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Superconnections and internal supersymmetry dynamics.
1Ministry of Science, Government of Israel, Jerusalem, Israel.
Summary
This study unifies quarks and leptons using internal supersymmetry (su(n/1)) and superconnections. The Higgs field naturally arises from superconnections, influencing particle interactions within this unified framework.
Area of Science:
- Theoretical Particle Physics
- Quantum Field Theory
- Supersymmetry
Background:
- Previous work proposed internal supersymmetry (su(n/1)) for unifying fundamental particles.
- Existing theories often introduce Higgs fields phenomenologically.
Purpose of the Study:
- To explore superconnections as a natural framework for internally supersymmetric theories.
- To investigate the role of the Higgs field within this superconnection formalism.
Main Methods:
- Utilizing the mathematical framework of superconnections as introduced by Quillen.
- Analyzing the structure of the superconnection and its curvature.
- Examining the implications of the supercovariant derivative.
Main Results:
- The Higgs field emerges as the "zero-th order part" of the superconnection.
- The Higgs mechanism is quadratically incorporated into the superconnection's curvature.
- The supercovariant derivative naturally couples the Higgs field to matter fields.
Conclusions:
- Superconnections provide a natural and unified setting for internally supersymmetric theories.
- This approach offers a more integrated explanation for the Higgs mechanism compared to previous models.
- The derived couplings align with those observed in the Weinberg-Salam theory.