Considerations on the hyperbolic complex Klein-Gordon equation

Journal Article · Tue Jun 15 00:00:00 EDT 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3397456· OSTI ID:21362156

Ulrych, S ^[1]

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1. Wehrenbachhalde 35, CH-8053 Zuerich (Switzerland)

This article summarizes and consolidates investigations on hyperbolic complex numbers with respect to the Klein-Gordon equation for fermions and bosons. The hyperbolic complex numbers are applied in the sense that complex extensions of groups and algebras are performed not with the complex unit, but with the product of complex and hyperbolic unit. The modified complexification is the key ingredient for the theory. The Klein-Gordon equation is represented in this framework in the form of the first invariant of the Poincare group, the mass operator, in order to emphasize its geometric origin. The possibility of new interactions arising from hyperbolic complex gauge transformations is discussed.

• OSTI ID: 21362156
• Journal Information: Journal of Mathematical Physics, Vol. 51, Issue 6; Other Information: DOI: 10.1063/1.3397456; (c) 2010 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
AXIOMATIC FIELD THEORY
BOSONS
FERMIONS
GAUGE INVARIANCE
GEOMETRY
GROUP THEORY
KLEIN-GORDON EQUATION
NONLINEAR PROBLEMS
POINCARE GROUPS
RELATIVISTIC RANGE
DIFFERENTIAL EQUATIONS
ENERGY RANGE
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM FIELD THEORY
SYMMETRY GROUPS
WAVE EQUATIONS