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arXiv quant-ph/0512191quant-phhep-thmath-phmath.MP
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非定域性III:量子场的一般非定域性

Nonlocality III: General Nonlocality in Quantum Fields

Hai-Jhun Wanng

摘要:

在量子场的低能极限下,费米子波表现出非定域性。在这篇\QTR{it}{ab initio}论文中,我们提出了一个复杂的几何模型,揭示了非定域性对自旋为1/2的物质粒子之间的相互作用的影响。为了使非定域性质在量子理论中得到适当的应用,通过使量子粒子的波函数所张成的复空间弯曲,推广了特殊酉群SU(n)和Lorentz群的旋量表示$D^{(1/2,1/2)}$.弯曲空间是用广义相对论中的几何学来描述的,用复空间代替实空间,并在空间上附加解析条件。费米子和玻色子的场方程分别与测地线运动方程和所考虑的空间的局部曲率相关联。费米子方程可以恢复狄拉克方程二次型的所有项。根据场方程发现,对于U(1)场[广义量子电动力学(QED)],当电磁场$\vec E$和$\vec B$满足$\vec E^2-\vec B^2\neq 0$时,玻色子将获得质量。在这个模型中,一个物理区域是经验定义的,它可以用玻色子场方程中出现的行列式来表征。将场方程应用于U(3)场[广义量子色动力学(QCD)],可以通过实现物理区域的边界来理解夸克的禁闭性质。

英文摘要:

The waves of fermions display nonlocality in low energy limit of quantum fields. In this \QTR{it}{ab initio} paper we propose a complex-geometry model that reveals the affection of nonlocality on the interaction between material particles of spin-1/2. To make nonlocal properties appropriately involved in a quantum theory, the special unitary group SU(n) and spinor representation $D^{(1/2,1/2)}$ of Lorentz group are generalized by making complex spaces--which are spanned by wave functions of quantum particles--curved. The curved spaces are described by the geometry used in General Relativity by replacing the real space with complex space and additionally imposing the analytic condition on the space. The field equations for fermions and for bosons are respectively associated with geodesic motion equations and with local curvature of the considered space. The equation for fermions can restore all the terms of quadratic form of Dirac equation. According to the field equation it is found that, for the U(1) field [generalized Quantum Electrodynamics (QED)], when the electromagnetic fields $\vec E$ and $\vec B$ satisfy $\vec E^2-\vec B^2\neq 0$, the bosons will gain masses. In this model, a physical region is empirically defined, which can be characterized by a determinant occurring in boson field equation. Applying the field equation to U(3) field [generalized Quantum Chromodynamics (QCD)], the quark-confining property can be understood by carrying out the boundary of physical region.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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