Quantum mechanics in magnetic backgrounds with manifest symmetry and locality

Funder: Cambridge Commonwealth, European and International Trust; doi: https://doi.org/10.13039/501100003343The usual methods for formulating and solving the quantum mechanics of a particle moving in a magnetic field respect neither locality nor any global symmetries which happen to be present. For example, Landau's solution for a particle moving in a uniform magnetic field in the plane involves choosing a gauge in which neither translation nor rotation invariance are manifest. We show that locality can be made manifest by passing to a redundant description in which the particle moves on a $U(1)$-principal bundle over the original configuration space and that symmetry can be made manifest by passing to a corresponding central extension of the original symmetry group by $U(1)$. With the symmetry manifest, one can attempt to solve the problem by using harmonic analysis and we provide a number of examples where this succeeds. One is a solution of the Landau problem in an arbitrary gauge (with either translation invariance or the full Euclidean group manifest). Another example is the motion of a fermionic rigid body, which can be formulated and solved in a manifestly local and symmetric way via a flat connection on the non-trivial $U(1)$-central extension of the configuration space $SO(3)$ given by $U(2)$

Semisimple extensions of the Standard Model gauge algebra

We show how one may classify all semisimple algebras containing the su(3) su(2) u(1) symmetry of the Standard Model and acting on some given matter sector, enabling theories beyond the Standard Model with unification (partial or total) of symmetries (gauge or global) to be cataloged. With just a single generation of Standard Model fermions plus a singlet neutrino, the only gauge symmetries correspond to the well-known algebras su(5), so(10), and su(4) su(2) su(2), but with two or more generations a limited number of exotic symmetries mixing flavor, color, and electroweak degrees of freedom become possible. We provide a complete catalog in the case of three generations or fewer and outline how our method generalizes to cases with additional matter

Quantification of Head Acceleration Events in Rugby League: An Instrumented Mouthguard and Video Analysis Pilot Study

Instrumented mouthguards (iMG) were used to collect head acceleration events (HAE) in men’s professional rugby league matches. Peak linear acceleration (PLA), peak angular acceleration (PAA) and peak change in angular velocity (∆PAV) were collected using custom-fit iMG set with a 5 g single iMG-axis recording threshold. iMG were fitted to ten male Super League players for thirty-one player matches. Video analysis was conducted on HAE to identify the contact event; impacted player; tackle stage and head loading type. A total of 1622 video-verified HAE were recorded. Approximately three-quarters of HAE (75.7%) occurred below 10 g. Most (98.2%) HAE occurred during tackles (59.3% to tackler; 40.7% to ball carrier) and the initial collision stage of the tackle (43.9%). The initial collision stage resulted in significantly greater PAA and ∆PAV than secondary contact and play the ball tackle stages (p &lt; 0.001). Indirect HAE accounted for 29.8% of HAE and resulted in significantly greater ∆PAV (p &lt; 0.001) than direct HAE, but significantly lower PLA (p &lt; 0.001). Almost all HAE were sustained in the tackle, with the majority occurring during the initial collision stage, making it an area of focus for the development of player protection strategies for both ball carriers and tacklers. League-wide and community-level implementation of iMG could enable a greater understanding of head acceleration exposure between playing positions, cohorts, and levels of play.</p

The resurrection of group selection as a theory of human cooperation

Two books edited by members of the MacArthur Norms and Preferences Network (an interdisciplinary group, mainly anthropologists and economists) are reviewed here. These books in large part reflect a renewed interest in group selection that has occurred among these researchers: they promote the theory that human cooperative behavior evolved via selective processes which favored biological and/or cultural group-level adaptations as opposed to individual-level adaptations. In support of this theory, an impressive collection of cross-cultural data are presented which suggest that participants in experimental economic games often do not behave as self-interested income maximizers; this lack of self-interest is regarded as evidence of group selection. In this review, problems with these data and with the theory are discussed. On the data side, it is argued that even if a behavior seems individually-maladaptive in a game context, there is no reason to believe that it would have been that way in ancestral contexts, since the environments of experimental games do not at all resemble those in which ancestral humans would have interacted cooperatively. And on the theory side, it is argued that it is premature to invoke group selection in order to explain human cooperation, because more parsimonious individual-level theories have not yet been exhausted. In summary, these books represent ambitious interdisciplinary contributions on an important topic, and they include unique and useful data; however, they do not make a convincing case that the evolution of human cooperation required group selection

Inverse Higgs phenomena as duals of holonomic constraints

The inverse Higgs phenomenon, which plays an important r\^ole in physical systems with Goldstone bosons (such as the phonons in a crystal) involves nonholonomic mechanical constraints. By formulating field theories with symmetries and constraints in a general way using the language of differential geometry, we show that many examples of constraints in inverse Higgs phenomena fall into a special class, which we call coholonomic constraints, that are dual (in the sense of category theory) to holonomic constraints. Just as for holonomic constraints, systems with coholonomic constraints are equivalent to unconstrained systems (whose degrees of freedom are known as essential Goldstone bosons), making it easier to study their consistency and dynamics. The remaining examples of inverse Higgs phenomena in the literature require the dual of a slight generalisation of a holonomic constraint, which we call (co)meronomic. Our formalism simplifies and clarifies the many ad hoc assumptions and constructions present in the literature. In particular, it identifies which are necessary and which are merely convenient. It also opens the way to studying much more general dynamical examples, including systems which have no well-defined notion of a target space

Undulating dark matter

We suggest that an interplay between microscopic and macroscopic physics can give rise to dark matter (DM) whose interactions with the visible sector fundamentally undulate in time, independent of celestial dynamics. A concrete example is provided by fermionic DM with an electric dipole moment (EDM) sourced by an oscillating axion-like field, resulting in undulations in the scattering rate. The discovery potential of light DM searches can be enhanced by additionally searching for undulating scattering rates, especially in detection regions where background rates are large and difficult to estimate, such as for DM masses in the vicinity of 1 MeV where DM-electron scattering dominantly populates the single electron bin. An undulating signal could also reveal precious dark sector information after discovery. In this regard we emphasise that, if the recent XENON1T excess of events is due to light DM scattering exothermically off electrons, future analyses of the time-dependence of events could offer clues as to the microscopic origins of the putative signal

An evolutionary perspective on health psychology: New approaches and applications

Although health psychologists' efforts to understand and promote health are most effective when guided by theory, health psychology has not taken full advantage of theoretical insights provided by evolutionary psychology. Here, we argue that evolutionary perspectives can fruitfully inform strategies for addressing some of the challenges facing health psychologists. Evolutionary psychology's emphasis on modular, functionally specialized psychological systems can inform approaches to understanding the myriad behaviors grouped under the umbrella of “health,” as can theoretical perspectives used by evolutionary anthropologists, biologists, and psychologists (e.g., Life History Theory). We detail some early investigations into evolutionary health psychology, and we provide suggestions for directions for future research