Coupling of Spin & Momentum (Papapetrou …Geometric Algebras, with Applications in Physics, Mathematics and Engineering, W. Baylis ed. (Birkhauser 1996). • J.S.R. Chisholm and R.S.

Coupling of Spin & Momentum (Papapetrou euqations) induced by

Curvature which does NOT Preserve n-vector rank.

Presentor: William M. Pezzaglia Jr. ([email protected]) Department of Physics, Santa Clara University, Santa Clara, CA 95053, USA

Pesentation at: 13th Pacific Coast Gravity Meeting, Institute for Theoretical Physics, UC Santa Barbara, 1997 Mar 21-22.

Abstract Suppose you parallel transport a vector around a closed loop, ... and it can back as a bivector? In this really brief 12 minute talk in which I will discuss the motivation, consequences and applications of such an idea. Specifically: (1) The spin-connection (spin-gauge theories of gravity) is a non-rank preserving curvature, (2) Classically this implies that Space, Particles and Laws must be poly-geometric, (3) The new curvature induces a natural coupling of spin & momentum as a geodesic in a polydimensional space.

The concepts presented in this talk were later expanded in the following talk at the ISAAC meeting (http://www.clifford.org/wpezzag/talk/97delaware/) and summarized in those conference proceedings (preprint gr-qc/9710027).

Index to Color Transparencies

1. Title Page

2. Automorphism Invariance induces Spin Coupling

3. Relation of Spin Space to Real Geometry

4. Riemann space vs. non-rank preserving curvature

5. The Clifford Polydimensional Manifold and Mechanics

6. Derivation of Papapetrou equations as a geodesic

7. Polygeometric Laws of Nature, Automorphism Invariant

8. Non-Rank Preserving Curvature and geodesics

9. Summary

10. References

• index of other talks at: http://www.clifford.org/~wpezzag/talks.html • This URL: http://www.clifford.org/wpezzag/talk/97santabarb/

Updated: 2005May20

References Note: concepts presented in this talk were later expanded in the following talk at the ISAAC meeting ((http://www.clifford.org/wpezzag/talk/97delaware/), and summarized in the preprint gr-qc/9710027: Physical Applications of a Generalized Clifford Calculus (Papapetrou equations and Metamorphic Curvature), which will appear in the conference proceedings.

• J. Crawford, Local automorphism invariance: Gauge boson mass without a Higgs particle, J. Math. Phys. 35, 2701 (1994); Hypergravity in Clifford Geometric Algebras, with Applications in Physics, Mathematics and Engineering, W. Baylis ed. (Birkhauser 1996).

• J.S.R. Chisholm and R.S. Farwell, Unified Spin Gauge Theory of Electroweak

and Gravitational Interactions, J. Phys. A22 1059 (1989); Spin gauge theories: principles and predictions, in Clifford Algebras and Their Applications in Mathematical Physics, proceedings of 3rd Conference, Belgium 1993, R. Delanghe et al (Kluwer 1993) pp. 367-374).

• W. Pezzaglia, Polydimensional Relativity, a Classical Generalization of the

Automorphism Invariance Principle, in the Proceedings of the 4th Conference on Clifford Algebras and their Applications in Mathematical Physics, Aachen, Germany 1996, K. Habetah ed., Kluwer (1998), pp. 305-317. Preprint gr-qc/9608052.

• W. Pezzaglia and A. Differ, A Clifford Dyadic Superfield from Bilateral

Interactions of Geometric Multipsin Dirac Theory, in Proceedings of XXIIth International Conf on Differential Geometric Methods in Theoretical Physics, Ixtapa-Zihuatanejo, Mexico 1993, J. Keller ed., Advances in Applied Clifford Algebras (Proc. Suppl.) 4 (S1) (1994) pp. 437-446. Preprint gr-qc/9311015

• I.B. Khriplovich, Particle with internal angular momentum in a gravitational

field, Sov. Phys. JETP 69, 217 (1989)

• index of other talks at: http://www.clifford.org/~wpezzag/talks.html • This URL: http://www.clifford.org/wpezzag/talk/97santabarb/

Updated: 2005May20