CRITERION FOR THE TRANSITION TO THE LAGRANGIAN OF A CLOSED SPACE
T.R. Mehdiyev1, R.H. Nayimbayova1, I.F. Yusibova1, Sh.N. Aliyeva1,2
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ABSTRACT

A generalization of the Lagrangian action principle for structured matter in a closed (self-acting) space is considered. It is shown that the traditional Lagrangian L(x, x ̇), based on a point representation of matter, loses its physical meaning in the presence of internal structure and environmental response. A criterion is formulated for the transition from the classical Lagrangian to the Riemannian action: when the properties of space depend on the state of matter, the metric is included in the dynamics along with the field. A geometrically self-consistent description is proposed, implemented in the LDS model, where the form and field act as a single geometric system.

Keywords: Lagrangian, Feynman integral, effective motion
DOI:10.70784/azip.2.2025415

Received: 19.11.2025
Internet publishing: 25.11.2025    AJP Fizika A 2025 04 az p.15-17

AUTHORS & AFFILIATIONS

1. Institute of Physics Ministry of Science and Education Republic of Azerbaijan, 131 H.Javid ave, Baku, AZ-1073, Azerbaijan
2. Azerbaijan State Oil and Industry University, Baku, AZ 1010, Azerbaijan
E-mail:

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