Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Field Equations in the Complex Quaternion Spaces   The paper aims to adopt the complex quaternion and octonion to formulate the
field equations for electromagnetic and gravitational fields. Applying the
octonionic representation enables one single definition to combine some physics
contents of two fields, which were considered to be independent of each other
in the past. J. C. Maxwell applied simultaneously the vector terminology and
the quaternion analysis to depict the electromagnetic theory. This method
edified the paper to introduce the quaternion and octonion spaces into the
field theory, in order to describe the physical feature of electromagnetic and
gravitational fields, while their coordinates are able to be the complex
number. The octonion space can be separated into two subspaces, the quaternion
space and the S-quaternion space. In the quaternion space, it is able to infer
the field potential, field strength, field source, field equations, and so
forth, in the gravitational field. In the S-quaternion space, it is able to
deduce the field potential, field strength, field source, and so forth, in the
electromagnetic field. The results reveal that the quaternion space is
appropriate to describe the gravitational features; meanwhile the S-quaternion
space is proper to depict the electromagnetic features.

6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
2
The categories of this paper are: math