2013/04/15 by Kaare Borchsenius, Borchsenius, Kaare
Mathematics · Medicine · Physics and Astronomy · #Algebraic and Geometric Analysis #Biofield Effects and Biophysics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1304.4024
openalex publication_date 2013/04/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We show that the quantized free relativistic point particle can be understood as a 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 show that a system of N particles has a U(N) symmetry that mixes the Clifford coordinates and momenta belonging to different particles. The inner products of these variables are assembled into Hermitian matrices X and P which are employed in defining a general unitarily invariant dynamical system. When X and P commute, this system can be gauged back into the original system of independent particles. When they do not commute, the system becomes irreducible and infinite and generates a space-time canonical system formally identical to Matrix Mechanics. The continuum limit is identified as a particular parametrization of a relativistic string in Clifford space.