Results for 'Group theory'

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  1.  93
    Particular Symmetries: Group Theory of the Periodic System.Pieter Thyssen & Arnout Ceulemans - 2020 - Substantia 4 (1):7-22.
    To this day, a hundred and fifty years after Mendeleev's discovery, the overal structure of the periodic system remains unaccounted for in quantum-mechanical terms. Given this dire situation, a handful of scientists in the 1970s embarked on a quest for the symmetries that lie hidden in the periodic table. Their goal was to explain the table's structure in group-theoretical terms. We argue that this symmetry program required an important paradigm shift in the understanding of the nature of chemical elements. (...)
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  2. The Reasonable Effectiveness of Mathematics: Partial Structures and the Application of Group Theory to Physics.Steven French - 2000 - Synthese 125 (1):103-120.
    Wigner famously referred to the 'unreasonable effectiveness' of mathematics in its application to science. Using Wigner's own application of group theory to nuclear physics. I hope to indicate that this effectiveness can be seen to be not so unreasonable if attention is paid to the various idealising moves undertaken. The overall framework for analysing this relationship between mathematics and physics is that of da Costa's partial structures programme.
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  3.  64
    Group Theory and Computational Linguistics.Dymetman Marc - 1998 - Journal of Logic, Language and Information 7 (4):461-497.
    There is currently much interest in bringing together the tradition of categorial grammar, and especially the Lambek calculus, with the recent paradigm of linear logic to which it has strong ties. One active research area is designing non-commutative versions of linear logic (Abrusci, 1995; Retoré, 1993) which can be sensitive to word order while retaining the hypothetical reasoning capabilities of standard (commutative) linear logic (Dalrymple et al., 1995). Some connections between the Lambek calculus and computations in groups have long been (...)
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  4.  76
    Models and Mathematics in Physics: The Role of Group Theory.Steven French - 1999 - In Jeremy Butterfield & Constantine Pagonis (eds.), From Physics to Philosophy. Cambridge University Press. pp. 187--207.
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  5.  27
    Group Theory and Orbital Fluctuations of the Hydrogen Atom.H. Kleinert - 1993 - Foundations of Physics 23 (5):769-807.
    We review some of the progress made in the past 27 years in understanding the group theoretic and path integral aspects of the hydrogen atom. The group theoretic development was triggered by A. O. Barut who suggested to me the search for a dynamical group larger than SO(4). In this way he became indirectly responsible also for important recent path integral developments.
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  6.  24
    Group Theory and Solutions of Classical Field Theories with Polynomial Nonlinearities.A. M. Grundland, J. A. Tuszyński & P. Winternitz - 1993 - Foundations of Physics 23 (4):633-665.
    In this paper we investigate a number of analytical solutions to the polynomial class of nonlinear Klein-Gordon equations in multidimensional spacetime. This is done in the context of classical φ4 and φ6 field theory, the former with and without the inclusion of an external force field conjugate to φ. Both massive (m≠0) and massless (m=0) cases are considered, as well as tachyonic solutions allowed (v>c). We first present a complete set of translationally invariant solutions for the φ4 model and (...)
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  7.  14
    Shattered Symmetry: Group Theory From the Eightfold Way to the Periodic Table.Pieter Thyssen & Arnout Ceulemans - 2017 - New York, NY, USA: Oxford University Press.
    The standard model of subatomic particles and the periodic table of the atoms have the common goal to bring order in the bewildering chaos of the constituents of matter. Their success relies on the presence of fundamental symmetries in their core. The purpose of the book is to share the admiration for the power and the beauty of these symmetries. The reader is taken on a journey from the basic geometric symmetry group of a circle to the sublime dynamic (...)
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  8.  11
    Group Theory: Birdtracks, Lie's, and Exceptional Groups.Predrag Cvitanovic - 2008 - Princeton University Press.
    This book is the first to systematically develop, explain, and apply diagrammatic projection operators to construct all semi-simple Lie algebras, both classical and exceptional.
