Re: extra dimensions

Posted by phobos on December 13, 19100 at 20:59:09:

In Reply to: Re: extra dimensions posted by ronron on December 13, 19100 at 18:06:49:

My last attempt on the subject of L^2.

Standard quantum mechanics represents the Hilbert space
of state vectors as elements of L^2. These normalizable
complex functions take x, y, z, and t as arguments. The
domain of the elements of L^2 is thus four dimensional.
In string theory, the elements of the Hilbert space in
the L^2 representation are functions of x,y,z,t,...
up to 11. That's all I'm trying to say.

Diagonalization of Hermitian Operators:
I believe the criteria are a bounded self-adjoint
completely continuous operator on some inner product
space. I think complete continuity can be relaxed if
one works on a Hilbert space. Any operator of this
form should be diagonalizable. (However, I reserve the
right to add restrictions as I think about this.)
The bottom line is that manipulations like one finds
in constructive quantum field theory rely heavily on
the theory of distributions, and one can be assured
that the steps taken therein are perfectly rigorous.

phobos

Follow Ups: (Reload page to see most recent)

• Re: extra dimensions ronron 12/19/100 (0)

Post a Followup

Name    : 
E-Mail  : 
Subject : 

Comments:

(The following are optional.)
Link URL   : 
Link Title : 
Image URL  :