Geometric Justification of the Fundamental Interaction Fields for the Classical Long-Range Forces

Abstract

Based on the principle of reparametrization invariance, the general structure of physically relevant classical matter systems is illuminated within the Lagrangian framework. In a straightforward way, the matter Lagrangian contains background interaction fields, such as a 1-form field analogous to the electromagnetic vector potential and symmetric tensor for gravity. The geometric justification of the interaction field Lagrangians for the electromagnetic and gravitational interactions are emphasized. The generalization to E-dimensional extended objects (p-branes) embedded in a bulk space M is also discussed within the light of some familiar examples. The concept of fictitious accelerations due to un-proper time parametrization is introduced, and its implications are discussed.The framework naturally suggests new classical interaction fields beyond electromagnetism and gravity. The simplest model with such fields is analyzed and its relevance to dark matter and dark energy phenomena on large/cosmological scales is inferred. Unusual pathological behavior in the Newtonian limit is suggested to be a precursor of quantum effects and of inflation-like processes at microscopic scales.

24 pages, no figures. arXiv admin note: substantial text overlap with arXiv:math-ph/0512082, arXiv:math-ph/0210021

References in corpus (4)

• Finsler spacetime geometry in Physics
• The Scale-Invariant Vacuum (SIV) Theory: A Possible Origin of Dark Matter and Dark Energy
• Scale-Invariant Dynamics of Galaxies, MOND, Dark Matter, and the Dwarf Spheroidals
• Scale Invariance, Horizons, and Inflation

Cited by in corpus (9)

• On the Relation of the Lunar Recession and the Length-of-the-Day
• Reparametrization Invariance and Some of the Key Properties of Physical Systems
• Action Principle for Scale Invariance and Applications (Part I)
• The Scale Invariant Vacuum Paradigm: main results and current progress
• The Scale Invariant Vacuum Paradigm: Main Results and Current Progress Review (Part II)
• Classical gauge principle -- From field theories to classical mechanics
• Is time the real line?
• An alternative explanation of the orbital expansion of Titan and other bodies in the Solar system
• SIV Guided Resolution of the Lithium-7 BBN Problem