# Principal fiber bundle description of number scaling for scalars and vectors: application to gauge theory

## Abstract

The purpose of this paper is to put the description of number scaling and its effects on physics and geometry on a firmer foundation, and to make it more understandable. A main point is that two different concepts, number and number value are combined in the usual representations of number structures. This is valid as long as one structure of each number type is being considered. It is not valid when different structures of each number type are being considered. Elements of base sets of number structures, considered by themselves, have no meaning. They acquire meaning or value as elements of a number structure. Fiber bundles over a space or space time manifold, M, are described. The fiber consists of a collection of many real or complex scaling factor, s. A vector space at a fiber level, s, has as scalars, real or complex number structures at the same level. Connections are described that relate scalar and vector space structures at both neighbor M locations and at neighbor scaling levels. Scalar and vector structure valued fields are described and covariant derivatives of these fields are obtained. Two complex vector fields, each with one real and one imaginary field, appear, withmore »

- Authors:

- Publication Date:

- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science - Office of Nuclear Physics

- OSTI Identifier:
- 1392600

- DOE Contract Number:
- AC02-06CH11357

- Resource Type:
- Journal Article

- Journal Name:
- Proceedings of SPIE - The International Society for Optical Engineering

- Additional Journal Information:
- Journal Volume: 9500; Journal ID: ISSN 0277-786X

- Publisher:
- SPIE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Donkor, Eric, Pirich, Andrew R., Hayduk, Michael, and Benioff, Paul.
```*Principal fiber bundle description of number scaling for scalars and vectors: application to gauge theory*. United States: N. p., 2015.
Web. doi:10.1117/12.2176080.

```
Donkor, Eric, Pirich, Andrew R., Hayduk, Michael, & Benioff, Paul.
```*Principal fiber bundle description of number scaling for scalars and vectors: application to gauge theory*. United States. doi:10.1117/12.2176080.

```
Donkor, Eric, Pirich, Andrew R., Hayduk, Michael, and Benioff, Paul. Thu .
"Principal fiber bundle description of number scaling for scalars and vectors: application to gauge theory". United States. doi:10.1117/12.2176080.
```

```
@article{osti_1392600,
```

title = {Principal fiber bundle description of number scaling for scalars and vectors: application to gauge theory},

author = {Donkor, Eric and Pirich, Andrew R. and Hayduk, Michael and Benioff, Paul},

abstractNote = {The purpose of this paper is to put the description of number scaling and its effects on physics and geometry on a firmer foundation, and to make it more understandable. A main point is that two different concepts, number and number value are combined in the usual representations of number structures. This is valid as long as one structure of each number type is being considered. It is not valid when different structures of each number type are being considered. Elements of base sets of number structures, considered by themselves, have no meaning. They acquire meaning or value as elements of a number structure. Fiber bundles over a space or space time manifold, M, are described. The fiber consists of a collection of many real or complex scaling factor, s. A vector space at a fiber level, s, has as scalars, real or complex number structures at the same level. Connections are described that relate scalar and vector space structures at both neighbor M locations and at neighbor scaling levels. Scalar and vector structure valued fields are described and covariant derivatives of these fields are obtained. Two complex vector fields, each with one real and one imaginary field, appear, with one complex field associated with positions in M and the other with position dependent scaling factors. A derivation of the covariant derivative for scalar and vector values fields gives the same vector fields. The derivation shoes that complex vector field associated with scaling fiber levels is the gradient of a complex scalar field. Use of these results in gauge theory shows that the imaginary part of the vector field associated with M positions acts like the electromagnetic field. The physical relevance of the other three fields, if any, is not known.},

doi = {10.1117/12.2176080},

journal = {Proceedings of SPIE - The International Society for Optical Engineering},

issn = {0277-786X},

number = ,

volume = 9500,

place = {United States},

year = {2015},

month = {5}

}