Conserved Currents in Supersymmetric Quantum Cosmology?

Abstract

In this paper we investigate whether conserved currents can be sensibly defined in supersymmetric minisuperspaces. Our analysis deals with k = +1 FRW and Bianchi class-A models. Supermatter in the form of scalar supermultiplets is included in the former. Moreover, we restrict ourselves to the first-order differential equations derived from the Lorentz and supersymmetry constraints. The "square-root" structure of N=1 supergravity was our motivation to contemplate this interesting research. We show that conserved currents cannot be adequately established except for some very simple scenarios. Otherwise, equations of the type ∇ a J a = 0 may only be obtained from Wheeler-DeWitt-like equations, which are derived from the supersymmetric algebra of constraints. Two appendices are included. In appendix A we describe some interesting features of quantum FRW cosmologies with complex scalar fields when supersymmetry is present. In particular, we explain how the Hartle-Hawking state can now be satisfactorily identified. In appendix B we initiate a discussion about the retrieval of classical properties from supersymmetric quantum cosmologies.

Supersymmetric Quantum Cosmology Shaken, Not Stirred

“…It seems that this is not possible unless vor very simple cases (see ref. [39,40] for more details);…”

“…Some interesting improvements towards this direction were made in ref. [39,40]. By employing φ = re iθ = φ + iφ 2 we were able to effectively decouple the two degrees of freedom associated with the complex scalar fields.…”

“…By employing φ = re iθ = φ + iφ 2 we were able to effectively decouple the two degrees of freedom associated with the complex scalar fields. The supersymmetry constraints became more manageable and a pleasant consequent of this approach was to provide a sensible framework where to discuss if conserved currents can be defined in supersymmetric quantum cosmology [39,40].…”

Excavations at the Kipapa Rockshelter, Kahikinui, Maui, Hawai'i

“…Seabirds may be a relatively large and predictable food resource for humans, due to their breeding habits. Petrels and shearwaters typically return to their nesting colony between February and April, and then depart in October and November (Moniz 1997). A number of additional characteristics of seabird ecology make them an abundant and predictable avian resource (Moniz 1997); this is demonstrated archaeologically as bird assemblages throughout Polynesia are dominated by seabird remains.…”

“…Petrels and shearwaters typically return to their nesting colony between February and April, and then depart in October and November (Moniz 1997). A number of additional characteristics of seabird ecology make them an abundant and predictable avian resource (Moniz 1997); this is demonstrated archaeologically as bird assemblages throughout Polynesia are dominated by seabird remains. It is worth noting that the Rattus exulans is known to prey on seabirds in general and, specifically, on Bulwer's Petrel when they are nesting (Tomich 1986).…”