Paul A. Benioff
1930-2022
Biographical sketch
- 1959 Ph.D., University of California at Berkeley
- 1960 Weizmann Fellow
- 1961 Ford Fellowship, Niels Bohr Institute
- 1961-1995 Argonne National Laboratory
- 1995-present Post-retirement Research Participant, Argonne National Laboratory
Visiting appointments
- 1979 & 1982 Visiting Scientist, CNRS Marseilles
- 1979 Visiting Professor, Tel Aviv University
Awards
Recent papers
- Representation of natural numbers in quantum mechanics
Paul Benioff
Phys. Rev. A 63, 032305 (2001) [11 pages]
- Efficient implementation and the product-state representation of numbers
Paul Benioff
Phys. Rev. A 64, 052310 (2001) [7 pages]
- Towards a Coherent Theory of Physics and Mathematics
Paul Benioff
Foundations of Physics. 32, 989-1029 (2002)
- The Representation of Numbers in Quantum Mechanics
Paul Benioff
Algorithmica 34, 529-559 (2002)
- Cyclic networks of quantum gates
Peter Cabauy and Paul Benioff
Phys. Rev. A 68, 032315 (2003) [14 pages]
- Tightening the Theory-Experiment Connection in Physics: $R_{n}$ Based Space and Time}
Paul Benioff
Int. J. Quantum Inform. 3, 1-8 (2005)
- Representation of complex rational numbers in quantum mechanics
Paul Benioff
Phys. Rev. A 72, 032314 (2005) [11 pages]
- Towards a Coherent Theory of Physics and Mathematics: The Theory-Experiment Connection
Paul Benioff
Foundations of Physics 35, 1825-1856 (2005)
- Complex Rational Numbers in Quantum Mechanics
Paul Benioff
Int. J. Mod. Phys. B 20, 1730-1741 (2006)
- A Representation of Real and Complex Numbers in Quantum Theory
Paul Benioff
Int. J. Pure and Appl. Math. 39, 297-339 (2007)
- Fields of quantum reference frames based on different representations
of rational numbers as states of qubit strings
Paul Benioff
J. Phys. Conf. Ser. 70, 012003-1:19 (2007)
- Reference Frame Fields based on Quantum Theory Representations of Real and Complex Numbers
Paul Benioff
Advances in Quantum Computation, K. Mahdavi and D. Koslover, Eds., Contemporary Mathematics Vol. 482, pp125-163, (2009)
- A Possible Approach to Inclusion of Space and Time in Frame Fields of Quantum Representations of Real and Complex Numbers
Paul Benioff
Advances in Mathematical Physics, Vol. 2009, ID 452738
- New Gauge Field from Extension of Space Time Parallel Transport of Vector Spaces to the Underlying Number Systems
Paul Benioff
Int. J. Theor. Phys. 50, 1887-1907 (2011)
- Representations of Each Number Type that Differ by Scale Factors
Paul Benioff
Advances in Pure Mathematics, Vol. 3, pp 394-404, 2013
- New Gauge Fields from Extension of Parallel Transport of Vector Spaces to Underlying Scalar Fields
Paul Benioff
Proc. SPIE Int. Soc. Opt. Eng. 8057:80570X (2011)
- Effects on quantum physics of the local availability of mathematics and space time dependent scaling factors for number systems
Paul Benioff
Chapter 2, in Quantum Theory, I. Cotaescu, Editor, Intech open access publisher, 2012
- Local availability of mathematics and number scaling: effects on quantum physics
Paul Benioff
Proceedings Volume 8400, Quantum Information and Computation X; 84000T (2012)
- Effects of gauge theory based number scaling on geometry
Paul Benioff
Proceedings Volume 8749, Quantum Information and Computation XI; 87490F (2013)
- Effects of mathematical locality and number scaling on coordinate chart use
Paul Benioff
Proceedings Volume 9123, Quantum Information and Computation XII; 91230Q (2014)
- Fiber bundle description of number scaling in gauge theory and geometry
Paul Benioff
Quantum Studies: Mathematics and Foundations volume 2, pages 289–313 (2015)
- Principal fiber bundle description of number scaling for scalars and vectors: Application to gauge theory
Paul Benioff
Proceedings Volume 9500, Quantum Information and Computation XIII; 95000X (2015)
- Space and time dependent scaling of numbers in mathematical structures: Effects on physical and geometric quantities
Paul Benioff
Quantum Information Processing volume 15, pages 1081–1102 (2016)
- Effects of a scalar scaling field on quantum mechanics
Paul Benioff
Quantum Information Processing volume 15, pages 3005–3034 (2016)
- Effect of number scaling on entangled states in quantum mechanics
Paul Benioff
Proceedings Volume 9873, Quantum Information and Computation IX; 98730D (2016)
- The no information at a distance principle and local mathematics: some effects on physics and geometry
Paul Benioff
Theoretical Information Studies, M. Burgin and G. Dodig-Crnkovic, Eds., World Scientific Publishing Co. 2020, pp 115-138
- Relation between observers and effects of number valuation in science
Paul Benioff
Journal of Cognitive Sciences, Vol.19-2, pp 229-251, (2018)
Theoretical Physics