*Thomas Ryckman*

- Published in print:
- 2005
- Published Online:
- April 2005
- ISBN:
- 9780195177176
- eISBN:
- 9780199835324
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195177177.003.0006
- Subject:
- Philosophy, Philosophy of Science

It is shown how Weyl intertwined phenomenological analysis and mathematical construction in building the foundation of his “pure infinitesimal geometry” underlying gravitation and electromagnetism. ...
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It is shown how Weyl intertwined phenomenological analysis and mathematical construction in building the foundation of his “pure infinitesimal geometry” underlying gravitation and electromagnetism. In response to the Einstein-Pauli objection, Weyl put forth a second version of his theory, arguing on various non-empirical grounds for the conceptual superiority of his gauge-theoretic approach to general relativity. Speculation is made regarding Weyl’s philosophical reasons for opposing Élie Cartan’s “moving frame” generalization of Weyl’s notion of an affine connection, and it is suggested that the basic approach of Weyl’s transcendental phenomenological foundation of differential geometry can be accommodated within the modern fiber bundle formulation of gauge field theories.Less

It is shown how Weyl intertwined phenomenological analysis and mathematical construction in building the foundation of his “pure infinitesimal geometry” underlying gravitation and electromagnetism. In response to the Einstein-Pauli objection, Weyl put forth a second version of his theory, arguing on various non-empirical grounds for the conceptual superiority of his gauge-theoretic approach to general relativity. Speculation is made regarding Weyl’s philosophical reasons for opposing Élie Cartan’s “moving frame” generalization of Weyl’s notion of an affine connection, and it is suggested that the basic approach of Weyl’s transcendental phenomenological foundation of differential geometry can be accommodated within the modern fiber bundle formulation of gauge field theories.

*Charles P. Enz*

- Published in print:
- 2002
- Published Online:
- January 2010
- ISBN:
- 9780198564799
- eISBN:
- 9780191713835
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198564799.003.0011
- Subject:
- Physics, History of Physics

This chapter begins with a description of Pauli’s letters to Jung expressing his dissatisfaction with the science enterprise. It then details his vision of gauge field theory, neutrinos, and his ...
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This chapter begins with a description of Pauli’s letters to Jung expressing his dissatisfaction with the science enterprise. It then details his vision of gauge field theory, neutrinos, and his election as member of the Swedish Academy of Sciences as successor to Albert Einstein in 1955.Less

This chapter begins with a description of Pauli’s letters to Jung expressing his dissatisfaction with the science enterprise. It then details his vision of gauge field theory, neutrinos, and his election as member of the Swedish Academy of Sciences as successor to Albert Einstein in 1955.

*Daniel Canarutto*

- Published in print:
- 2020
- Published Online:
- December 2020
- ISBN:
- 9780198861492
- eISBN:
- 9780191894374
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198861492.003.0005
- Subject:
- Mathematics, Applied Mathematics, Mathematical Physics

After a sketch of Lagrangian field theory on jet bundles, the notion of a gauge field is introduced as a section of an affine bundle which is naturally constructed without any involvement with ...
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After a sketch of Lagrangian field theory on jet bundles, the notion of a gauge field is introduced as a section of an affine bundle which is naturally constructed without any involvement with structure groups. An original approach to gauge field theory in terms of covariant differentials (alternative to the jet bundle approach) is then developed, and the adaptations needed in order to deal with general theories are laid out. A careful exposition of the replacement principle allows comparisons with approaches commonly found in the literature.Less

After a sketch of Lagrangian field theory on jet bundles, the notion of a gauge field is introduced as a section of an affine bundle which is naturally constructed without any involvement with structure groups. An original approach to gauge field theory in terms of covariant differentials (alternative to the jet bundle approach) is then developed, and the adaptations needed in order to deal with general theories are laid out. A careful exposition of the replacement principle allows comparisons with approaches commonly found in the literature.

*Daniel Canarutto*

- Published in print:
- 2020
- Published Online:
- December 2020
- ISBN:
- 9780198861492
- eISBN:
- 9780191894374
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198861492.001.0001
- Subject:
- Mathematics, Applied Mathematics, Mathematical Physics

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 ...
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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.Less

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.