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Jul
24

Tagged in: torsion, string theory

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

http://en.wikipedia.org/wiki/Nambu–Goto_action

and the antisymmetric part with the Kalb-Ramond term

http://en.wikipedia.org/wiki/Kalb–Ramond_field

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"

http://xxx.lanl.gov/pdf/1207.5170v1.pdf

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