跳至主要内容

Complex Spacetime Frame: Four-Vector Identities and Tensors

Read full paper at:
http://www.scirp.org/journal/PaperInformation.aspx?PaperID=51408#.VGlR5mfHRK0

Author(s) 
This paper provides derivation of some basic identities for complex four-component vectors defined in a complex four-dimensional spacetime frame specified by an imaginary temporal axis. The resulting four-vector identities take exactly the same forms of the standard vector identities established in the familiar three-dimensional space, thereby confirming the consistency of the definition of the complex four-vectors and their mathematical operations in the general complex spacetime frame. Contravariant and covariant forms have been defined, providing appropriate definitions of complex tensors, which point to the possibility of reformulating differential geometry within a spacetime frame.
Cite this paper
Omolo, J. (2014) Complex Spacetime Frame: Four-Vector Identities and Tensors. Advances in Pure Mathematics, 4, 567-579. doi: 10.4236/apm.2014.411065. 
 

[1] Akeyo Omolo, J. (2014) On a Derivation of the Temporal Unit Vector of Space-Time Frame. Journal of Applied Mathematics and Physics, in Press.
[2] Poincare, H. (1906) Sur la dynamique de l’e’lectron (On the Dynamics of the Electron). Rendiconti del Circolo Matematico di Palermo, 21, 129.
[3] Lorentz, H.A. (1904) Electromagnetic Phenomena in a System Moving with Any Velocity Smaller than That of Light. Proceedings of the Royal Netherlands Academy of Arts and Sciences, 6, 809
[4] Einstein, A. (2003) The Meaning of Relativity. Routledge Classics, London and New York.
[5] Charbonneau, P. (2013) Solar and Stellar Dynamics. Saas-Fee Advanced Course, 39, 215.
[6] Arfken, G.B. and Weber, H.J. (1995) Mathematical Methods for Physicists. Academic Press Inc., San Diego.
[7] Landau, L.D. and Lifshitz, E.M. (1975) The Classical Theory of Fields. Pergamon Press Ltd., Oxford.
[8] Dirac, P.A.M. (1975) General Theory of Relativity. John Wiley and Sons Inc., New York.
[9] Bogoslovsky, G.Y. (2007) Some Physical Displays of the Space Anisotropy Relevant to the Feasibility of Its Being Detected at a Laboratory. arXiv:0706.2621 [gr-qc]
[10] Gibbons, G.W., Gomis, J. and Pope, C.N. (2007) General Very Special Relativity in Finsler Geometry. Physical Review D, 76, Article ID: 081701. http://dx.doi.org/10.1103/PhysRevD.76.081701                eww141117lx
标签：

评论

发表评论

此博客中的热门博文

A Comparison of Methods Used to Determine the Oleic/Linoleic Acid Ratio in Cultivated Peanut (Arachis hypogaea L.)

Cultivated peanut ( Arachis hypogaea L.) is an important oil and food crop. It is also a cheap source of protein, a good source of essential vitamins and minerals, and a component of many food products. The fatty acid composition of peanuts has become increasingly important with the realization that oleic acid content significantly affects the development of rancidity. And oil content of peanuts significantly affects flavor and shelf-life. Early generation screening of breeding lines for high oleic acid content greatly increases the efficiency of developing new peanut varieties. The objective of this study was to compare the accuracy of methods used to classify individual peanut seed as high oleic or not high oleic. Three hundred and seventy-four (374) seeds, spanning twenty-three (23) genotypes varying in oil composition (i.e. high oleic (H) or normal/not high oleic (NH) inclusive of all four peanut market-types (runner, Spanish, Valencia and Virginia), were individually tested ...
发表评论
阅读全文

Location Optimization of a Coal Power Plant to Balance Costs against Plant’s Emission Exposure

Fuel and its delivery cost comprise the biggest expense in coal power plant operations. Delivery of electricity from generation to consumers requires investment in power lines and transmission grids. Placing a coal power plant or multiple power plants near dense population centers can lower transmission costs. If a coalmine is nearby, transportation costs can also be reduced. However, emissions from coal plants play a key role in worsening health crises in many countries. And coal upon combustion produces CO 2 , SO 2 , NO x , CO, Metallic and Particle Matter (PM10 & PM2.5). The presence of these chemical compounds in the atmosphere in close vicinity to humans, livestock, and agriculture carries detrimental health consequences. The goal of the research was to develop a methodology to minimize the public’s exposure to harmful emissions from coal power plants while maintaining minimal operational costs related to electric distribution losses and coal logistics. The objective was...
发表评论
阅读全文

Evaluation of the Safety and Efficacy of Continuous Use of a Home-Use High-Frequency Facial Treatment Appliance

At present, many home-use beauty devices are available in the market. In particular, many products developed for facial treatment use light, e.g., a flash lamp or a light-emitting diode (LED). In this study, the safety of 4 weeks’ continuous use of NEWA TM , a high-frequency facial treatment appliance, every alternate day at home was verified, and its efficacy was evaluated in Japanese individuals with healthy skin aged 30 years or older who complained of sagging of the facial skin.  Transepidermal water loss (TEWL), melanin levels, erythema levels, sebum secretion levels, skin color changes and wrinkle improvement in the facial skin were measured before the appliance began to be used (study baseline), at 2 and 4 weeks after it had begun to be used, and at 2 weeks after completion of the 4-week treatment period (6 weeks from the study baseline). In addition, data obtained by subjective evaluation by the subjects themselves on a visual analog scale (VAS) were also analyzed. Fur...
发表评论
阅读全文