330 research outputs found
The companion equations and the moyal-nahm equations
No full textThe first part of this thesis is concerned with the companion equations. These are equations of motion for the companion Lagrangian which is proposed to be the Lagrangian for a field theory associated with strings and branes, similar to the Klein-Gordon field description for particles. The form of this Lagrangian can be related to the Hamilton-Jacobi formalism for strings and branes. Some solutions to the companion equations are found and their integrability is discussed. There is an equivalence between the equations of motion for different companion Lagrangians when some constraints are applied. Under these constraints, the companion equations for a Lagrangian without a square root are equivalent to the companion equations for a Lagrangian with a square root but in one dimension less. The appearance of Universal Field Equations, generalised Bateman equations, in the companion equations leads to the study of an iterative procedure for Lagrangians which are homogeneous of weight one in the first derivatives in the fields the theory describes. The Universal Field equations appear after several iterations. Also, it is shown how Lagrangians for a large family of field theories are a divergence or vanish on the space of solutions of the equations of motion. Such theories could be called 'pseudo-topological'.The second part of this thesis is concerned with finding solutions to the Moyal-Nahm equations in four and eight dimensions. These equations are the Nahm equations, which give a set of solutions to self-dual Yang-Mills, but with the commutators replaced with Moyal brackets. Solutions are found in terms of generalised Wigner functions. Also, matrix representations of the algebra generated by the equivalent Nahm equations in eight dimensions are obtained. Solutions to the Nahm equations in eight dimensions are also given
Hinge epistemology
No full textThe book explores the history and theoretical developments of a new epistemological trend - "hinge epistemology" - which originates in the works of G. E. Moore and L. Wittgenstein, and which is gaining center stage in contemporary debates.In Hinge Epistemology, eminent epistemologists investigate Wittgenstein's concept of basic certainty or 'hinge certainty'. The volume begins by examining the salient features of 'hinges': Are they propositions that enjoy a special kind of non-evidential justification? Are they objects of knowledge or ways of acting mistaken for known propositions? Various attempts are then made to integrate hinges in the development of a viable epistemology: Can they shed light on the conditions of satisfaction for knowledge and justification? Do they offer a solution to scepticism? Finally, the application of hinges is explored in such areas as common knowledge and intellectual loyalty. The volume attests to the importance of hinge certainty and Wittgenstein's On Certainty for mainstream epistemology
Introduction: Hinge Epistemology
No full textThis introduction gives a summary of the content of the special issue Hinge Epistemology, grouping the papers in three sections: (1) more exegetical accounts of Wittgenstein's notion of hinge certainties and their bearing on a theory of justification and knowledge as well as on the topic of external world scepticism; (2) papers critical of the very notion of hinge certainty; and (3) papers that apply the notion to various areas of epistemology and compare Wittgenstein's views to those of other philosophers
A Kähler Compatible Moyal Deformation of the First Heavenly Equation
No full textWe construct a noncommutative Kähler manifold based on a non-linear perturbation of Moyal integrable deformations of D=4 self-dual gravity. The deformed Kähler manifold preserves all the properties of the commutative one, and we obtain the associated noncommutative Kähler potential using the Moyal deformed gravity approach. We apply this construction to the Atiyah-Hitchin metric and its Kähler potential, which is useful in the description of interactions among magnetic monopoles at low energies.The authors would like to thank the referees for their valuable remarks and suggestions to improve this work. D. Martínez-Carbajal acknowledges support from Universidad Autónoma Metropolitana (UAM, México)
Mind, Language and Action: Proceedings of the 36th International Wittgenstein Symposium
No full textThe volume contains most invited papers to the Austrian Ludwig Wittgenstein's Society Symposium in Kirchberg 2013 "Mind, Language and Action". They are divided into four sections: Wittgenstein, Enactivism, Language Acquisition, Actio
Wittgenstein and pragmatism: habits, rules and forms of life
No full textRoberta Dreon, Foreword
Luigi Perissinotto, Concept-formations and facts of nature in Wittgenstein
Garry L.Hagberg, Peirce, Wittgenstein, and the sense of pragmatism
Anna Boncompagni, «I’ll show you a thing we humans do». Facts of life in Wittgenstein and Peirce
Daniele Moyal-Sharrock, Can Wittgenstein be called a pragmatist?
Rosa M.Calcaterra, The ambiguity of norms. Steps towards a new pragmatic anthropology
Roberta Dreon, Understanding rules as habits. Developing a pragmatist anthropological approach
Guido Baggio, The concept of “behavior” in psychology, epistemology, and economics. Starting from G.H.Mea
Isospectral Hamiltonians from Moyal products
No full textRecently Scholtz and Geyer proposed a very efficient method to compute metric operators for non-Hermitian Hamiltonians from Moyal products. We develop these ideas further and suggest to use a more symmetrical definition for the Moyal products, because they lead to simpler differential equations. In addition, we demonstrate how to use this approach to determine the Hermitian counterpart for a pseudo-Hermitian Hamiltonian. We illustrate our suggestions with the explicitly solvable example of the −x 4-potential and the ubiquitous harmonic oscillator in a complex cubic potential
Noncommutative Induced Gauge Theories on Moyal Spaces
No full text24 pages, 6 figures. Talk given at the "International Conference on Noncommutative Geometry and Physics", April 2007, Orsay (France)Noncommutative field theories on Moyal spaces can be conveniently handled within a framework of noncommutative geometry. Several renormalisable matter field theories that are now identified are briefly reviewed. The construction of renormalisable gauge theories on these noncommutative Moyal spaces, which remains so far a challenging problem, is then closely examined. The computation in 4-D of the one-loop effective gauge theory generated from the integration over a scalar field appearing in a renormalisable theory minimally coupled to an external gauge potential is presented. The gauge invariant effective action is found to involve, beyond the expected noncommutative version of the pure Yang-Mills action, additional terms that may be interpreted as the gauge theory counterpart of the harmonic term, which for the noncommutative -theory on Moyal space ensures renormalisability. A class of possible candidates for renormalisable gauge theory actions defined on Moyal space is presented and discussed
John Locke, Essai philosophique concernant l'entendement humain, Traduit par Pierre Coste, Édité par Georges J. D. Moyal, 2004
No full textGroult Martine. John Locke, Essai philosophique concernant l'entendement humain, Traduit par Pierre Coste, Édité par Georges J. D. Moyal, 2004. In: Dix-huitième Siècle, n°37, 2005. Politiques et cultures des Lumières. pp. 680-681
Noncommutative Induced Gauge Theories on Moyal Spaces
No full text24 pages, 6 figures. Talk given at the "International Conference on Noncommutative Geometry and Physics", April 2007, Orsay (France)Noncommutative field theories on Moyal spaces can be conveniently handled within a framework of noncommutative geometry. Several renormalisable matter field theories that are now identified are briefly reviewed. The construction of renormalisable gauge theories on these noncommutative Moyal spaces, which remains so far a challenging problem, is then closely examined. The computation in 4-D of the one-loop effective gauge theory generated from the integration over a scalar field appearing in a renormalisable theory minimally coupled to an external gauge potential is presented. The gauge invariant effective action is found to involve, beyond the expected noncommutative version of the pure Yang-Mills action, additional terms that may be interpreted as the gauge theory counterpart of the harmonic term, which for the noncommutative -theory on Moyal space ensures renormalisability. A class of possible candidates for renormalisable gauge theory actions defined on Moyal space is presented and discussed
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