数学中场论的某些新探索及其在物理学中的应用

摘要/Abstract

摘要：当数学分析中的空间维数和微积分的阶数n等推广到分数及各种数系时，场论及其公式也可以相应推广.笔者专门探讨了此时的Gauss定理，Stokes定理及相应的梯度、散度、旋度的推广，其中旋度可能有几种不同的形式，这又可以结合分形及复数维.最后探讨了在物理学中的应用，简述了由标量、矢量发展出的张量、旋量、扭量等.

关键词： 场论, 梯度, 散度, 旋度, 物理应用, 张量, 旋量, 扭量

Abstract: When the space-dimension of mathematics and the rank n of calculus are extended to fraction and various number-systems,the field theory and its formulas may be correspondingly extended.In these cases,Gauss law and Stokes law,and corresponding the extensions on gradient,divergence and curl are searched,in which there may be different forms of extensive curl.It may combine the fractal and complex-dimension.Moreover,the applications in physics are researched.The development from scalar and vector to tensor,spinor and twistor,etc.is stated briefly.

Key words: field theory, gradient, divergence, curl, physical application, tensor, spinor, twistor

张一方. 数学中场论的某些新探索及其在物理学中的应用[J]. journal6, 2010, 31(1): 47-53.

ZHANG Yi-Fang. Some New Researches of Field Theory in Mathematics and the Applications in Physics[J]. journal6, 2010, 31(1): 47-53.

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