Re: extra dimensions
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Posted by ronron on December 13, 19100 at 18:06:49:
In Reply to: Re: extra dimensions posted by phobos on December 11, 19100 at 18:04:42:
comments on notes: [state vectors, operators, observables] no, state vectors in a function space are not
self-adjoint operators in the space. the vectors
are the set members, with the self-adjoint operators
being the dynamical variables, observables. i
misspoke. still, as i state in below post, it
seems that you will be "losing" generality if
you limit the domain of l^2 to 11 or 26, etc....
this is a point i can't get around. i know
that l^2 is of infinite dimension, so i don't follow
how the domain of the functions in l^2 forming an
11 dimensional space can at the same time preserve
and integrate all the QM results. [theory of distributions] yes it's perfectly viable. it's just not without
mathematical objection, that's all i claim. it
uses the idea, for example, that any self-adjoint
operator can be put into diagonal form, and i don't
believe this is correct. since the dist theory
acts as though this were true, you run into the
need for the functionals like the dirac delta fcn.
the von Neumann formulation is fine to look at but
not too useful when solving a problem. [String Theory texts] yes i have a copy of Polchinski (vol I, introduction).
too difficult for me, and for the reason you stated:
they make frequent mention of QFT about which i know
nothing. also have two other QFT texts that are
hard to follow. i'll check out the Peskin/Schroeder
text. there's another reasonable book from the same series
as the Nakahara book you suggested that deals with
supersymmetry and then works into the bosonic string
formulation. not a bad point after some general
background in gauge fields. thanks, ronron
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