#### Filter Results:

- Full text PDF available (11)

#### Publication Year

1962

2008

- This year (0)
- Last 5 years (0)
- Last 10 years (1)

#### Publication Type

#### Co-author

#### Journals and Conferences

Learn More

In order to obtain a consistent formulation of octonionic quantum mechanics (OQM), we introduce left-right barred operators. Such operators enable us to find the translation rules between octonionic numbers and 8×8 real matrices (a translation is also given for 4×4 complex matrices). We develop an octonionic relativistic free wave equation, linear in the… (More)

In order to obtain a consistent formulation of octonionic quantum mechanics (OQM), we introduce left-right barred operators. Such operators enable us to find the translation rules between octonionic numbers and 8 × 8 real matrices (a translation is also given for 4 × 4 complex matrices). The use of a complex geometry allows us to overcome the hermiticity… (More)

We discuss how to represent the non-associative octonionic structure in terms of the associative matrix algebra using the left and right octonionic operators. As an example we construct explicitly some Lie and Super Lie algebra. Then we discuss the notion of octonionic Grassmann numbers and explain its possible application for giving a superspace… (More)

Since a long time, it has been conjectured that there exists a possible connection between the different members of the ring division algebra (R, C,H,O) and the critical dimensions of the Green-Schwarz superstring action [1–3]. Especially, the octonionic case has gained much attention due to its possible relation to the 10 dimensions physics [4–10]. Not… (More)

An off-shell formulation for 6 and 10 dimensions simple supersymmetric Yang-Mills theories is presented. While the fermionic fields couple to left action of S3 and S7 respectively, the auxiliary ones couple to right action (and vice versa). To close the algebra off-shell, left and right actions must commute. For 6 dimensions quaternions work fine. The 10… (More)

We investigate Clifford Algebras structure over non-ring division algebras. We show how projection over the real field produces the standard Attiyah-Bott-Shapiro classification. Quaternions and octonions may be presented as a linear algebra over the field of real numbers R with a general element of the form Y = y0e0 + yiei, y0, yi ∈ R (1) where i = 1, 2, 3… (More)

- Merfat Fayez, Khaled Abdel-Khalek
- The Journal of the Egyptian Medical Association
- 1962

- QUATERNION ANALYSIS, Khaled Abdel-Khalek
- 2008

Quaternion analysis is considered in full details where a new analyticity condition in complete analogy to complex analysis is found. The extension to octonions is also worked out.

We investigate the seven sphere as a soft Lie algebra i.e. an algebra with structure functions instead of structure constants. We calculate its structure functions explicitly and also discuss some relevant points such as the validity of the Jacobi identities. Furthermore, we emphasis some important features such as the pointwise reduction, closure and some… (More)

- Manal-Ismail El-Hawary, F A el-Shobaki, +4 authors Ahmed A Khashaba
- The Gazette of the Egyptian Paediatric…
- 1975

The study deals with investigations on anaemia due to iron or protein calorie deficiency and that associating acute glomerulonephritis, nephrosis and schistosoma haematobium. The rate of intestinal iron absorption using an oral dose of ferrous sulphate equivalent to 4 mg clemental iron/kg body weight was studied. The supplementing action of ascorbic acid in… (More)