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  9.  41
    Group Theory and Geometric Psychology.William C. Hoffman - 2001 - Behavioral and Brain Sciences 24 (4):674-676.
    The commentary is in general agreement with Roger Shepard's view of evolutionary internalization of certain procedural memories, but advocates the use of Lie groups to express the invariances of motion and color perception involved. For categorization, the dialectical pair is suggested. [Barlow; Hecht; Kubovy & Epstein; Schwartz; Shepard; Todorovic].
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  10.  62
    From the Periphery: The Genesis of Eugene P. Wigner's Application of Group Theory to Quantum Mechanics. [REVIEW]Michael Chayut - 2001 - Foundations of Chemistry 3 (1):55-78.
    This paper traces the origins of Eugene Wigner's pioneering application of group theory to quantum physics to his early work in chemistry and crystallography. In the early 1920s, crystallography was the only discipline in which symmetry groups were routinely used. Wigner's early training in chemistry, and his work in crystallography with Herman Mark and Karl Weissenberg at the Kaiser Wilhelm institute for fiber research in Berlin exposed him to conceptual tools which were absent from the pedagogy available to (...)
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  11.  29
    The Emergence of Selection Rules and Their Encounter with Group Theory, 1913–1927.Arianna Borrelli - 2009 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 40 (4):327-337.
  12.  4
    Linear Differential Equations and Group Theory From Riemann to Poincaré by Jeremy Gray. [REVIEW]David Rowe - 1988 - Isis 79:151-152.
  13.  4
    Linear Differential Equations and Group Theory From Riemann to PoincaréJeremy Gray.David E. Rowe - 1988 - Isis 79 (1):151-152.
  14.  18
    Review of S. Sternberg, Group Theory and Physics[REVIEW]Mark Steiner - 1995 - Philosophia Mathematica 3 (3):313-316.
  15. Shlomo Sternberg, Group Theory and Physics.M. Steiner - 1995 - Philosophia Mathematica 3 (3):313-313.
  16.  16
    The Emergence of Selection Rules and Their Encounter with Group Theory, 1913–1927.Arianna Borrelli - 2009 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 40 (4):327-337.
  17.  9
    Geometry as an Extension of the Group Theory.A. Prusińska & L. Szczerba - 2002 - Logic and Logical Philosophy 10:131.
    Klein’s Erlangen program contains the postulate to study thegroup of automorphisms instead of a structure itself. This postulate, takenliterally, sometimes means a substantial loss of information. For example, thegroup of automorphisms of the field of rational numbers is trivial. Howeverin the case of Euclidean plane geometry the situation is different. We shallprove that the plane Euclidean geometry is mutually interpretable with theelementary theory of the group of authomorphisms of its standard model.Thus both theories differ practically in the language (...)
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  18.  20
    When Group Membership Gets Personal: A Theory of Identity Fusion.William B. Swann, Jolanda Jetten, Ángel Gómez, Harvey Whitehouse & Brock Bastian - 2012 - Psychological Review 119 (3):441-456.
  19. Intersubjectivity and Group Theory in the Thought of Sartre.Francisco Javier Higuero - 2008 - Convivium: revista de filosofía 21:55-69.
     
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  20.  30
    A Theory of Group Rationality.Husain Sarkar - 1982 - Studies in History and Philosophy of Science Part A 13 (1):55.
  21.  11
    Recursively Presented Abelian Groups: Effective P-Group Theory. I.Charlotte Lin - 1981 - Journal of Symbolic Logic 46 (3):617-624.
  22. Group Agency: The Possibility, Design, and Status of Corporate Agents.Christian List & Philip Pettit - 2011 - Oxford University Press.
    Are companies, churches, and states genuine agents? Or are they just collections of individuals that give a misleading impression of unity? This question is important, since the answer dictates how we should explain the behaviour of these entities and whether we should treat them as responsible and accountable on the model of individual agents. Group Agency offers a new approach to that question and is relevant, therefore, to a range of fields from philosophy to law, politics, and the social (...)
