论物质谱的代数结构
On algebraic structure of matter spectrum
摘要：
研究了物质谱的一种代数结构。它表明，一个基本的数学结构，躺在地面的物质谱（海森堡介绍），是一个两级希尔伯特空间。希尔伯特空间的两级结构由以下两个对定义：1）具有算子代数和基本对称性的可分希尔伯特空间; 2）具有动力学和规范对称性的不可分（物理）希尔伯特空间，即物质谱的状态（能级）空间。每个物质态的光谱由Gel'fand-Naimark-Segal结构中的循环表示定义。给出了物理希尔伯特空间到凝聚子空间的一种分解。这种分解允许人们在平等的基础上描述所有观测到的态谱，包括物质谱的轻子、介子和重子扇区。根据海森堡的理论，我们假设不存在基本粒子，存在基本对称性。本文还指出，物质谱的所有对称性可分为三种：基本对称性、动力学对称性和规范对称性。
英文摘要：
An algebraic structure of matter spectrum is studied. It is shown that a base mathematical construction, lying in the ground of matter spectrum (introduced by Heisenberg) , is a two-level Hilbert space. Two-level structure of the Hilbert space is defined by the following pair: 1) a separable Hilbert space with operator algebras and fundamental symmetries; 2) a nonseparable (physical) Hilbert space with dynamical and gauge symmetries, that is, a space of states (energy levels) of the matter spectrum. The each state of matter spectrum is defined by a cyclic representation within Gel'fand-Naimark-Segal construction. A decomposition of the physical Hilbert space onto coherent subspaces is given. This decomposition allows one to describe the all observed spectrum of states on an equal footing, including lepton, meson and baryon sectors of the matter spectrum. Following to Heisenberg, we assume that there exist no fundamental particles, there exist fundamental symmetries. It is shown also that all the symmetries of matter spectrum are divided onto three kinds: fundamental, dynamical and gauge symmetries.
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