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Tag » torsion

Thanks to Art Wagner for sending me Hammond's clearly written paper.

"There is yet other evidence of the probity of this
approach reaching back to the 1970s. It was shown
that general relativity with torsion could be formu-
lated as a local gauge theory under the Poincare
group. Now, we know there are two Casimir in-
variants of this group, P^2 and L^2
–the square of the translation operator and Pauli-Lubanski spin operator.
Although this was formulated with a symmetric
metric tensor, so was the spin theory resulting from
the torsion potential.[7] In that case, the ideas not
only carry over to the non-symmetric case, they pro-
vide an interpretation as well as a raisond’tre for the
non-symmetric metric tensor. In any case, we have
come to think of mass and spin as being associated
with the gravitational field, and the above results
show a very natural framework for just that.

In this approachthere is a natural string coupling:
The symmetric part of the metric tensor is associ-
ated with the Nambo-Goto term


and the antisymmetric part with the Kalb-Ramond term


This gives a natural union between gravity and string theory

The necessity of torsion, from a potential, has already been
demonstrated in two ways. First it was in shown
in [11] the correct law for the conservation of total
angular momentum plus spin can only be achieved
with torsion. This in itself is a strong enough argu-
ment for its presence, but it was also shown that it
is necessary from gauge invariance arguments.

In the final analysis then, we have particles with
intrinsic spin giving rise to a field. The potential
of this field is the antisymmetric part of the met-
ric tensor. This is a new physical interpretation of
the antisymmetric part of the metric tensor entirely
different from previous work"

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