Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-10-19
Int. J. Pure Appl. Math. Sci. 3 (2006) 127-138
Physics
High Energy Physics
High Energy Physics - Theory
Version accepted for publication in International Journal of Pure & Applied Mathematical Sciences (IJPAMS)
Scientific paper
We investigate the possibility of semigroup extensions of the isometry group of an identification space, in particular, of a compactified spacetime arising from an identification map $p: \RR^n_t \to \RR^n_t / \Gamma$, where $\RR^n_t$ is a flat pseudo-Euclidean covering space and $\Gamma$ is a discrete group of primitive lattice translations on this space. We show that the conditions under which such an extension is possible are related to the index of the metric on the subvector space spanned by the lattice vectors: If this restricted metric is Euclidean, no extensions are possible. Furthermore, we provide an explicit example of a semigroup extension of the isometry group of the identification space obtained by compactifying a Lorentzian spacetime over a lattice which contains a lightlike basis vector. The extension of the isometry group is shown to be isomorphic to the semigroup $(\ZZ^{\times},\cdot)$, i.e. the set of nonzero integers with multiplication as composition and 1 as unit element. A theorem is proven which illustrates that such an extension is obstructed whenever the metric on the covering spacetime is Euclidean.
No associations
LandOfFree
Semigroup extensions of isometry groups of compactified spacetimes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Semigroup extensions of isometry groups of compactified spacetimes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Semigroup extensions of isometry groups of compactified spacetimes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-373410