Geometrical properties of Riemannian superspaces, observables and physical states

TL;DR

This paper explores the geometric and quantum properties of Riemannian superspaces, highlighting the N=1 case's correct fermionic degrees of freedom, quantum state structures, and novel fermionic effects in vacuum solutions.

Contribution

It introduces a non-degenerate supermetric for N=1 superspace that correctly accounts for fermionic degrees of freedom and modifies classical mass constraints, with a new quantum representation and fermionic vacuum effects.

Findings

The N=1 supermetric has the correct fermionic degrees of freedom.

Quantum states are described via a new Majorana-Weyl representation.

A novel fermionic oscillatory effect in vacuum solutions is demonstrated.

Abstract

Classical and quantum aspects of physical systems that can be described by Riemannian non degenerate superspaces are analyzed from the topological and geometrical points of view. For the N=1 case the simplest supermetric introduced in [Physics Letters B \textbf{661}, (2008),186] have the correct number of degrees of freedom for the fermion fields and the super-momentum fulfil the mass shell condition, in sharp contrast with other cases in the literature where the supermetric is degenerate. This fact leads a deviation of the 4-impulse (e.g. mass constraint) that can be mechanically interpreted as a modification of the Newton's law. Quantum aspects of the physical states and the basic states and the projection relation between them, are completely described due the introduction of a new Majorana-Weyl representation of the generators of the underlying group manifold. A new oscillatory fermionic effect in the $B_{0}$ part of the vaccum solution involving the chiral and antichiral components of this Majorana bispinor is explicitly shown.