Originally posted by ranyart
Starting withIn general I have problems understanding how definitions on the worldsheet work out in terms of background propagation.
Then usingV(k) ?ß ƒÃƒÊƒË(k)VƒÊƒË(k) ?ß ƒÃƒÊƒË(k) ?ç dƒÊƒÁ ƒÁab?ÝaXƒÊ?ÝbXƒËeik⋅X
is a vertex operator coupling strings to fluctuations in the background metric GƒÊƒË. Note that like all vertex operators, V is an integral over the world-sheet since it can be inserted at any point.
Uhmm[?] care to insert this into Present Spacetime? what you mean(and if one goes back to the original paper of Jiangping Hu and Shou-Cheng Zhang) one cannot explicitly transform hydrodynamical modes from within a Boundery to the external boundery, it can only go one-way.
If one inserts a dynamical background that is part of a worldsheet that is not based in 3-dimensional PRESENT spacetime, then effectively you are folding/unfolding space/past/future inwardly, which is exactly what Hu and Zhang mentions in their Paper, I quote;Since the dimension of total configuration space is higher than the dimension of base space, this theory bares similarities to Kaluza-Klein Theory, but with two important differences. First the total confiruration space is topologically non-trivial fiber bundle. Second the iso-spin space does not have a small radius. This leads to the "embarrassment of riches" problem. In order to solve this problem we need to find a mechanism where higher iso-spin states obtain mass gaps dynamically, through interactions. This way the low energy degrees of freedom would scale correctly with the dimension of base space. end.
Then:The underlying mathematical structure of the current approach is the noncommutative
geometry [18] de ned by Eq. (2). Unlike previous approaches [19], this relation
treats all four Euclidean dimensions on equal footing. If we interpret X4 as energy, which is
dual to time, this quantization rule seem to connect space, time, spin and the fundamental
length unit l0 in an uni ed fashion. In the lowest SO(5) level, there is no ordinary non-relativistic kinetic energy. All the single particle states are representations of this algebra.
The non-trivial features identi ed in this work all have their roots in this algebra.
Now why is it that all string theories have problems with background propergation?[?]
I don't doubt your sincerity, but help me out here. Could you begin again by raising just one very specific issue of concern to you in a brief - very very brief - clear and uncomplicated way?
Originally posted by jeff
I don't doubt your sincerity, but help me out here. Could you begin again by raising just one very specific issue of concern to you in a brief - very very brief - clear and uncomplicated way?
Originally posted by ranyart
A Note On The Chern-Simons
And Kodama Wavefunctions
Edward Witten
Institute For Advanced Study, Princeton NJ 08540 USA
Yang-Mills theory in four dimensions formally admits an exact Chern-Simons wavefunction.
It is an eigenfunction of the quantum Hamiltonian with zero energy. It is known to be unphysical for a variety of reasons, but it is still interesting to understand what it describes.
We show that in expanding around this state, positive helicity gauge bosons have positive energy and negative helicity ones have negative energy. We also show that the Chern-Simons state is the supersymmetric partner of the naive fermion vacuum in which one
does not fill the fermi sea. Finally, we give a sort of explanation of “why” this state exists.
Similar properties can be expected for the analogous Kodama wavefunction of gravity.
Ed Witten:In the nonabelian case, and e are not invariant under homotopically non-trivial gauge
transformations. We ignore this. Along with the unnormalizability, lack of CPT invariance, etc., and additional properties that we will see below, this is one more reason that the Chern-Simons
state is formal and does not really correspond to a sensible physical theory.
arXiv:gr-qc/0306083 v1
yeah, that sounds like what CVJ says in his book. but that s the first part that i didn t follow. why is it natural to assign nondynamical degrees of freedom to the endpoints of a string? what does the phrase "nondynamical degrees of freedom" even mean? can you give me an example of a more pedestrian quantum theory where we do this? does anything like this ever happen in QED?Originally posted by jeff
In quantum systems it's natural to assign to distinguished points nondynamical internal degrees of freedom giving rise to global symmetries, i.e. conserved charges that don't contribute to the hamiltonian or ruin any pre-existing symmetry.
they have trivial world sheet dynamics because they don t appear in the lagrangian?
In string theory we can charge the endpoints of open strings with chan-paton degrees of freedom. Although these charges may interact with external gauge fields, during interactions of several open strings (open strings interact at their endpoints), they flow only along the world-sheet boundaries swept out by the endpoints and so are conserved. Since chan-paton charges have trivial world-sheet dynamics - that is, world-sheet interactions can't change them - consistency requires that only identically charged endpoints may interact.
Originally posted by jeff
If the chan-paton degrees of freedom in the 2D quantum conformal field theory governing the physics of open strings are to be useful, they must produce in the low energy limit the familiar yang-mills interactions of particles as they appear in the arena of QFT.