On a microscopic representation of space-time

Journal Article · Mon Oct 15 04:00:00 EDT 2012 · Physics of Atomic Nuclei

DOI:https://doi.org/10.1134/S1063778812100031· OSTI ID:22069335

Dahm, R ^[1]

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1. Beratung fuer Informationssysteme und Systemintegration (Germany)

We start from a noncompact Lie algebra isomorphic to the Dirac algebra and relate this Lie algebra in a brief review to low-energy hadron physics described by the compact group SU(4). This step permits an overall physical identification of the operator actions. Then we discuss the geometrical origin of this noncompact Lie algebra and 'reduce' the geometry in order to introduce in each of these steps coordinate definitions which can be related to an algebraic representation in terms of the spontaneous symmetry breakdown along the Lie algebra chain su*(4) {yields} usp(4) {yields} su(2) Multiplication-Sign u(1). Standard techniques of Lie algebra decomposition(s) as well as the (physical) operator identification give rise to interesting physical aspects and lead to a rank-1 Riemannian space which provides an analytic representation and leads to a 5-dimensional hyperbolic space H{sub 5} with SO(5, 1) isometries. The action of the (compact) symplectic group decomposes this (globally) hyperbolic space into H{sub 2} Circled-Plus H{sub 3} with SO(2, 1) and SO(3, 1) isometries, respectively, which we relate to electromagnetic (dynamically broken SU(2) isospin) and Lorentz transformations. Last not least, we attribute this symmetry pattern to the algebraic representation of a projective geometry over the division algebra H and subsequent coordinate restrictions.

• OSTI ID: 22069335
• Journal Information: Physics of Atomic Nuclei, Journal Name: Physics of Atomic Nuclei Journal Issue: 10 Vol. 75; ISSN 1063-7788; ISSN PANUEO
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
COORDINATES
HADRONS
ISOSPIN
LORENTZ TRANSFORMATIONS
MANY-DIMENSIONAL CALCULATIONS
QUANTUM FIELD THEORY
RIEMANN SPACE
SO GROUPS
SP GROUPS
SPACE-TIME
SU-2 GROUPS
SYMMETRY BREAKING