Historical roots of gauge invariance

Gauge invariance is the basis of the modern theory of electroweak and strong interactions (the so called Standard Model). The roots of gauge invariance go back to the year 1820 when electromagnetism was discovered and the first electrodynamic theory was proposed. Subsequent developments led to the discovery that different forms of the vector potential result in the same observable forces. The partial arbitrariness of the vector potential A brought forth various restrictions on it. div A = 0 was proposed by J. C. Maxwell; 4-div A = 0 was proposed L. V. Lorenz in the middle of 1860's . In most of the modern texts the latter condition is attributed to H. A. Lorentz, who half a century later was one of the key figures in the final formulation of classical electrodynamics. In 1926 a relativistic quantum-mechanical equation for charged spinless particles was formulated by E. Schrodinger, O. Klein, and V. Fock. The latter discovered that this equation is invariant with respect to multiplication of the wave function by a phase factor exp(ieX/hc) with the accompanying additions to the scalar potential of -dX/cdt and to the vector potential of grad X. In 1929 H. Weyl proclaimed this invariance as a general principle and called it Eichinvarianz in German and gauge invariance in English. The present era of non-abelian gauge theories started in 1954 with the paper by C. N. Yang and R. L. Mills.Comment: final-final, 34 pages, 1 figure, 106 references (one added with footnote since v.2); to appear in July 2001 Rev. Mod. Phy

James MacCullagh’s ether: An optical route to Maxwell’s equations?

In attempts to perfect Fresnel’s theory of double refraction, MacCullagh discovered an elegant geometrical proof of the wave surface, the true boundary conditions at the limits of the refracting crystal, and a simple Lagrangian for the whole theory. By renouncing mechanical modeling in favor of a more abstract dynamical method, he unveiled the structure which optics came to share with Maxwell’s electrodynamics

Accessibility and inclusivity in online teaching

The radical uptake of technology-enhanced learning practices and online education in recent years has made tertiary education more feasible for a more socially and culturally diverse student body. Despite these developments, there is limited published research which explores how this new frontier of tertiary education teaching is experienced by students. In particular, our understanding of how online education impacts students with specific learning difficulties (SpLDs, such as autistic spectrum disorders, dyslexia, dyspraxia) is limited. There are notable differences in the needs and preferences of online students with and without SpLDs, and this must be reflected in teaching provision. Despite a growing awareness for issues of accessibility, provisions are often designed without robust consultation with those learners most directly affected by changing practice, i.e. students with SpLDs. A better understanding of how students with SpLDs use and experience online education is a prerequisite to developing truly inclusive teaching and learning practices, which provide all students with equal opportunities in tertiary education. This chapter will explore the current literature surrounding accessibility for students with SpLDs in tertiary education online learning. More specifically, it will outline some of the key barriers faced by SpLD students accessing online learning and discuss ways in which these could be managed proactively (beyond a box-ticking exercise in “reasonable adjustment”). Finally, it will highlight some key considerations and recommendations for designing online teaching experiences which emphasise accessibility and inclusion for all students in tertiary education

A beginning exploration of text generation abilities in university students with a history of reading difficulties

There is a fundamental lack of understanding of how university students with a history of reading difficulties perform on various demanding literacy tasks. We compared the text generation skills, measured with timed summary writing and proofreading tasks, of university students with a history of reading difficulties to those of students with no such history. We further examined whether between-group differences in text generation skills remained after controlling for transcription skills (spelling and handwriting fluency), word reading, and reading comprehension. Forty-six university students with a history of reading difficulties were matched on age, gender, and non-verbal intelligence to 46 students without this history. We found that the students with a history of reading difficulties performed poorer on both measures of text generation than students without this history. When differences in transcription skills, word reading, and reading comprehension were controlled, we found that only differences in timed summary writing remained significant. These results suggest that students with a history of reading difficulties experience challenges with specific aspects of text generation that are beyond what one would expect from their difficulties with transcription and word reading. We suggest that, if not addressed, text generation deficits are likely to create obstacles for academic success

Forecasted Range Shifts of Arid-Land Fishes in Response to Climate Change

Climate change is poised to alter the distributional limits, center, and size of many species. Traits may influence different aspects of range shifts, with trophic generality facilitating shifts at the leading edge, and greater thermal tolerance limiting contractions at the trailing edge. The generality of relationships between traits and range shifts remains ambiguous however, especially for imperiled fishes residing in xeric riverscapes. Our objectives were to quantify contemporary fish distributions in the Lower Colorado River Basin, forecast climate change by 2085 using two general circulation models, and quantify shifts in the limits, center, and size of fish elevational ranges according to fish traits. We examined relationships among traits and range shift metrics either singly using univariate linear modeling or combined with multivariate redundancy analysis. We found that trophic and dispersal traits were associated with shifts at the leading and trailing edges, respectively, although projected range shifts were largely unexplained by traits. As expected, piscivores and omnivores with broader diets shifted upslope most at the leading edge while more specialized invertivores exhibited minimal changes. Fishes that were more mobile shifted upslope most at the trailing edge, defying predictions. No traits explained changes in range center or size. Finally, current preference explained multivariate range shifts, as fishes with faster current preferences exhibited smaller multivariate changes. Although range shifts were largely unexplained by traits, more specialized invertivorous fishes with lower dispersal propensity or greater current preference may require the greatest conservation efforts because of their limited capacity to shift ranges under climate change