# Bulletin of the American Physical Society

# APS April Meeting 2023

## Volume 68, Number 6

##
Minneapolis, Minnesota (Apr 15-18)

Virtual (Apr 24-26); Time Zone: Central Time

### Session XX01: V: Poster Session II (10:00am-11:00am CDT)

10:00 AM,
Wednesday, April 26, 2023

Room: Virtual Room 1

Chair: Kassahun Betre, San Jose State University; Labani Mallick, Caltech

### Abstract: XX01.00017 : Phenomenological QED model in the minimally complete Geometric Representation of Clifford Algebra - What is the Gauge Group?*

#### Presenter:

peter cameron

(Michigan/MIT/Brookhaven (retired))

#### Author:

peter cameron

(Michigan/MIT/Brookhaven (retired))

#### Collaboration:

none

In geometric representation of Clifford algebra, Pauli matrices are the basis vectors of 3D space, Dirac those of 4D spacetime. Vacuum wavefunction is comprised of the Pauli algebra's 8 components - 1 scalar point, 3 vector lines (orientational degrees-of-freedom), 3 bivector areas, and 1 trivector volume. Interaction is modeled by the Clifford product, sum of dimension-reducing dot and increasing wedge products. The 8 wavefunction components one might take to be E8 root vectors, gauge group generators via the Clifford product.

The 4 fundamental constants (electric charge quantum

*e*, Planck's angular momentum quantum

*h*, speed of light

*c*, and magnetic permeability of space

*μ*) that define the QED coupling constant

*α*permit assigning unique geometrically and topologically appropriate electric and magnetic flux quanta to each of the 8 vacuum wavefunction components. This removes the 3-fold degeneracy of vector and bivector, and increases dimensionality to 10D. Time emerges from interactions, via wedge products' dimension-increasing property. Taking quantum interaction impedances of the modes to be components of the 8 x 8 x 8 S-matrix makes it the gauge group as well. Do we call this E8 x E8 x E8?

In physical spacetime the S-matrix has 6 degrees-of-freedom, 3 each space and phase. Each orientation requires its own phase. Time is the integral of phase, collapses 6D phase space to 4D spacetime. Do we call the physical S-matrix E6, the largest possible unification group according to Georgi? Is Weinberg's preference for E8 x E8 compacted to E6 realized in this approach?

*none

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