An Introduction to Topos Physics Export

@article{citeulike:2551144, abstract = {The basic notion of how topoi can be utilized in physics is presented here. Topos and category theory serve as valuable tools which extend our ordinary set-theoretical conceptions, can further the study of quantum logic and give rise to new and 'neo-realistic' descriptions of quantum physics, i.e. make possible the construction of a general scheme for quantum physics, which 'looks like' the classical one. A novel way of writing theories of physics, by representing a formal language of a physical system, into an appropriate topos, is analyzed here. This novel approach is initiated by C.J. Isham and A. Doering and the major part of this paper comes from there; however there has been an effort in simplifying the basic ideas and do this work accessible to 'less experts' of the field. A minor, but not less important, part of this paper is devoted to resuming, in a concise way the background knowledge of logic, quantum logic and category theory, that is necessary for anyone who wishes to follow the whole topos approach.}, archivePrefix = {arXiv}, author = {Tsatsos, Marios}, citeulike-article-id = {2551144}, citeulike-linkout-0 = {http://arxiv.org/abs/0803.2361}, citeulike-linkout-1 = {http://arxiv.org/pdf/0803.2361}, day = {16}, eprint = {0803.2361}, keywords = {category-theory, math-ph, topos-theory}, month = {Mar}, posted-at = {2009-04-29 23:28:49}, priority = {2}, title = {An Introduction to Topos Physics}, url = {http://arxiv.org/abs/0803.2361}, year = {2008} }

TY - JOUR ID - citeulike:2551144 L3 - citeulike-article-id:2551144 N2 - The basic notion of how topoi can be utilized in physics is presented here. Topos and category theory serve as valuable tools which extend our ordinary set-theoretical conceptions, can further the study of quantum logic and give rise to new and 'neo-realistic' descriptions of quantum physics, i.e. make possible the construction of a general scheme for quantum physics, which 'looks like' the classical one. A novel way of writing theories of physics, by representing a formal language of a physical system, into an appropriate topos, is analyzed here. This novel approach is initiated by C.J. Isham and A. Doering and the major part of this paper comes from there; however there has been an effort in simplifying the basic ideas and do this work accessible to 'less experts' of the field. A minor, but not less important, part of this paper is devoted to resuming, in a concise way the background knowledge of logic, quantum logic and category theory, that is necessary for anyone who wishes to follow the whole topos approach. TI - An Introduction to Topos Physics KW - category-theory KW - math-ph KW - topos-theory AU - Tsatsos, Marios PY - 2008/Mar/16/ UR - http://arxiv.org/abs/0803.2361 ER -