTCS) is an extension of quantum field theory from Minkowski spacetime to a general curved spacetime. This theory uses a semi-classical approach; it treats spacetime as a fixed, classical background, while giving a quantum-mechanical description of the matter and energy propagating through that spacetime. A general prediction of this theory is that particles can be created by time-dependent gravitational fields (multigraviton pair production), or by time-independent gravitational fields that contain horizons. The most famous example of the latter is the phenomenon of Hawking radiation emitted by black holes.

<span class="mw-page-title-main">Mário Schenberg</span> Brazilian electrical engineer, physicist, art critic and writer

Mário Schenberg was a Brazilian electrical engineer, physicist, art critic and writer.

In physics, the algebra of physical space (APS) is the use of the Clifford or geometric algebra Cl3,0(R) of the three-dimensional Euclidean space as a model for (3+1)-dimensional spacetime, representing a point in spacetime via a paravector.

<span class="mw-page-title-main">Steve Vickers (computer scientist)</span>

Steve Vickers is a British mathematician and computer scientist. In the early 1980s, he wrote ROM firmware and manuals for three home computers, the ZX81, ZX Spectrum, and Jupiter Ace. The latter was produced by Jupiter Cantab, a short-lived company Vickers formed together with Richard Altwasser, after the two had left Sinclair Research. Since the late 1980s, Vickers has been an academic in the field of geometric logic, writing over 30 papers in scholarly journals on mathematical aspects of computer science. His book Topology via Logic has been influential over a range of fields. In October 2018, he retired as senior lecturer at the University of Birmingham. As announced on his university homepage, he continues to supervise PhD students at the university and focus on his research.

In mathematical physics, spacetime algebra (STA) is the application of Clifford algebra Cl1,3(R), or equivalently the geometric algebra G(M4) to physics. Spacetime algebra provides a "unified, coordinate-free formulation for all of relativistic physics, including the Dirac equation, Maxwell equation and General Relativity" and "reduces the mathematical divide between classical, quantum and relativistic physics."

In special relativity, an observer is a frame of reference from which a set of objects or events are being measured. Usually this is an inertial reference frame or "inertial observer". Less often an observer may be an arbitrary non-inertial reference frame such as a Rindler frame which may be called an "accelerating observer".

In mathematics, especially (higher) category theory, higher-dimensional algebra is the study of categorified structures. It has applications in nonabelian algebraic topology, and generalizes abstract algebra.

In the study of geometric algebras, a k-blade or a simple k-vector is a generalization of the concept of scalars and vectors to include simple bivectors, trivectors, etc. Specifically, a k-blade is a k-vector that can be expressed as the exterior product of 1-vectors, and is of gradek.

<span class="mw-page-title-main">Gauge theory</span> Physical theory with fields invariant under the action of local "gauge" Lie groups

In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, do not change under local transformations according to certain smooth families of operations. Formally, the Lagrangian is invariant.

Mathematics is a broad subject that is commonly divided in many areas that may be defined by their objects of study, by the used methods, or by both. For example, analytic number theory is a subarea of number theory devoted to the use of methods of analysis for the study of natural numbers.

Gauge theory gravity (GTG) is a theory of gravitation cast in the mathematical language of geometric algebra. To those familiar with general relativity, it is highly reminiscent of the tetrad formalism although there are significant conceptual differences. Most notably, the background in GTG is flat, Minkowski spacetime. The equivalence principle is not assumed, but instead follows from the fact that the gauge covariant derivative is minimally coupled. As in general relativity, equations structurally identical to the Einstein field equations are derivable from a variational principle. A spin tensor can also be supported in a manner similar to Einstein–Cartan–Sciama–Kibble theory. GTG was first proposed by Lasenby, Doran, and Gull in 1998 as a fulfillment of partial results presented in 1993. The theory has not been widely adopted by the rest of the physics community, who have mostly opted for differential geometry approaches like that of the related gauge gravitation theory.

In geometric algebra, the outermorphism of a linear function between vector spaces is a natural extension of the map to arbitrary multivectors. It is the unique unital algebra homomorphism of exterior algebras whose restriction to the vector spaces is the original function.

Stephen Gull is a British physicist based at St John's College, Cambridge credited, together with Anthony N. Lasenby, Joan Lasenby and Chris J. L. Doran, with raising the interest of the physics community to the mathematical language and methods of geometric algebra and geometric calculus. These have been rediscovered and refined by David Hestenes, who built on the fundamental work of William Kingdon Clifford and Hermann Grassmann. In 1998, together with Lasenby and Doran, he proposed gauge theory gravity.

References

  1. John Vince: Geometric Algebra: An Algebraic System for Computer Games and Animation, Springer, 2009, ISBN   978-1-84882-379-2, p. 3
  2. Val L. Fitch, Daniel R. Marlow, Margit Ann Elisabeth Dementi: Critical problems in physics: proceedings of a conference celebrating the 250th anniversary of Princeton university, Princeton University Press, 1997, ISBN   0-691-05785-0, p. 165
  3. J. Lasenby, A.N. Lasenby, C.J.L. Doran: A unified mathematical language for physics and engineering in the 21st century, Phil. Trans. R. Soc. Lond. A 358, 21-39 (2000) (abstract, full text)
  4. Lasenby, Anthony.; Chris Doran; Stephen Gull (1998), "Gravity, gauge theories and geometric algebra", Philosophical Transactions of the Royal Society A , 356: 487–582, arXiv: gr-qc/0405033 , Bibcode:1998RSPTA.356..487L, doi:10.1098/rsta.1998.0178
  5. Doran, "New form of the Kerr solution" (2000), Physical Review D
  6. "Dr Christopher JL Donan". Sidney Sussex College. Retrieved 2015-12-07.