Symmetry, Reference Frames, and Relational Quantities in Quantum Mechanics

We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical language to introduce and study quantum reference systems, showing that the orthodox "absolute" quantities are good representatives of observable relative quantities if the reference state is suitably localised. We use this relational formalism to critique the literature on the relationship between reference frames and superselection rules, settling a long-standing debate on the subject

Orbital anisotropy and low-energy excitations of the quasi-one-dimensional conductor beta-Sr0.17V2O5

The electronic structure of the quasi-one-dimensional vanadium beta-bronze β-Sr0.17V2O5 has been measured in detail using soft x-ray absorption spectroscopy, x-ray emission spectroscopy, and resonant inelastic soft x-ray scattering. Together, these measurements have been used to derive the experimental site-resolved (k-integrated) band structure of a material whose electronic structure is difficult to obtain from first principles. The occupied states, probed by x-ray emission measurements, demonstrate the O 2p-V 3d bonding hybridization at the bottom of the O 2p band, with the V 3dxy "magnetic orbitals" well separated in energy. These results are consistent with the carriers being small polarons. The strong anisotropy in the absorption spectrum is used to identify the energy and character of the unoccupied states. Additionally, absorption measurements at the V L-edge are compared with atomic multiplet calculations, clarifying the interpretation of the experimental multiplet structure and consistent with the presence of both V5+ and V4+ species. Site-specific electronic excitations, probed by resonant inelastic x-ray scattering at the V L-edge, are observed at an energy of 1.1 eV, and are suggested to correspond to transitions from the partially filled dxy magnetic orbital into the unoccupied dxy,yz orbitals. © 2011 American Physical Society.status: publishe

Seven hundred years of fraternal orders

For hundreds of years there has been an allure in popular culture to the notion of a band of brothers. From before Shakespeare's Henry V, through Schiller's Wilhelm Tell, to the twenty-first century TV mini-series Band of Brothers, the phrase has evoked images of men fiercely loyal to one another, united for a cause greater than themselves. This interest has not been reflected in concerted scholarly attention to the long-term influence of fraternal organizations. This chapter introduces the theme of the volume in a literature review and contextualizes the authors' contributions