Three aspects of bosonized supersymmetry and linear differential field equation with reflection

Recently it was observed by one of the authors that supersymmetric quantum mechanics (SUSYQM) admits a formulation in terms of only one bosonic degree of freedom. Such a construction, called the minimally bosonized SUSYQM, appeared in the context of integrable systems and dynamical symmetries. We show that the minimally bosonized SUSYQM can be obtained from Witten's SUSYQM by applying to it a nonlocal unitary transformation with a subsequent reduction to one of the eigenspaces of the total reflection operator. The transformation depends on the parity operator, and the deformed Heisenberg algebra with reflection, intimately related to parabosons and parafermions, emerges here in a natural way. It is shown that the minimally bosonized SUSYQM can also be understood as supersymmetric two-fermion system. With this interpretation, the bosonization construction is generalized to the case of N=1 supersymmetry in 2 dimensions. The same special unitary transformation diagonalises the Hamiltonian operator of the 2D massive free Dirac theory. The resulting Hamiltonian is not a square root like in the Foldy-Wouthuysen case, but is linear in spatial derivative. Subsequent reduction to `up' or `down' field component gives rise to a linear differential equation with reflection whose `square' is the massive Klein-Gordon equation. In the massless limit this becomes the self-dual Weyl equation. The linear differential equation with reflection admits generalizations to higher dimensions and can be consistently coupled to gauge fields. The bosonized SUSYQM can also be generated applying the nonlocal unitary transformation to the Dirac field in the background of a nonlinear scalar field in a kink configuration.Comment: 18 pages, LaTeX, minor typos corrected, ref updated, to appear in Nucl. Phys.

Cosmic Neutrino Background as a Ferromagnet

If cosmic background neutrinos interact very weakly with each other, through spin-spin interactions, then they may have experienced a phase transition, leading to a ferromagnetic ordering. The small magnetic field resulting from ferromagnetic ordering -- if present before galaxy formation -- could act as a primordial seed of the magnetic fields observed in several galaxies. Our findings suggest that the magnetization could occur in the right epoch, if the exchange boson of neutrino-neutrino interaction is a massless boson beyond the Standard Model, with a coupling constant of $2.2\times 10^{-13} \left(\frac{m_\nu}{10^{-4}\,\rm{eV}}\right)^2<g<2.3\times 10^{-7}$. The estimation of the magnetic seed is $2.3 \times 10^{-27}\,\rm{G}\lesssim B_{\rm CNB}\lesssim 6.8\times 10^{-10}G$.Comment: 4 pages. Accepted for publication in Physics Letters

Assessing Urban Parklands: Novel Use of Game Cameras to Study Park User Behavior in the Baldwin Hills

The preservation and conservation of public open spaces are essential in urban settings as they promote the growth and sustainability of local communities and surrounding environments. The Baldwin Hills Conservancy manages the Baldwin Hills Park System and aims to promote recreation, restoration and protection of urban parks. This study’s goal is to provide park managers a longitudinal study of the attitudes and behaviors of park visitors. The study includes the use of game cameras to examine visitation and access to the parks, which serves as a passive, novel methodology in order to study human movement patterns into and around the park. This poster will describe the methods and summarize preliminary data collected during the period October 30, 2015 through April 30, 2016. A total of 129 days of data were collected in four locations in the parks, which included 7679 images and 133 hours of time lapse video. Of the data collected, a subset of 1,001 images from one location, a park entrance, were selected and assigned into categories. Preliminary analysis of these data indicate several initial trends that are identified and discussed. Ongoing efforts include full-scale data collection. As part of the Baldwin Hills Park User Study, the methodology and findings of this.https://digitalcommons.lmu.edu/cures_posters/1016/thumbnail.jp