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  23.  16
    A Descriptive View of Combinatorial Group Theory.Simon Thomas - 2011 - Bulletin of Symbolic Logic 17 (2):252-264.
    In this paper, we will prove the inevitable non-uniformity of two constructions from combinatorial group theory related to the word problem for finitely generated groups and the Higman—Neumann—Neumann Embedding Theorem.
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  24.  15
    Group Decision and Social Interaction: A Theory of Social Decision Schemes.James H. Davis - 1973 - Psychological Review 80 (2):97-125.
  25.  5
    A Sentence Made by Men: Muted Group Theory Revisited.Pat Gannon-Leary & Celia J. Wall - 1999 - European Journal of Women's Studies 6 (1):21-29.
    This article takes a fresh look at the Ardeners' muted group theory, originally applied in social anthropology and later taken up by the women's movement. The theory has wider applicability in aiding understanding of the communication processes between females and males but there is a need for a combination of disparate types of research extending the focus beyond mutedness as a structural product to the processes by which women are rendered mute, involving a broader analysis of the (...)
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  26.  10
    The Relevance of Bentley for Group Theory: Founding Father or Mistaken Identity?Grant Jordan - 1999 - History of the Human Sciences 12 (1):27-54.
    A. F. Bentley’s The Process of Government (1908) is widely accepted as an important source of contemporary interest group study. This paper argues to the contrary that Bentley’s arguments in this area are obscure and have contributed little to the programme of modern interest group research. His importance is as a contributor to the debate on the nature of social science and social science method and not as the starting-point for interest group analysis. The judgement about his (...)
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  27.  34
    Dying for the Group: Towards a General Theory of Extreme Self-Sacrifice.Harvey Whitehouse - 2018 - Behavioral and Brain Sciences 41:1-64.
    Whether upheld as heroic or reviled as terrorism, people have been willing to lay down their lives for the sake of their groups throughout history. Why? Previous theories of extreme self-sacrifice have highlighted a range of seemingly disparate factors, such as collective identity, outgroup hostility, and kin psychology. In this paper, I attempt to integrate many of these factors into a single overarching theory based on several decades of collaborative research with a range of special populations, from tribes in (...)
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  28.  26
    "Group Decision and Social Interaction: A Theory of Social Decision Schemes": Errata.James H. Davis - 1973 - Psychological Review 80 (4):302-302.
  29.  68
    Must Group Agents Be Rational? List and Pettit's Theory of Judgement Aggregation and Group Agency.Robert Sugden - 2012 - Economics and Philosophy 28 (2):265-273.
    ExtractAs a writing partnership, Christian List and Philip Pettit are probably best known for a paper in Economics and Philosophy that describes and generalizes the ‘discursive dilemma’. That paper is one of the main points of reference for what is now a large literature on the aggregation of judgements – a literature to which List and Pettit have continued to contribute, individually and jointly. Their new book Group Agency reviews and synthesizes that body of work, and proposes an analysis (...)
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  30.  11
    Dynamics of Group-Based Emotions: Insights From Intergroup Emotions Theory.Eliot R. Smith & Diane M. Mackie - 2015 - Emotion Review 7 (4):349-354.
    Over-time variability characterizes not only individual-level emotions, but also group-level emotions, those that occur when people identify with social groups and appraise events in terms of their implications for those groups. We discuss theory and research regarding the role of emotions in intergroup contexts, focusing on their dynamic nature. We then describe new insights into the causes and consequences of emotional dynamics that flow from conceptualizing emotions as based in group membership, and conclude with research recommendations.
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  31.  61
    Evolutionary Theory and Group Selection: The Question of Warfare.Doyne Dawson - 1999 - History and Theory 38 (4):79–100.
    Evolutionary anthropology has focused on the origins of war, or rather ethnocentricity, because it epitomizes the problem of group selection, and because war may itself have been the main agent of group selection. The neo-Darwinian synthesis in biology has explained how ethnocentricity might evolve by group selection, and the distinction between evoked culture and adopted culture, suggested by the emerging synthesis in evolutionary psychology, has explained how it might be transmitted. Ethnocentric mechanisms could have evolved by genetic (...)
