Projective Loop Quantum Gravity I. State Space

Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. Beside the physical motivations for this approach, it could help designing a quantum state space holding the states we need. In [Oko{\l}\'ow 2013, arXiv:1304.6330] the description of a theory of Abelian connections within this framework was developed, an important insight being to use building blocks labeled by combinations of edges and surfaces. The present work generalizes this construction to an arbitrary gauge group G (in particular, G is neither assumed to be Abelian nor compact). This involves refining the definition of the label set, as well as deriving explicit formulas to relate the Hilbert spaces attached to different labels. If the gauge group happens to be compact, we also have at our disposal the well-established Ashtekar-Lewandowski Hilbert space, which is defined as an inductive limit using building blocks labeled by edges only. We then show that the quantum state space presented here can be thought as a natural extension of the space of density matrices over this Hilbert space. In addition, it is manifest from the classical counterparts of both formalisms that the projective approach allows for a more balanced treatment of the holonomy and flux variables, so it might pave the way for the development of more satisfactory coherent states.Comment: 81 pages, many figure

Doing public participatory archaeology with “difficult” conflict heritage : Experiences from Finnish Lapland and the Scottish Highlands

Public participatory archaeology can take many forms, and there is no ‘one size fits all’ approach to engaging with communities and non-professional enthusiasts. Similarly, not all archaeological heritage is the same, and some comes with the label of ‘difficult’, ‘contested’ or ‘dark’ heritage. Particularly, in this article I explore how archaeological heritage that is connected with periods of conflict, namely the Second World War, fares in the sphere of public archaeology. My case studies from Scotland and Finland also illustrate very different community heritage models, and I reflect on the role of the public archaeologist in these scenarios.Peer reviewe

Single-atom interferometer based on two-dimensional spatial adiabatic passage

In this work we propose a novel single-atom interferometer based on a fully two-dimensional spatial adiabatic passage process using a system of three identical harmonic traps in a triangular geometry. While the transfer of a single atom from the ground state of one trap to the ground state of the most distant one can successfully be achieved in a robust way for a broad range of parameter values, we point out the existence of a specific geometrical configuration of the traps for which a crossing of two energy eigenvalues occurs and the transfer of the atom fails. Instead the wavefunction is robustly split into a coherent superposition between two of the traps. We show that this process can be used to construct a single-atom interferometer and discuss its performance in terms of the final population distribution among the asymptotic eigenstates of the individual traps. This interferometric scheme could be used to study space dependent fields from ultrashort to relatively large distances, or the decay of the coherence of superposition states as a function of the distance.Comment: 8 pages, 9 figure

Dissociation between Cervical Mucus and Urinary Hormones during the Postpartum Return of Fertility in Breastfeeding Women

Identifying the return of fertility with cervical mucus observations is challenging during the postpartum period. Use of urinary measurements of estrogen and progesterone can assist in understanding the return to fertility during this period. The purposes of this study were to describe the postpartum return of fertility by an analysis of total estrogen (TE) and pregnanediol glucuronide (PDG) profiles and to correlate these profiles with cervical mucus observations. Twenty-six participants collected urine samples during the postpartum period and recorded mucus scores. TE and PDG hormones were analyzed and compared with mucus scores. During amenorrhea, mucus reflected TE changes in only 35 percent of women; after amenorrhea, typical mucus patterns were seen in 33 percent of cycles. We concluded that postpartum mucus and hormone profiles are significantly dissociated but that monitoring urinary hormones may assist in identifying the return of fertility. We also identified different hormonal patterns in the return to fertility. The postpartum period is a challenging time for identifying the return of fertility. The purposes of this study were to describe the hormonal patterns during the return of fertility and to correlate these patterns with cervical mucus observations. Twenty-six postpartum women collected urine samples and recorded mucus scores. Urinary estrogen and progesterone hormones were analyzed and compared with mucus scores. Before the return of menses, mucus reflected hormonal changes in only 35 percent women and after first menses in 33 percent of cycles. We found that hormone profiles do not correlate well with mucus observations during the postpartum return of fertility