Free States and Particles

Abstract

Classical mechanics utilizes the idealized concept of a pointlike particle — a point in the real s-dimensional position space ${\mathbb {M}}^s$, especially $s=3$, or in the phase space $\mathbb P^{2ns}$ for n particles. With the position-momentum uncertainty of quantum mechanics, and, also, with the detection of spin (“intrinsic angular momentum”), this concept became inappropriate or fuzzy, to say the least. Particle properties are characterized by invariants and eigenvalues for operations: The experimental setup decides about the properties which will be measured with their eigenvalues.