A gauge theoretic approach to elasticity with microrotations

We formulate elasticity theory with microrotations using the framework of gauge theories, which has been developed and successfully applied in various areas of gravitation and cosmology. Following this approach, we demonstrate the existence of particle-like solutions. Mathematically this is due to the fact that our equations of motion are of Sine-Gordon type and thus have soliton type solutions. Similar to Skyrmions and Kinks in classical field theory, we can show explicitly that these solutions have a topological origin.Comment: 15 pages, 1 figure; revised and extended version, one extra page; revised and extended versio

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

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