Formulation and Quantization of Field Equations on Fractal Space-Time
(2025) In International Journal of Theoretical Physics 64(7).- Abstract
This paper explores the framework of fractal calculus and its application to classical and quantum field theories. We begin with a brief overview of the fundamental concepts of fractal calculus. Building on this foundation, we introduce the formulation of the classical scalar field within a fractal space. The study is then extended to the quantization of the fractal field, where we examine how fractal geometry influences the quantization process. As a key example, we consider the fractal version of the Klein-Gordon equation and analyze how the fractal dimension affects the behavior of the field. Graphical representations are provided to illustrate the impact of fractal dimensions on the solutions. The paper concludes with a summary of... (More)
This paper explores the framework of fractal calculus and its application to classical and quantum field theories. We begin with a brief overview of the fundamental concepts of fractal calculus. Building on this foundation, we introduce the formulation of the classical scalar field within a fractal space. The study is then extended to the quantization of the fractal field, where we examine how fractal geometry influences the quantization process. As a key example, we consider the fractal version of the Klein-Gordon equation and analyze how the fractal dimension affects the behavior of the field. Graphical representations are provided to illustrate the impact of fractal dimensions on the solutions. The paper concludes with a summary of the results and their potential implications for future research in fractal field theory.
(Less)
- author
- Khalili Golmankhaneh, Alireza ; Pasechnik, Roman LU ; Jørgensen, Palle E.T. and Li, Shuming
- organization
- publishing date
- 2025-07
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- 03.50.-z, 03.65.Pm, 11.10.Lm, Fractal calculus, Fractal field theory, Fractal Klein-Gordon equation
- in
- International Journal of Theoretical Physics
- volume
- 64
- issue
- 7
- article number
- 183
- external identifiers
-
- scopus:105008325198
- ISSN
- 0020-7748
- DOI
- 10.1007/s10773-025-06052-z
- language
- English
- LU publication?
- yes
- additional info
- Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.
- id
- fac3d756-e31c-44f6-b307-12aee97394d9
- date added to LUP
- 2025-12-15 15:16:31
- date last changed
- 2025-12-15 15:17:24
@article{fac3d756-e31c-44f6-b307-12aee97394d9,
abstract = {{<p>This paper explores the framework of fractal calculus and its application to classical and quantum field theories. We begin with a brief overview of the fundamental concepts of fractal calculus. Building on this foundation, we introduce the formulation of the classical scalar field within a fractal space. The study is then extended to the quantization of the fractal field, where we examine how fractal geometry influences the quantization process. As a key example, we consider the fractal version of the Klein-Gordon equation and analyze how the fractal dimension affects the behavior of the field. Graphical representations are provided to illustrate the impact of fractal dimensions on the solutions. The paper concludes with a summary of the results and their potential implications for future research in fractal field theory.</p>}},
author = {{Khalili Golmankhaneh, Alireza and Pasechnik, Roman and Jørgensen, Palle E.T. and Li, Shuming}},
issn = {{0020-7748}},
keywords = {{03.50.-z; 03.65.Pm; 11.10.Lm; Fractal calculus; Fractal field theory; Fractal Klein-Gordon equation}},
language = {{eng}},
number = {{7}},
series = {{International Journal of Theoretical Physics}},
title = {{Formulation and Quantization of Field Equations on Fractal Space-Time}},
url = {{http://dx.doi.org/10.1007/s10773-025-06052-z}},
doi = {{10.1007/s10773-025-06052-z}},
volume = {{64}},
year = {{2025}},
}