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  32.  2
    C. TRETKOFF [1988] Complexity, Combinatorial Group Theory and the Language of Palutators, Theoret. Comput. Sci., 56. Pp. 253-275. [REVIEW]J. Stillwell, V. Stoltenberg-Hansen & Jv Tucker - 1999 - In Edward R. Griffor (ed.), Handbook of Computability Theory. Elsevier. pp. 140--445.
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  33.  32
    Macintyre Angus. On Ω1-Categorical Theories of Abelian Groups. Fundamenta Mathematicae, Vol. 70 , Pp. 253–270.Macintyre Angus. On Ω1-Categorical Theories of Fields. Fundamenta Mathematicae, Vol. 71 , Pp. 1–25.Reineke Joachim. Minimale Gruppen. Zeitschrift Für Mathematische Logik Und Grundlagen der Mathematik, Vol. 21 , Pp. 357–359.Baldwin J. T. And Saxl Jan. Logical Stability in Group Theory. The Journal of the Australian Mathematical Society, Vol. 21 Ser. A , Pp. 267–276.Zil'bér B. I.. Gruppy I Kol'ca, Téoriá Kotoryh Katégorična . Fundamenta Mathematicae, Vol. 95 , Pp. 173–188.Baur Walter, Cherlin Gregory, and Macintyre Angus. Totally Categorical Groups and Rings. Journal of Algebra, Vol. 57 , Pp. 407–440.Cherlin Gregory. Groups of Small Morley Rank. Annals of Mathematical Logic, Vol. 17 , Pp. 1–28.Cherlin G. And Shelah S.. Superstable Fields and Groups. Annals of Mathematical Logic, Vol. 18 , Pp. 227–270.Poizat Bruno. Sous-Groupes Définissables D 'Un Groupe Stable. [REVIEW]Anand Pillay - 1984 - Journal of Symbolic Logic 49 (1):317-321.
  34.  15
    Smielew W.. Decision Problem in Group Theory. Ebd., Sonderabdruck 1948, S. 373–376.Rózsa Péter - 1949 - Journal of Symbolic Logic 14 (1):63-64.
  35.  3
    Boone William W.. Certain Simple, Unsolvable Problems of Group Theory V–VI. Koninklijke Nederlandse Akademie van Wetenschappen, Proceedings, Series A, Vol. 60 , Pp. 22–27, 227–232; Also Indagationes Mathematicae, Vol. 19 , Pp. 22–27, 227–232. [REVIEW]Michael O. Rabin - 1957 - Journal of Symbolic Logic 22 (4):373-374.
  36.  4
    Boone William W.. Certain Simple, Unsolvable Problems of Group Theory I–IV. Koninklijke Nederlandse Akademie van Wetenschappen, Proceedings, Series A, Vol. 57 , Pp. 231–237, 492–497, and Vol. 58 , Pp. 252–256, 571–577; Also Indagationes Mathematicae, Vol. 16 , Pp. 231–237, 492–497, and Vol. 17 , Pp. 252–256, 571–577. [REVIEW]Michael O. Rabin - 1957 - Journal of Symbolic Logic 22 (4):372-373.
  37.  3
    Review: William W. Boone, Certain Simple, Unsolvable Problems of Group Theory I-IV. [REVIEW]Michael O. Rabin - 1957 - Journal of Symbolic Logic 22 (4):372-373.
  38. Review: William W. Boone, Certain Simple, Unsolvable Problems of Group Theory V-VI. [REVIEW]Michael O. Rabin - 1957 - Journal of Symbolic Logic 22 (4):373-374.
  39.  10
    Büchi J. Richard and Wright Jesse B.. The Theory of Proportionality as an Abstraction of Group Theory. Mathematische Annalen, Vol. 130 No. 2 , Pp. 102–108. [REVIEW]Hugo Ribeiro - 1957 - Journal of Symbolic Logic 22 (4):369-369.
