×

Quantum theory and Galois fields. (English) Zbl 1101.81091

The author constructs quantum field theory over the Galois field (GFQT) \(\text{GF}(p^2)=\mathbb Zp+i\mathbb Z_p\) where \(p\) is a prime number of the type \(4n+3\). It is obtained that in this theory, the existence of antiparticles immediately follows from the fact that the Galois field is finite, and no locality is required to explain why a particle and its antiparticle have the same mass and spin but opposite charges, as well as the spin-statistics connection. All this makes GFQT an extremely interesting theory that sheds a new light on the fundamental problems of physics.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
12E20 Finite fields (field-theoretic aspects)
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Weinberg S., Dreams of a Final Theory (1992)
[2] DOI: 10.1017/CBO9781139644167
[3] DOI: 10.1016/B978-0-12-473250-6.50005-4
[4] Pauli W., Handbuch der Physik 1 (1958)
[5] Fock V. A., ZhETF 42 pp 1135–
[6] DOI: 10.1103/PhysRev.151.1023
[7] DOI: 10.1103/RevModPhys.21.400 · Zbl 0036.26704
[8] Berestetsky V. B., Relativistic Quantum Theory 1 (1968)
[9] Rosenfeld L., N. Bohr and the Development of Physics (1955)
[10] DOI: 10.1103/PhysRev.124.925 · Zbl 0103.21402
[11] Weinberg S., Gravitation and Cosmology (1972)
[12] DOI: 10.2307/1968551 · Zbl 0020.29601
[13] DOI: 10.1007/978-3-642-53393-8
[14] DOI: 10.1103/RevModPhys.21.392 · Zbl 0035.26803
[15] DOI: 10.1007/978-3-642-96045-1
[16] Ireland K., Graduate Texts in Mathematics-87, in: A Classical Introduction to Modern Number Theory (1987)
[17] Nambu Y., Quantum Field Theory and Quantum Statistics (1987)
[18] DOI: 10.1088/0034-4885/67/3/R03
[19] DOI: 10.1142/9789812701596_0022
[20] DOI: 10.1140/epjd/e2005-00208-4
[21] Inonu E., Nuovo Cimento pp 705–
[22] DOI: 10.1103/RevModPhys.75.559 · Zbl 1205.83082
[23] DOI: 10.1007/BF00400170
[24] DOI: 10.1103/PhysRevD.24.371
[25] Wigner E. P., The World Treasury of Physics, Astronomy and Mathematics (1991)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.