Frame independence of the fundamental length in relativistic quantum field theory

Journal Article · Mon Feb 15 04:00:00 EST 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3276441· OSTI ID:21335910

Nagamachi, S ^[1]; Bruening, E ^[2]

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

Some time ago we proposed a relativistic quantum field theory with a fundamental length in terms of tempered ultrahyperfunctions [Bruening, E. and Nagamachi, S., 'Relativistic quantum field theory with a fundamental length', J. Math. Phys. 45, 2199 (2004); e-print arXiv:math-ph/0804.1663; 'Solutions of a linearized model of Heisenberg's fundamental equation II', J. Math. Phys. 49, 052304 (2008)]. The definition of the fundamental length by Bruening and Nagamachi ['Relativistic quantum field theory with a fundamental length', J. Math. Phys. 45, 2199 (2004)] seems to depend on the Lorentz frame which is used to define it. In this article we show that this is actually not the case. In addition we discuss in some detail the geometric and analytic realization of the fundamental length and point out some important difference to standard relativistic quantum field theory in the sense of Gaarding and Wightman.

• OSTI ID: 21335910
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 2 Vol. 51; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EQUATIONS
GEOMETRY
LORENTZ INVARIANCE
MATHEMATICAL SOLUTIONS
RELATIVISTIC RANGE
WIGHTMAN FIELD THEORY