**Matti Pitkanen** (*matpitka@pcu.helsinki.fi*)

*Wed, 25 Aug 1999 08:09:17 +0300 (EET DST)*

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On Tue, 24 Aug 1999 WDEshleman@aol.com wrote:

*> In a message dated 8/24/99 2:19:56 AM Eastern Daylight Time,
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*> matpitka@pcu.helsinki.fi writes:
*

*>
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*> > In any case, the basic philosophy of quantum TGD is eliminative:
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*> > this means that entire quantum physics (apart from quantum jump)
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*> > is reduced to infinite-dimensional configuration space geometry
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*> > with spinor structure. The success of this philosophy
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*> > convinces me even more than indidividual applications.
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*>
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*> Matti,
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*> An "infinite-dimensional configuration space geometry" subjectively,
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*> but not an "infinite-dimensional space geometry" objectively?
*

Infinite-dimensional configuration space geometry as something objective,

pregiven, totally fixed by the mere requirement of mathematical existence

implying huge symmetries fixing the metric and spinor structure

completely.

String modelists have similar dream but they have not realized that

infinite-dimensional geometry is the proper framework to realize this

dream.

The main motivation for this dream comes from the fact that in

infinite-dimensional calculus infinities are encountered at

every step. In infinite-dimensional geometry, existence of Riemann

connection forces huges isometry group and structure

of infinite-dimensional symmetric space G/H, finite Ricci tensor

forces vacuum Einstein equations for configurations space, etc..

G/H structure has strong implications: finite-dimensional symmetric spaces

have been listed by Cartan. Physically it says that all points

of symmetric space are physically equivalent: cosmological principle

generalized.

My original motivation came from a work of mathematician Frieden who

constructed Kahler geometry of loop space (maps from circle to

Lie group) and demonstrated that

it was unique and had infinite-dimensional Kac Moody type group

as group of isometries. This geometry had one failure: Ricci

scalar was infinite, which suggests that strings are not yet

the final story. Second failure: loop group geometry is

not Diff^2 invariant (you read correctly: Diff^2!: in TGD Diff^4

acts as gauge symmetry in space of 3-surfaces).

Best,

MP

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