1304.4024 (Kaare Borchsenius)

Constructing Quantum Mechanics from a Clifford substructure of the
relativistic point particle    [PDF]

Kaare Borchsenius

We show that the quantized free relativistic point particle is equivalent to a classical string in a Clifford Space which generates the space-time coordinates through its inner product. The generating algebra is preserved by a unitary symmetry which becomes the symmetry of the quantum states. We start by resolving the space-time canonical variables of the point particle into inner products of Weyl spinors with components in a Clifford algebra. Next, we build a dynamical system of N particles which has a U(N) symmetry that mixes the coordinates and momenta belonging to different particles. The reverse problem is formulated in terms of the commutation relations [X,P]=ik. For k=0, the system can be gauged back into a system of independent particles. For k#0, the system becomes an irreducible and infinite system of coupled particles and generates a space-time canonical system formally identical to that of Matrix Mechanics. The continuum limit is identified as a particular parametrization of a relativistic string in Clifford Space.

View original: http://arxiv.org/abs/1304.4024