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Higherdimensional algebra and topological quantum field theory
 Jour. Math. Phys
, 1995
"... For a copy with the handdrawn figures please email ..."
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Cited by 140 (14 self)
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For a copy with the handdrawn figures please email
Third’ Quantization of Vacuum Einstein Gravity and Free YangMills Theories
, 2006
"... All day today! Certain pivotal results from various applications of Abstract Differential Geometry (ADG) to gravity and gauge theories are presently collected and used to argue that we already possess a geometrically (pre)quantized, second quantized and manifestly background spacetime manifold indep ..."
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Cited by 1 (1 self)
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All day today! Certain pivotal results from various applications of Abstract Differential Geometry (ADG) to gravity and gauge theories are presently collected and used to argue that we already possess a geometrically (pre)quantized, second quantized and manifestly background spacetime manifold independent vacuum Einstein gravitational field dynamics. The arguments carry also mutatis mutandis to the case of free YangMills theories, since from the ADGtheoretic perspective gravity is regarded as another gauge field theory. The powerful algebraicocategorical, sheaf cohomological conceptual and technical machinery of ADG is then employed, based on the fundamental ADGtheoretic conception of a field as a pair (E, D) consisting of a vector sheaf E and an algebraic connection D acting categorically as a sheaf morphism on E’s local sections, to introduce a ‘universal’, because expressly functorial, field quantization scenario coined third quantization. Although third quantization is fully covariant, on intuitive and heuristic grounds alone it formally appears to follow a canonical route; albeit, in a purely algebraic and, in contradistinction to geometric (pre)quantization and (canonical) second quantization, manifestly background geometrical spacetime manifold independent fashion, as befits ADG. All in all, from the ADGtheoretic vantage, vacuum Einstein gravity and free YangMills theories are regarded as external spacetime manifold unconstrained, third quantized, pure gauge field theories. The paper abounds with philosophical smatterings and speculative remarks about the potential import and significance of our results to current and future Quantum Gravity research. A postscript gives a brief account of this author’s personal encounters with Rafael Sorkin and his work.
A derivation of Einstein’s vacuum field equations
, 2009
"... In his work on General Relativity ([2]), Einstein started from the field formulation of Newton’s gravitational theory due to Poisson, i.e., the equation ∇ 2 φ = 4πκρ where φ is the gravitational potential, ∇ 2 φ = ∑ ..."
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In his work on General Relativity ([2]), Einstein started from the field formulation of Newton’s gravitational theory due to Poisson, i.e., the equation ∇ 2 φ = 4πκρ where φ is the gravitational potential, ∇ 2 φ = ∑
Manifestly Covariant Relativity 1
, 2006
"... According to Einstein’s principle of general covariance, all laws of nature are to be expressed by manifestly covariant equations. In recent work, the covariant law of energymomentum conservation has been established. Here, we show that this law gives rise to a fully covariant theory of gravitation ..."
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According to Einstein’s principle of general covariance, all laws of nature are to be expressed by manifestly covariant equations. In recent work, the covariant law of energymomentum conservation has been established. Here, we show that this law gives rise to a fully covariant theory of gravitation and that Einstein’s field equations yield total energymomentum conservation. 1 This paper appeared in the Hadronic Journal 17, 139 (1994). It predates the four related articles which are listed on page 5. 1 “The general laws of nature are to be expressed by equations which hold good for all systems of coordinates, that is, are covariant with respect to any substitutions whatever (generally covariant).”[1] The great beauty of Einstein’s theory of general relativity has been justly celebrated over the decades. The mathematical beauty of the theory consists
Book Review The Evolution of an Idea Reviewed by Robyn Arianrhod The Noether Theorems: Invariance and Conservation Laws in the Twentieth Century
"... Emmy Noether, the most famous female mathematician of the twentieth century, was the daughter of mathematician Max Noether. She received her doctorate at Erlangen in 1907 (when she was twentyfive) for a thesis on the topic of algebraic invariants. She soon became part of the brilliant circle led by ..."
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Emmy Noether, the most famous female mathematician of the twentieth century, was the daughter of mathematician Max Noether. She received her doctorate at Erlangen in 1907 (when she was twentyfive) for a thesis on the topic of algebraic invariants. She soon became part of the brilliant circle led by Felix Klein and David Hilbert at Göttingen, and popular legend says she influenced even Einstein. Of course, legends tend to abound about pioneering female mathematicians, but in this case there is some substance to the claim, as The Noether Theorems shows. In the interest of clarifying the intended readership, let me hasten to add that this book is not a series of portraits of colorful personalities; rather, it is a deeply scholarly work, tersely written but generously footnoted, that celebrates Noether’s most famous achievements. It begins with an English translation of Noether’s paper “Invariant variational problems”, published originally in German (“Invariante Variationsprobleme”) in 1918, which will delight mathematicians and mathematical physicists who use these theorems without having read the original version. But The Noether Theorems does more than celebrate Emmy Noether and her theorems: as the subtitle suggests, it traces what Yvette KosmannSchwarzbach calls the “evolution of ideas ” about the relationship between mathematical invariance and conservation laws, and it will be of great interest to historians of mathematics. For those who simply wish to get a feel for the work and influence of this famous female mathematician but Robyn Arianrhod is an adjunct research fellow in the school of mathematical sciences at Monash University. Her email address is robyn.arianrhod@ monash.edu.
Rotational Transformation Between Schwarzschild Metric And Kerr Metric
"... Abstract: Transformation between Schwarzschild metric [1] and Kerr metric [2] is obtained for weak field at large distance (r>> GM) with low angular velocity (a ω << r 2). It has been found that the relativistic rotational transformation exists within a domain r < c/ω. The transformation is dependen ..."
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Abstract: Transformation between Schwarzschild metric [1] and Kerr metric [2] is obtained for weak field at large distance (r>> GM) with low angular velocity (a ω << r 2). It has been found that the relativistic rotational transformation exists within a domain r < c/ω. The transformation is dependent on the spacetime coordinates, and locally consistent with the Lorentz transformation. The rotational transformation obtained in this article is a direct result of Einstein’s field equation. The rotational time dilation and the angle contraction are obtained to be locally consistent with the translational time dilation and length contraction of special relativity. Keywords: general relativity, Schwarzschild, Kerr, rotational transformation, time dilation, angle contraction.
Rotational Time Dilation and Angle Contraction
"... Abstract: Rotational time dilation and angular contraction are discussed in comparison with the time deletion and length contraction of special relativity. The related issues of clock paradox and simultaneity are explored in rotational scenario. The non Euclidian nature of a relativistic rotation is ..."
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Abstract: Rotational time dilation and angular contraction are discussed in comparison with the time deletion and length contraction of special relativity. The related issues of clock paradox and simultaneity are explored in rotational scenario. The non Euclidian nature of a relativistic rotation is analyzed in both θ t and θ r subspace. It has been shown that the constancy of the speed of light is intrinsically incompatible with rotational motion. The related issue of simultaneity and rotational space warping are also discussed. Keywords: relativity, rotation, rotating disk, time dilation, angle contraction. 1