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Fractal Quantum Nambu Mechanics

Khalili Golmankhaneh, Alireza ; Pasechnik, Roman LU ; Jørgensen, Palle E.T. and Li, Shuming (2026) In Foundations of Physics 56(1).
Abstract

This paper develops a comprehensive framework for the extension of classical and quantum mechanics to fractal settings. We begin by summarizing the classical formulation of Fractal Nambu Mechanics and then introduce its quantization. The Fractal Hamilton-Jacobi Theory is established to describe dynamical systems evolving over fractal time and space, followed by a fractal generalization of the quantum Hamilton-Jacobi framework. We further formulate the Fractal Nambu-Hamilton-Jacobi Theory and propose its quantum counterpart–the Quantum Fractal Nambu-Hamilton-Jacobi Theory. These constructions demonstrate how the structure of Nambu mechanics, when combined with local fractal calculus, can provide new insights into systems with multiple... (More)

This paper develops a comprehensive framework for the extension of classical and quantum mechanics to fractal settings. We begin by summarizing the classical formulation of Fractal Nambu Mechanics and then introduce its quantization. The Fractal Hamilton-Jacobi Theory is established to describe dynamical systems evolving over fractal time and space, followed by a fractal generalization of the quantum Hamilton-Jacobi framework. We further formulate the Fractal Nambu-Hamilton-Jacobi Theory and propose its quantum counterpart–the Quantum Fractal Nambu-Hamilton-Jacobi Theory. These constructions demonstrate how the structure of Nambu mechanics, when combined with local fractal calculus, can provide new insights into systems with multiple invariants and non-smooth geometric evolution.

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author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
28A80, 70H20, 81S10, Fractal calculus, Fractal Hamilton–Jacobi theory, Fractal Nambu mechanics, Fractal Quantum Nambu mechanics
in
Foundations of Physics
volume
56
issue
1
article number
1
publisher
Springer
external identifiers
  • scopus:105022706678
ISSN
0015-9018
DOI
10.1007/s10701-025-00901-x
language
English
LU publication?
yes
id
10bc7b7b-4397-4936-8dd9-a3d6cac6e5c5
date added to LUP
2026-02-16 10:47:45
date last changed
2026-03-09 11:44:36
@article{10bc7b7b-4397-4936-8dd9-a3d6cac6e5c5,
  abstract     = {{<p>This paper develops a comprehensive framework for the extension of classical and quantum mechanics to fractal settings. We begin by summarizing the classical formulation of Fractal Nambu Mechanics and then introduce its quantization. The Fractal Hamilton-Jacobi Theory is established to describe dynamical systems evolving over fractal time and space, followed by a fractal generalization of the quantum Hamilton-Jacobi framework. We further formulate the Fractal Nambu-Hamilton-Jacobi Theory and propose its quantum counterpart–the Quantum Fractal Nambu-Hamilton-Jacobi Theory. These constructions demonstrate how the structure of Nambu mechanics, when combined with local fractal calculus, can provide new insights into systems with multiple invariants and non-smooth geometric evolution.</p>}},
  author       = {{Khalili Golmankhaneh, Alireza and Pasechnik, Roman and Jørgensen, Palle E.T. and Li, Shuming}},
  issn         = {{0015-9018}},
  keywords     = {{28A80; 70H20; 81S10; Fractal calculus; Fractal Hamilton–Jacobi theory; Fractal Nambu mechanics; Fractal Quantum Nambu mechanics}},
  language     = {{eng}},
  number       = {{1}},
  publisher    = {{Springer}},
  series       = {{Foundations of Physics}},
  title        = {{Fractal Quantum Nambu Mechanics}},
  url          = {{http://dx.doi.org/10.1007/s10701-025-00901-x}},
  doi          = {{10.1007/s10701-025-00901-x}},
  volume       = {{56}},
  year         = {{2026}},
}