It is shown that because R4 is a critical space for a knot, the dimension of a connection C, on what is effectively four manifold (dim,&'(")) ~4, must be of a dim C2 = 2. It is reasoned that this result is the topological reason for the quasi two dimensionality of a quantum path in 8") and is a mani
โฆ LIBER โฆ
Hausdorff dimension of a particle path in a quantum manifold
โ Scribed by Nicolini, Piero; Niedner, Benjamin
- Book ID
- 111978840
- Publisher
- The American Physical Society
- Year
- 2011
- Tongue
- English
- Weight
- 192 KB
- Volume
- 83
- Category
- Article
- ISSN
- 1550-7998
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Path integral method is used to derive a generalized Schrodinger type equation for a particle in a Riemannian space. Contributing trajectories are restricted to the physical paths, which decomposes this equation into its infinite components, one of them being similar to the Klein-Gordon equation.