Josep Maria Parra

Josep Maria Parra
Residence	Spain

Josep Maria Parra (also cited as Josep M. Parra and Josep Manel Parra i Serra) is a Catalan physicist at the Universitat de Barcelona, known for his work on Clifford (geometric) algebra and its applications to theoretical physics.

Education

• Doctorate, Universitat de Barcelona, 1985 — dissertation Contribució a l'estudi de les àlgebres de Clifford: aplicacions a la física ("Contribution to the study of Clifford algebras: applications to physics")

Career

He has been a member of the Departament de Física Fonamental at the Facultat de Física of the Universitat de Barcelona (Diagonal 647, 08028 Barcelona), and is also associated with the Laboratori de Física Matemàtica of the Institut d'Estudis Catalans.

Scientific contributions

Parra's research centres on real Clifford geometric algebra as a unified language for physics, in the tradition of the geometric algebra of Hermann Grassmann, William Kingdon Clifford and David Hestenes. His work includes:

• Reformulations of the Dirac equation and of the Dirac–Darwin–Hestenes equation in the language of geometric algebra.
• Complex Lorentz rotations acting on vectors and pseudovectors within real Clifford geometric algebras.
• The introduction of r-fold (r-direct product) Clifford algebras, applied with Josep M. Pozo to give a compact definition of superenergy tensors and a simple proof of the dominant superenergy property in arbitrary dimension.
• A revision of the Petrov classification of the Weyl tensor using real geometric Clifford algebra, yielding a new canonical tensorial form directly comparable with the spinorial classification.
• Symbolic and numeric computation with Clifford algebras, including the syntax and use of computer algebra packages such as Clifford.m and Nabla.m.

He has also written on Clifford algebra and the didactics of mathematics, advocating the use of geometric algebra throughout physics teaching.

Publications

• R. Abłamowicz, J. M. Parra and P. Lounesto (editors), Clifford Algebras with Numeric and Symbolic Computations, Birkhäuser, Boston, 1996.
• J. M. Parra, "On Dirac and Dirac–Darwin–Hestenes Equations", in Clifford Algebras and their Applications in Mathematical Physics, Kluwer.
• J. M. Pozo and J. M. Parra, "Clifford Algebra Approach to Superenergy Tensors", contribution to the proceedings of ERE99, Bilbao, 1999 (arXiv:gr-qc/9911041).
• J. M. Pozo and J. M. Parra, "Tensors, Spinors and Multivectors in the Petrov Classification", Advances in Applied Clifford Algebras 17 (2007), 663–678.

External links

• "Clifford Algebra Approach to Superenergy Tensors" (arXiv)
• Josep Manel Parra at the Mathematics Genealogy Project