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

*Fri, 8 Oct 1999 20:45:08 +0300 (EET DST)*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Hitoshi Kitada: "[time 917] Re: [time 913] RE: [time 912] Re: [time 911] RE: [time 910] Re: [time 909] About your proof of unitarity"**Previous message:**Matti Pitkanen: "[time 915] RE: [time 910] Re: [time 909] About your proof of unitarity"**In reply to:**Ben Goertzel: "[time 911] RE: [time 910] Re: [time 909] About your proof of unitarity"**Next in thread:**Hitoshi Kitada: "[time 917] Re: [time 913] RE: [time 912] Re: [time 911] RE: [time 910] Re: [time 909] About your proof of unitarity"

On Tue, 8 Oct 2019, Ben Goertzel wrote:

*> >
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*> > In a few cases... I had been studying Feynman integral myself. It
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*> > is hard to
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*> > say that it has been given a definition mathematically.
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*> >
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*>
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*> In 2D it has been dealt with nicely using analytic continuation, but no one
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*> has made this work
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*> for real 4D space as far as I know
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*>
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*> Some people have dealt with the Feynman integral using some nice Hilbert
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*> space mathematics, but I forget
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*> the references
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I have been editing a book about functional integrals.

What is known and obvious is that Feynmann integral cannot be defined as

a measure unlike Wiener integral. This makes the calculation of Feynmann

integral tricky. One must do analytical continuation and perturbative

approach is in practice the only possible approach.

*>
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*> My inclination is to discretize everything, and then everything becomes
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*> automatically definable, i.e. it becomes
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*> a finite sum over a large number of combinations rather than a divergent
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*> integral.
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*>
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*> The measure underlying the Feynman integral is not clear. Here I would like
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*> to introduce a notion of subjective
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*> simplicity, whereby e.g. the weight of a path in the measure is the a priori
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*> simplicity of the path. As a first
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*> approximation algorithmic information could be used for a simplicity
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*> measure. But I have never pursued this idea
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*> mathematically, althought it makes sense to me intuitively.
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*>
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The need to get rid of Feynmann parth integrals defined

by imaginary exponent exp(iS) and replacement of

them with configuration space integrals with real exponent defining

genuine integration measure is one of the motivations of TGD

approach.

It turned out that ordinary functional integral approach based

on exp(iS_K) is horribly divergent due to the nonlinearity of Kahler

action S_K. Kahler function (absolute minimum of Kahler action) as a

functional of *3-surface* (rather than 4-surface) is however nonlocal and

the standard divergences resulting from nonlinear local interaction

terms can be avoided. There are also divergences related to

Gaussian determinants but Kahler geometry makes possible elimination

of these divergences.

*> Also, if you believe the "mind over matter" results from the Princeton labs,
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*> these could be explained by the mind altering
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*> the simplicity measure underlying the Feynman integrals governing particle
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*> motion. But this is raw speculation
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*> of course!!
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The sum over degenerate absolute minimum spacetime surface

associated with given 3-surface X^3 could mimick path integral.

Just a thought....

*>
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*> ben
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*>
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*>
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**Next message:**Hitoshi Kitada: "[time 917] Re: [time 913] RE: [time 912] Re: [time 911] RE: [time 910] Re: [time 909] About your proof of unitarity"**Previous message:**Matti Pitkanen: "[time 915] RE: [time 910] Re: [time 909] About your proof of unitarity"**In reply to:**Ben Goertzel: "[time 911] RE: [time 910] Re: [time 909] About your proof of unitarity"**Next in thread:**Hitoshi Kitada: "[time 917] Re: [time 913] RE: [time 912] Re: [time 911] RE: [time 910] Re: [time 909] About your proof of unitarity"

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