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Re: Strings a minumum topology

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Posted by paultrr on September 15, 2003 at 04:15:20:

In Reply to: Re: Strings a minumum topology posted by paultrr on September 15, 2003 at 03:36:05:

One generally first encounters the Instanton in Yangs-Mills Theory where the instantons are self-dual solutions of Euclidean SU(2) Yang-Mills equations. But the Instanton also shows up in cosmology, such as the Instanton of time proposed by Hawking, the Instanton zero point condition of the ZPF from quantum theory, etc. Although a medium of instantons possesses larger classical action than the trivial configuration, this medium could be favored at quantum level and in fact, some articles have suggested that the Yangs-Mill's vacuum is built upon instantons in general.

Going over to LQFT, there has been a tendency to avoid the Instanton of time in general. However, a careful distinction can be made between the Instanton manifold itself and the rest of the brane and bulk structure where this manifold simply becomes the storage medium, so to speak of the quantum information itself that the smallest units of space and time are constructed from. In this respect the Instanton manifold becomes both imaginary and real at the same time which would be in keeping with the general outlook of Yangs-Mills theory from the Standard Model. In following this approach while there remains a smallest unit of space-time which is not an Instanton itself, the Instanton is actually a submanifold of it and as such, a submanifold of the brane itself from which the bulk gets generated.

The view of an Instanton varies somewhat depending upon weither one's model is background dependent or not. GR, non-background dependent, has an Instanton in general commonly known as a singularity. The Instanton's from higher dimensional theory tend to avoid the breakdown of physics one encounters under GR by approach the Instanton subject from a different direction, not as a collapse, but as simply an instant in time and space with zero duration. The time issue is partly what makes the difference. With an Instanton one has zero time, so any effects discribed on such a manifold take place in a zero time span. A wavefunction spread to infinity by Plank scale effects has much the same character as the Instanton in relation to time, since no passage of time occurs for any effect generated. Take this and the fact that most common brane world models tend to center the brane manifold around the Plank scale and the type of manifolds discribed by both LQFT and Instanton theory become rather self evident. They both deal with the brane level itself while String Theory deals with larger scales short of the Standard Model scale.

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