Fractional spacetime, dimension equation

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SUMMARY

The discussion centers on the application of fractional derivatives in General Relativity (GR) and the implications for local group symmetry represented by SO(3-ε, 1+ε). Participants debate the existence of references for an equation governing ε, emphasizing the distinction between fractional derivatives and fractional dimensions. The conversation highlights the complexity of discussing fractional dimension parameters within the context of Lie groups, particularly SO(p,n), necessitating a thorough explanation of the underlying concepts.

PREREQUISITES
  • Understanding of fractional calculus and its applications.
  • Familiarity with General Relativity (GR) principles.
  • Knowledge of Lie groups, specifically SO(p,n) structures.
  • Basic concepts of fractal geometry and fractional dimensions.
NEXT STEPS
  • Research fractional derivatives in General Relativity.
  • Explore the mathematical framework of Lie groups and their symmetries.
  • Study the implications of fractional dimensions in fractal geometry.
  • Investigate existing literature on local group symmetries in theoretical physics.
USEFUL FOR

The discussion is beneficial for theoretical physicists, mathematicians specializing in geometry, and researchers exploring advanced concepts in General Relativity and fractional calculus.

jk22
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Suppose we use fractional derivatives (https://en.m.wikipedia.org/wiki/Fractional_calculus) in GR, hence we have a local group symmetry ##SO(3-\epsilon,1+\epsilon)## does any reference exist about an equation for ##\epsilon## ?, since it could depend on coordinates too.
 
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Woah there Tex! Fractional derivatives is one thing (a purely algebraic concept). Fractional dimensions is another (ah la fractal geometry). But I don't think you can sensibly talks about fractional dimension parameters for Lie groups such as SO(p,n). If you wish to then you need to go into the lengthy coherent exposition of exactly what you mean but that, including explaining whether you're still even talking about a group much less a Lie group.
 
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