质量算符和五维概率分布空间的规范场理论(英文)

鉴于量子场论中普遍存在的粒子产生和湮灭,把描述场量的独立变量个数从量子力学波函数的4个常规时空坐标推广到了5个,其中第5个独立变量对应为粒子的内禀固有时,但是粒子运动的背景还是4维的常规时空。在场函数中固有时之所以可以看作为独立于常规时空坐标的变量,不仅是量子物理所特有的概率性描述语言所允许的,而且有可能是描述量子场论中广泛存在的粒子产生和湮灭现象所必需的。与此对应,在量子场论中,引入了质量算符((?)=-i(?))。由此,自由费米场在推广到五维概率分布空间和引入质量算符的基础上,根据相互作用的规范原理,引入了矢量规范相互作用和标量规范相互作用,同时所有的基本粒子的质量项都由质量算符自然地呈现。在此物理图像下,原则上基本粒子的质量应该通过求解相互作用耦合下的质量算符的本征值得到。此外,理论中存在普遍耦合的标量规范场和质量算符天然地联系在一起,有可能和引力作用对应起来。

Mass Operator and Gauge Field Theory with Five-variable Field Functions

To investigate the mass generating problem without Higgs mechanism we present a model in which a new scalar gauge coupling is naturally introduced. Because of the existence of production and annihilation for particles in quantum eld theory, we extend the number of independent variables from conventional four space-time dimensions to ve ones in order to describe all degrees of freedom for eld functions while the conventional space-time is still retained to be the background. The potential fth variable is nothing but the proper time of particles. In response, a mass operator should be introduced. After that, the lagrangian for free fermion elds in terms of ve independent variables and mass operator is written down. By applying the gauge principle, three kinds of vectorgauge couplings and one kind of scalar gauge coupling are naturally introduced. In the current scenario,the mass spectrum for all fundamental particles is accounted for in principle by solving the eigenvalue of mass operator under the function of all kinds of interactions. Moreover, there no any auxiliary mechanism including spontaneous symmetry breaking get involved in the model. Therefore, traditional problems in the standard model such as the vacuum energy problem are removed from our model, as well as the hierarchy problem on the mass spectrum for fundamental particles.