引力与强相互作用在非结合代数上的归纳
Induction of gravity and strong interactions on non-associative algebra
摘要：
在这项工作中，我们把时空看作是流形上场的对偶表示。如果我们接受这样的观点，算符表象中的函数空间就变成了粒子的概率幅f（x）。由于f（x）模的概率解释是由f（x）和f*（x）对偶性得出的，所以寻找波函数表示的问题归结为除代数的Frobenius定理。然后，我们构造了引力模型和强相互作用模型，作为场相互作用代数到八元数非结合代数的推广的逻辑蕴涵。Penrouse方法在时空旋量表示中的应用与所提出的方法相结合，进一步导致我们的手征的相互作用和缺乏右中微子和左旋量的单原子态。我们还证明了当距离大于普朗克长度时，所得到的模型与广义相对论和SU（3）是一致的。所得到的模型也包含了广义相对论的推广，扭转给定的手征场的模型。重要的是，我们的方法的应用程序给我们爱因斯坦方程的引力常数等于平方普朗克质量的相互作用场的非结合性的后果。基于八元数代数的矩阵表示和特殊的乘法规则，构造了强相互作用模型。强相互作用是由具有常重力的八元数代数的矢量场引起的，而常重力又是由弱相互作用标准理论中的一对带电$W$矢量玻色子引起的。夸克禁闭问题被描述为“黑洞“内部的旋量解。
英文摘要：
In this work we take view on space-time as dual representation of fields on manifold. Given we accept such view, the space of functions in operator representation becomes probability amplitudes f(x) of a particle. Since the probabilistic interpretation of f(x) module follows from f(x) and f*(x) duality, the problem of finding representation of wave function reduces to Frobenius theorem for division algebras. We then construct the gravity model and the model of strong interactions as a logical implication of the extension of fields interaction algebra to non-associative algebra of octonions. The application of Penrouse approach in spinor representation of space-time combined with the proposed approach further leads us to chirality of interactions and absence of right neutrino and left spinors in singleton state. We also show the obtained model is consistent with general theory of relativity and SU(3) for distances larger than Planck length. The obtained model also contains the generalization of general theory of relativity to the model with torsion given the chirality of the field. Importantly, the application of our approach gives us Einstein equation with gravity constant equal to squared Planck mass as consequence of non-associativity of interactions fields. We construct strong interaction model based on matrix representation of octonion algebra with special multiplication rule. The strong interaction is induced by vector fields of octonion algebra with constant gravity force, which is in turn induced by a pair of charged $W$ vector bosons from standard theory of weak interactions. The problem of quark confinement is presented as a spinor solution inside "black hole".
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