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The Study on the Differential and Integral Calculus in pseudoeuclidean Space

Journal of Applied Mathematics and Physics 2017年第9期5卷 1739-1749页

作者： Gennady Tarabrin Department of Applied Mathematics Volgograd State Technical University Volgograd Russia

In the vector space of real vectors, comparison was executed of the multilinear forms, covariant derivatives, the total differentials and derivatives in the direction which are calculated with different metrics—with Euclidean metric and with pseudoeuclidean metric of a zero index. Comparison was executed of the Taylor’s formulas to different metrics. What is established by us is that multilinear forms of different metrics have different values;covariant derivatives have identical values;the total differentials and derivatives in the direction have different values. In Euclidean space, Taylor’s formula with any order of accuracy assigned in advance is equal, but in pseudoeuclidean space Taylor’s formula is not equal with any order of accuracy. It is concluded that in space with a pseudoeuclidean metric, the computing sense of the differential and integral calculus created in Euclidean space is lost and the possibility of mathematical model operation of real physical processes in vector space with pseudoeuclidean metric is called into question.

关键词： The Vector Spaces Taylor’s Formula pseudoeuclidean Metric

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The Unified Geometrical Theory of Fields and Particles

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Applied Mathematics 2014年第3期5卷 347-351页

作者： Amagh Nduka Department of Physics and Mathematics Federal University of Technology Owerri Nigeria

Wave-particle duality is a familiar concept in the theories of the fundamental processes. We have, for example, electromagnetic waves with the photon as the corresponding particle, gravitational waves with the graviton as the corresponding particle, and Dirac waves with the electron as the corresponding particle. All these theories are stand-alone theories having nothing in common. The outstanding problem is a unified theory of particles and fields. In this paper, we discuss a unified geometrical theory of fields and particles.

关键词： Wave-Particle Duality Boson Fermion Euclidean pseudoeuclidean Reducible Irreducible Discrete Geometry 4-Operator Invariant Operator

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