A framework for quantum theory of elementary physical entities

Abstract

A unified framework, which is directly established on the quantum ground, is proposed for elementary physical entities, called \emph{modes} in this paper. The framework is mainly built upon five basic assumptions, which loosely speaking have the following contents. (i) The state space of each mode is given by the direct product of a momentum-state space and a spinor-state space, the latter of which is certain representation space of the $SL(2,C)$ group (a covering group of the Lorentz group); (ii) spinor states of modes have a layer-type structure and modes are either fermionic or bosonic, depending on their helicity properties; (iii) there are three fundamental processes -- free evolution, vacuum fluctuation (emergence or vanishing of a pair of fermionic modes that possess exactly opposite physical properties), and two fundamental interaction processes (change of two fermionic modes into one bosonic mode and the reverse); (iv) vacuum fluctuation happens instantly; and (v) the time evolution operator is constructed from operators, which map state spaces of incoming modes of fundamental processes to those of outgoing modes. The time evolution operator turns out to be a function of quantum fields that are constructed from creation and annihilation operators for free-mode states, whose interaction part has a local feature. As an example, a simple model of modes is studied and is compared with the first-generation part of the standard model (SM). Concerning electroweak interactions, the studied model has a time evolution operator, whose main body is formally similar to that of the SM. Besides, it predicts $\frac 13$ and $\frac 23$ electronic changes for quark-type modes, gives an interpretation to the color degree of freedom, and contains certain modes that behave like dark matters.