Re: the basis of relativity

Baugh wrote:
> By the same token, the necessity of including ghost particles in the
> successful quantum field theories is not an argument for their
> physicality. The success of the theory argues that they must be
> included in the mathematical calculations but not that we should
> take their "reality" seriously and go looking for ghosts.

Ghosts can seem fairly physical... from Tony Smith's website:

The BRST operator is invariant under the subgroup of the ( 26 + 2 )
pseudo-euclidean group of motions which preserves the null vector v.
This is nothing but the ( 25 + 1 ) conformal group, which does not act
linearly in Minkowski spacetime but does on the larger space.
Symmetries of the BRST operator induce symmetries in the cohomology,
hence we would expect that the spectrum should assemble itself into
representations on the conformal group. We know that the physical
spectrum of the bosonic string only possesses ( 25 + 1 ) Poincare
covariance, so what happens to the special conformal
transformations?... bosonic ghosts ... have a (countably) infinite
number of inequivalent vacua which can be understood as the momenta in
one of two auxiliary compactified dimensions introduced by the
bosonisation procedure. The picture changing operator interpolates
between these different vacua, commuting with the BRST operator and
thus introducing an infinite degeneracy in the cohomology. ...
... the special conformal transformations ... change the picture. By
definition a picture-changing operator is a BRST invariant operator
which changes the picture, whence the special conformal transformations
are picture-changing operators. A remarkable fact of this treatment is
that the appearance of the lorentzian torus is very natural. In other
words, by enhancing the gauge principle on the world*** to
incorporate the extra U(1) gauge invariance we are forced to
reinterpret bosonic string vacua corresponding to propagation on a
given manifold M, as propagation in a manifold which at least locally
is of the form M x T 2 where T 2 is the lorentzian torus corresponding
to the bosons ... This theory is precisely the F-theory introduced ...[
by Vafa in hep-th/9602022 ]... except that there the compactness of the
extra two coordinates was an ad hoc assumption. ...".

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