Invariants and conservation laws of physical quantities in Minkowski space

TL;DR

This paper derives invariants and conservation laws of physical quantities in Minkowski space from 4-tensors, unifying various conservation laws and explaining vortex ring stability through four-dimensional kinematic equations.

Contribution

It introduces a unified framework for invariants and conservation laws in Minkowski space using 4-tensors, linking energy-momentum conservation to wave phenomena and vortex stability.

Findings

Derived two forms of conservation law equations in Minkowski space.

Unified energy-momentum conservation law encompasses energy, momentum, and angular momentum.

Explained vortex ring stability via four-dimensional kinematic conservation equations.

Abstract

It is shown that invariants and relativistically invariant laws of conservation of physical quantities in Minkowski space follow from 4-tensors of the second rank, which are four-dimensional derivatives of 4-vectors, tensor products of 4-vectors and inner products of 4-tensors of the second rank. Two forms of the system of equations of conservation laws for a number of physical quantities in Minkowski space are obtained. The four-dimensional law of conservation of energy-momentum combines the three-dimensional laws of conservation of energy, momentum and angular momentum. The equations of the four-dimensional laws of conservation of physical quantities in explicit or implicit form contain the wave part Based on a system of four-dimensional kinematic conservation equations, the reason for the stability of vortex rings in liquids and gases is explained.