Chiral Lattice Fermions, Minimal Doubling, and the Axial Anomaly

Exact chiral symmetry at finite lattice spacing would preclude the axial anomaly. In order to describe a continuum quantum field theory of Dirac fermions, lattice actions with purported exact chiral symmetry must break the flavor-singlet axial symmetry. We demonstrate that this is indeed the case by using a minimally doubled fermion action. For simplicity we consider the Abelian axial anomaly in two dimensions. At finite lattice spacing and with gauge interactions, the axial anomaly arises from non-conservation of the flavor-singlet current. Similar non-conservation also leads to the axial anomaly in the case of the naive lattice action. For minimally doubled actions, however, fine tuning of the action and axial current is necessary to arrive at the anomaly. Conservation of the flavor non-singlet vector current additionally requires the current to be fine tuned. Finally we determine that the chiral projection of a minimally doubled fermion action can be used to arrive at a lattice theory with an undoubled Dirac fermion possessing the correct anomaly in the continuum limit.Comment: 15 pages, 1 figure, symmetries corrected, Symanzik analysis for currents added, marginal operators expose

A Probabilistic Defense of Proper De Jure Objections to Theism

A common view among nontheists combines the de jure objection that theism is epistemically unacceptable with agnosticism about the de facto objection that theism is false. Following Plantinga, we can call this a “proper” de jure objection—a de jure objection that does not depend on any de facto objection. In his Warranted Christian Belief, Plantinga has produced a general argument against all proper de jure objections. Here I first show that this argument is logically fallacious (it makes subtle probabilistic fallacies disguised by scope ambiguities), and proceed to lay the groundwork for the construction of actual proper de jure objections

On the Use of Cherenkov Telescopes for Outer Solar System Body Occultations

Imaging Atmosphere Cherenkov Telescopes (IACT) are arrays of very large optical telescopes that are well-suited for rapid photometry of bright sources. I investigate their potential in observing stellar occultations by small objects in the outer Solar System, Transjovian Objects (TJOs). These occultations cast diffraction patterns on the Earth. Current IACT arrays are capable of detecting objects smaller than 100 metres in radius in the Kuiper Belt and 1 km radius out to 5000 AU. The future Cherenkov Telescope Array (CTA) will have even greater capabilities. Because the arrays include several telescopes, they can potentially measure the speeds of TJOs without degeneracies, and the sizes of the TJOs and background stars. I estimate the achievable precision using a Fisher matrix analysis. With CTA, the precisions of these parameter estimations will be as good as a few percent. I consider how often detectable occultations occur by members of different TJO populations, including Centaurs, Kuiper Belt Objects (KBOs), Oort cloud objects, and satellites and Trojans of Uranus and Neptune. The great sensitivity of IACT arrays means that they likely detect KBO occultations once every O(10) hours when looking near the ecliptic. IACTs can also set useful limits on many other TJO populations.Comment: 22 pages, 11 figures, accepted by MNRA