  40.  18
    Multi-Posets in Algebraic Logic, Group Theory, and Non-Commutative Topology.Wolfgang Rump - 2016 - Annals of Pure and Applied Logic 167 (11):1139-1160.
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  41.  10
    Jeremy Gray. Linear Differential Equations and Group Theory From Riemann to Poincaré. Basel & Boston: Birkhauser, 1986. Pp. Xxv + 460. ISBN 3-7643-3318-9 , 0-8176-3318-9 . $51.00. [REVIEW]Caroline Series - 1988 - British Journal for the History of Science 21 (1):112-114.
  42.  40
    The Development of Renormalization Group Methods for Particle Physics: Formal Analogies Between Classical Statistical Mechanics and Quantum Field Theory.Doreen Fraser - 2020 - Synthese 197 (7):3027-3063.
    Analogies between classical statistical mechanics and quantum field theory played a pivotal role in the development of renormalization group methods for application in the two theories. This paper focuses on the analogies that informed the application of RG methods in QFT by Kenneth Wilson and collaborators in the early 1970's. The central task that is accomplished is the identification and analysis of the analogical mappings employed. The conclusion is that the analogies in this case study are formal analogies, (...)
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  43. Reintroducing Group Selection to the Human Behavioral Sciences.David Sloan Wilson & Elliott Sober - 1994 - Behavioral and Brain Sciences 17 (4):585-608.
    In both biology and the human sciences, social groups are sometimes treated as adaptive units whose organization cannot be reduced to individual interactions. This group-level view is opposed by a more individualistic one that treats social organization as a byproduct of self-interest. According to biologists, group-level adaptations can evolve only by a process of natural selection at the group level. Most biologists rejected group selection as an important evolutionary force during the 1960s and 1970s but a (...)
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  44. Herbert H. Hyman and Eleanor Singer, "Readings in Reference Group Theory and Research". [REVIEW]Karl-Dieter Opp - 1972 - Theory and Decision 3 (2):185.
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  45. Review: P. S. Novikov, Unsolvability of the Conjugacy Problem in Group Theory[REVIEW]J. L. Britton - 1958 - Journal of Symbolic Logic 23 (1):52-54.
  46. Review: P. S. Novikov, Algorithmic Unsolvability of the Word Problem in Group Theory[REVIEW]J. L. Britton - 1958 - Journal of Symbolic Logic 23 (1):50-52.
  47. Infestation or Pest Control: The Introduction of Group Theory Into Quantum Mechanics.Otávio Bueno & Steven French - 1999 - Manuscrito 22 (2):37-68.
     
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  48.  31
    Weyl and Von Neumann: Symmetry, Group Theory, and Quantum Mechanics.Otavio Bueno - unknown
    In this paper, I shall discuss the heuristic role of symmetry in the mathematical formulation of quantum mechanics. I shall first set out the scene in terms of Bas van Fraassen’s elegant presentation of how symmetry principles can be used as problem-solving devices (see van Fraassen [1989] and [1991]). I will then examine in what ways Hermann Weyl and John von Neumann have used symmetry principles in their work as a crucial problem-solving tool. Finally, I shall explore one consequence of (...)
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  49.  24
    Review: William W. Boone, Frank B. Cannonito, Roger C. Lyndon, Word Problems, Decision Problems and Burnside Problem in Group Theory[REVIEW]C. R. J. Clapham - 1976 - Journal of Symbolic Logic 41 (4):785-788.
  50.  59
    William W. Boone, Frank B. Cannonito, and Roger C. Lyndon. Introduction. Word Problems, Decision Problems and the Burnside Problem in Group Theory, Edited by W. W. Boone, F. B. Cannonito, and R. C. Lyndon, Studies in Logic and the Foundations of Mathematics, Vol. 71, North-Holland Publishing Company, Amsterdam and London1973, Pp. Ix–Xii. [REVIEW]C. R. J. Clapham - 1976 - Journal of Symbolic Logic 41 (4):785-788.
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