Formulation and Quantization of Field Equations on Fractal Space-Time

Khalili Golmankhaneh A., Pasechnik R., Jørgensen P. E. T., Li S.

International Journal of Theoretical Physics, cilt.64, sa.7, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 64 Sayı: 7
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1007/s10773-025-06052-z
  • Dergi Adı: International Journal of Theoretical Physics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: 03.50.-z, 03.65.Pm, 11.10.Lm, Fractal calculus, Fractal field theory, Fractal Klein-Gordon equation
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

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.