扩张流形框架下的旋量场、CPTM对称性和宇宙学常数的小性
Spinor fields, CPTM symmetry and smallness of cosmological constant in framework of extended manifold
摘要：
本文讨论了Dirac旋量场的一个扩展流形模型。对一对Dirac旋量场构造了两个由电荷-宇称-时间-质量（CPTM）对称性联系起来的拉格朗日量，每个旋量场定义在一个单独的流形中。流形中的物质场之间的相互作用是通过引力引入的。构造了一般系统的费米子有效作用量，并计算了蝌蚪单圈旋量图和部分单圈真空图，其中两个外引力离壳场对有效作用量有贡献.证明了在不同形式的第二旋量拉格朗日量中，有一种特殊的第二旋量拉格朗日量，它的总有效作用量中的上述图被取消。结果，这些图对宇宙学常数没有贡献，旋量场的零点能量对作用量的贡献也为零。框架中每个流形的宇宙学常数的非零首阶值与每个分离流形的物质密度或密度差成比例，这取决于所选择的引力场与费米子相互作用的模型。在模型中的暗物质的外观，以及进一步的应用程序的方法进行了讨论。
英文摘要：
A model of an extended manifold for the Dirac spinor field is considered. Two Lagrangians related by CPTM (charge-parity-time-mass) symmetry are constructed for a pair of the Dirac spinor fields with each spinor field defined in a separate manifold. An interaction between the matter fields in the manifolds is introduced through gravity. A fermionic effective action of the general system is constructed and a tadpole one-loop spinor diagram and part of the one-loop vacuum diagrams with two external gravitational off-shell fields which contribute to the effective action are calculated. It is demonstrated that among different versions of the second spinor Lagrangian there is a special one for which a cancellation of the mentioned diagrams in the total effective action takes place. As a result, the diagrams do not contribute to the cosmological constant, as well there is a zero contribution of the zero point energies of the spinor fields to the action. The non-zero leading order value of the cosmological constant for each manifold in the framework is proportional to the matter density of each separated manifold or difference of the densities, depending on the chosen model of interaction of gravitational fields with fermions. An appearance of the dark matter in the model is shortly discussed as well as further applications of the approach.
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