Morita Equivalence, Picard Groupoids and Noncommutative Field Theories

The motivation for supersymmetry. The algebra, the superspace, and the representations. Field theory models and the non-renormalisation theorems. Spontaneous and explicit breaking of super-symmetry. The generalisation of the Montonen–Olive duality conjecture in supersymmetric theories. The remarkable properties of extended supersymmetric theories. A brief discussion of twisted supersymmetry in connection with topological field theories. Attempts to build a supersymmetric extention of the standard model and its experimental consequences. The property of gauge supersymmetry to include general relativity and the supergravity models.

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Introduction

10.1093/oso/9780198810315.003.0001 ◽

2018 ◽

Author(s):

Marjorie Levinson

Keyword(s):

Modern Philosophy ◽

Early Modern ◽

Martin Heidegger ◽

Conceptual Structure ◽

Field Theories ◽

Self Organization ◽

Physical Sciences ◽

Early Modern Philosophy

The Introduction explains the combination of a narrative arc and conceptual structure in the organization of the book. The former, primarily diachronic, discussion is concerned with the development of the field of Romanticism since the 1980s, presented through both a review of scholarship and exemplary readings of well-known lyric poems. The latter, predominantly synchronic, presentation entails an argument for the analytical value of field theories of form—that is, frameworks drawn from early modern philosophy (Spinoza) and postclassical life- and physical sciences, especially models of self-organization. As an alternative to the external, retrospective perspective provided by, for example, Rita Felski in The Limits of Critique, it draws on the work of Martin Heidegger, Pierre Macherey, and the poet-critic J. H. Prynne to offer a conjunctural approach.

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Gauge Field Theory in Natural Geometric Language

10.1093/oso/9780198861492.001.0001 ◽

2020 ◽

Author(s):

Daniel Canarutto

Keyword(s):

Particle Physics ◽

Quantum Physics ◽

Brst Symmetry ◽

Natural Extension ◽

Integrated Approach ◽

Arbitrary Spin ◽

Field Theories ◽

Quantum Field Theories ◽

Standard View ◽

Spinor Bundle

This monograph addresses the need to clarify basic mathematical concepts at the crossroad between gravitation and quantum physics. Selected mathematical and theoretical topics are exposed within a not-too-short, integrated approach that exploits standard and non-standard notions in natural geometric language. The role of structure groups can be regarded as secondary even in the treatment of the gauge fields themselves. Two-spinors yield a partly original ‘minimal geometric data’ approach to Einstein-Cartan-Maxwell-Dirac fields. The gravitational field is jointly represented by a spinor connection and by a soldering form (a ‘tetrad’) valued in a vector bundle naturally constructed from the assumed 2-spinor bundle. We give a presentation of electroweak theory that dispenses with group-related notions, and we introduce a non-standard, natural extension of it. Also within the 2-spinor approach we present: a non-standard view of gauge freedom; a first-order Lagrangian theory of fields with arbitrary spin; an original treatment of Lie derivatives of spinors and spinor connections. Furthermore we introduce an original formulation of Lagrangian field theories based on covariant differentials, which works in the classical and quantum field theories alike and simplifies calculations. We offer a precise mathematical approach to quantum bundles and quantum fields, including ghosts, BRST symmetry and anti-fields, treating the geometry of quantum bundles and their jet prolongations in terms Frölicher's notion of smoothness. We propose an approach to quantum particle physics based on the notion of detector, and illustrate the basic scattering computations in that context.

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