Solution of a linearized model of Heisenberg's fundamental equation II

Journal Article · Thu May 15 04:00:00 EDT 2008 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2921636· OSTI ID:21100283

Bruening, E ^[1]; Nagamachi, S ^[2]

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1. School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X54001, Durban 4000 (South Africa)
2. Department of Applied Physics and Mathematics, Faculty of Engineering, The University of Tokushima, Tokushima 770-8506 (Japan)

We propose to look at (a simplified version of) Heisenberg's fundamental field equation [see Heisenberg, W., Introduction to the Unified Field Theory of Elementary Particles (Wiley, New York, 1966)] as a relativistic quantum field theory with a fundamental length, as introduced by Bruening and Nagamachi [J. Math. Phys. 45, 2199 (2004)], and give a solution in terms of Wick power series of free fields which converge in the sense of ultrahyperfunctions but not in the sense of distributions. The solution of this model has been prepared by Nagamachi and Bruening [arXiv:0804.1663] by calculating all n-point functions by using path integral quantization. The functional representation derived in this part is essential for the verification of our condition of extended causality. The verification of the remaining defining conditions of a relativistic quantum field theory is much simpler through the use of Wick power series. Accordingly in this second part, we use Wick power series techniques to define our basic fields and derive their properties.

• OSTI ID: 21100283
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 5 Vol. 49; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CAUSALITY
FIELD EQUATIONS
HEISENBERG PICTURE
MATHEMATICAL SOLUTIONS
PATH INTEGRALS
POWER SERIES
QUANTIZATION
QUANTUM FIELD THEORY
RELATIVISTIC RANGE
UNIFIED-FIELD THEORIES
VERIFICATION