Why is quantum physics based on complex numbers?

Finite Fields and their Applications

Volumn 12, Issue 3, 2006, Pages 336-356

  Lev, Felix M ^a  

^a Artwork Conversion Software Inc   (United States)

Author keywords

Finite fields; Modular representations; Quantum theory

Indexed keywords

ALGEBRA; FINITE AUTOMATA; NUMBER THEORY;

FINITE FIELDS; HILBERT SPACE; MODULAR REPRESENTATIONS;

QUANTUM THEORY;

EID: 33747242673     PISSN: 10715797     EISSN: 10902465     Source Type: Journal    
DOI: 10.1016/j.ffa.2005.07.006     Document Type: Article

References (20)

1. Bateman H., and Erdelyi A. Higher Transcendental Functions (1953), McGraw-Hill, New York
2. Beltrametti E. Rotations and Lorentz group in a finite geometry. J. Math. Phys. 9 (1968) 1027-1035
3. Beltrametti E. Dirac spinors covariant currents and the Lorentz group, over a finite geometry. Nuovo Cimento 55A (1968) 301-317
4. H. Doughty, Private Communication of June 24th, 2004;
5. Vourdas A. Quantum systems with finite Hilbert space. Rep. Progr. Phys. 67 (2004) 267-320
6. M. Planat, M. Saniga, Abstract algebra, projective geometry and time encoding of quantum information, quant-ph/0503159
7. M. Planat, H. Rosu, Mutually unbiased phase states, phase uncertainties and Gauss sums, Eur. Phys. J., D, to be published.
8. * SU ( 2 ) shift operators and representations of SO(5). J. Math. Phys. 24 (1983) 1015-1020
9. J.C. Jantzen, Representation of Lie algebras in prime characteristics, Representation theories and algebraic geometry, NATO Asi Series, Series C, Mathematical Physics Science, vol. 514, Kluwer Academic Publisher, Dordrecht, 1998, pp. 185-235.
10. Lev F.M. Representations of de Sitter algebras over a finite field and their possible interpretations. Sov. J. Nucl. Phys. 48 (1988) 903-912
11. Lev F.M. Modular representations as a possible basis of finite physics. J. Math. Phys. 30 (1989) 1985-1998
12. Lev F.M. Finiteness of physics and its possible consequences. J. Math. Phys. 34 (1993) 490-527
13. Lev F.M. Massless elementary particles in a quantum theory over a Galois field. Theoret. Math. Phys. 138 (2004) 208-225
14. Lev F.M. Could only fermions be elementary?. J. Phys. A 37 (2004) 3285-3304
15. Levy-Leblond J.-M. Who is afraid of non-Hermitian operators? Phase and angle in quantum mechanics. Ann. Phys. (N.Y.) 101 (1976) 319-341
16. Bender C.M., Brody D.C., and Jones H.F. Must a Hamiltonian be Hermitian?. Am. J. Phys. 71 (2003) 1095-1102
17. Mostafazadeh A. Pseudo-Hermiticity and generalized PT and CPT symmetries. J. Math. Phys. 44 (2003) 974-989
18. Van der Waerden B.L. Algebra I (1967), Springer, Berlin, Heidelberg, New York
19. Ireland K., and Rosen M. A Classical Introduction to Modern Number Theory. Graduate Texts in Mathematics vol. 87 (1987), Springer, New York, Heidelberg, Berlin
20. Zassenhaus H. The representations of Lie algebras of prime characteristics. Proc. Glasgow Math. Assoc. 2 (1954) 1-36