The spin-statistics connection in quantum gravity

Abstract

It is well-known that in spite of sharing some properties with conventional particles, topological geons in general violate the spin-statistics theorem. On the other hand, it is generally believed that in quantum gravity theories allowing for topology change, using pair creation and annihilation of geons, one should be able to recover this theorem. In this paper, we take an alternative route, and use an algebraic formalism developed in previous work. We give a description of topological geons where an algebra of "observables" is identified and quantized. Different irreducible representations of this algebra correspond to different kinds of geons, and are labeled by a non-abelian "charge" and "magnetic flux". We then find that the usual spin-statistics theorem is indeed violated, but a new spin-statistics relation arises, when we assume that the fluxes are superselected. This assumption can be proved if all observables are local, as is generally the case in physical theories. Finally, we also discuss how our approach fits into conventional formulations of quantum gravity.

A NOVEL SPIN-STATISTICS THEOREM IN (2 + 1)DCHERN–SIMONS GRAVITY

“…Our discussion can be viewed a generalization of previous work [18,19], where a spin-statistics relation was derived for geonic states arising in a Yang-Mills theory coupled to a Higgs field in the Higgs phase, where the symmetry is spontaneously broken down to a finite gauge group H. In [19] we showed the existence of a class of "localized" states in quantum gravity arising indirectly from the Yang-Mills theory which did obey the spin-statistics relation derived here. However, those states form a very restricted class.…”

QUANTUM TOPOLOGY CHANGE IN (2+1)d

“…Although this issue has been extensively studied in the literature, our formalism may shed new light on some points. This subject will be investigated in a forthcoming paper [3].…”

“…As an illustration of the above mentioned differences, in a typical process considered in [25], one can make a test vortex go through or around a handle, whereas in our case one can conceive of "test geons" going through other handles. Our procedure allows a natural generalization towards quantum gravity, which is the issue of another paper [3].…”

Bosonic and Fermionic Behavior in Gravitational Configurations

“…Some concern can be risen by the imaginary character of the λ's imposed by Eqs. (15); however, in explicit calculations these eigenvalues arise always as square roots of general functions which may have positive and negative values, depending on the parameters of the metric, giving place to real and imaginary λ's. For instance, in our example of Eq.…”

“…When an eigenvalue is real, the only solution to Eqs. (15) is that its associated n is equal to zero, but when the eigenvalue is imaginary the n can be any integer, leading to an infinite set of discrete solutions. Now, let us consider the case in which the quantum conditions are not trivially satisfied, i. e., Eqs.…”