Fundamental length hypothesis in a gauge theory context
The new gauge formulation of the electromagnetic interaction theory, containing the fundamental length l as a universal scale like h and c, is worked out. A key part belongs to the 4-dimensional de Sitter p-space, with the curvature radius h/lc. In the new approach the electromagnetic potential becomes a 5-vector associated with de Sitter group 0(4.1). The extra fifth component, called the tau-photon, similar to scalar and longitudinal photons, does not correspond to an independent dynamical degree of freedom. Respectively, the new local gauge group is larger than the ordinary one and depends intrinsically on the fundamental length l. The gauge invariant equations of motion, replacing the Dirac-Maxwell equations, are set up. The new formulation is minimal with respect to the 5-potential but is not so in terms of the usual 4-potential. As a result, the underlying physics looks much richer than the ordinary electromagnetic phenomena. The new scheme predicts the existence of the electric dipole moments for charged particles, leading to a direct violation of P- and CP-symmetries, and the new universal correction to the (g-2)-anomaly. Further, some new group of internal symmetry, SU/sub tau/(2), arises that can be used to describe the ..mu..e-symmetry of the electromagnetic interactions. It turns out that SU/sub -/(2)-symmetry is violated by the 4-fermion type interaction, induced by tau-photons, with associated ocupling constant approx...cap alpha..l/sup 2/. This novel interaction might give rise to the ..mu..e-mass difference and processes like ..mu.. ..-->.. 3e, ..mu.. ..-->.. ..gamma.., etc. In the limit l ..-->.. 0, the new field equations turn into the Dirac-Maxwell equations for the electron, muon and electromagnetic fields. The upper bound for the fundamental length l is discussed taking into account the various experimental data. 4 references.
- Research Organization:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
- DOE Contract Number:
- EY-76-C-02-3000
- OSTI ID:
- 6460774
- Report Number(s):
- FERMILAB-CONF-78/71-THY; CONF-7809126-1; TRN: 79-009830
- Resource Relation:
- Conference: Integrative conference on group theory and mathematical physics, Austin, TX, USA, Sep 1978
- Country of Publication:
- United States
- Language:
- English
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CHARGED PARTICLES
ELECTRIC DIPOLE MOMENTS
ELECTROMAGNETIC INTERACTIONS
ELEMENTARY LENGTH
GAUGE INVARIANCE
ELECTRONS
FIELD THEORIES
MASS DIFFERENCE
LIMITING VALUES
MUONS
COUPLING CONSTANTS
CP INVARIANCE
DE SITTER GROUP
DIRAC EQUATION
EQUATIONS OF MOTION
FERMI INTERACTIONS
FIELD EQUATIONS
FOUR-DIMENSIONAL CALCULATIONS
MAXWELL EQUATIONS
O GROUPS
P INVARIANCE
PHOTONS
POTENTIAL SCATTERING
SU-2 GROUPS
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BASIC INTERACTIONS
DIFFERENTIAL EQUATIONS
DIPOLE MOMENTS
DISTANCE
DYNAMICAL GROUPS
ELASTIC SCATTERING
ELECTRIC MOMENTS
ELEMENTARY PARTICLES
EQUATIONS
FERMIONS
INTERACTIONS
INVARIANCE PRINCIPLES
LEPTONS
LIE GROUPS
MASSLESS PARTICLES
PARTICLE PROPERTIES
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645202* - High Energy Physics- Particle Interactions & Properties-Theoretical- Electromagnetic Interactions & Properties