A Mathematical Base for Fibre Bundle Formulation of Lagrangian Quantum Field Theory

Iliev, Bozhidar Z

doi:10.1063/1.3582756

Title: A Mathematical Base for Fibre Bundle Formulation of Lagrangian Quantum Field Theory

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Abstract

The paper contains a differential-geometric foundations for an attempt to formulate Lagrangian (canonical) quantum field theory on fibre bundles. In it the standard Hilbert space of quantum field theory is replace with a Hilbert bundle; the former playing a role of a (typical) fibre of the letter one. Suitable sections of that bundle replace the ordinary state vectors and the operators on the system's Hilbert space are transformed into morphisms of the same bundle. In particular, the field operators are mapped into corresponding field morphisms.

Authors:

Iliev, Bozhidar Z ^[1]

Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tzarigradsko chaussee, 1784 Sofia (Bulgaria)

Publication Date:: Thu Apr 07 00:00:00 EDT 2011

OSTI Identifier:: 21513181

Resource Type:: Journal Article

Journal Name:: AIP Conference Proceedings

Additional Journal Information:: Journal Volume: 1340; Journal Issue: 1; Conference: International workshop on complex structures, integrability and vector fields, Sofia (Bulgaria), 13-17 Sep 2010; Other Information: DOI: 10.1063/1.3582756; (c) 2011 American Institute of Physics; Journal ID: ISSN 0094-243X

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; FIBERS; FIELD OPERATORS; FUNCTIONAL ANALYSIS; HILBERT SPACE; LAGRANGIAN FIELD THEORY; LAGRANGIAN FUNCTION; PARTIAL DIFFERENTIAL EQUATIONS; QUANTUM FIELD THEORY; QUANTUM MECHANICS; BANACH SPACE; DIFFERENTIAL EQUATIONS; EQUATIONS; FIELD THEORIES; FUNCTIONS; MATHEMATICAL OPERATORS; MATHEMATICAL SPACE; MATHEMATICS; MECHANICS; QUANTUM OPERATORS; SPACE

Citation Formats


                    Iliev, Bozhidar Z. A Mathematical Base for Fibre Bundle Formulation of Lagrangian Quantum Field Theory.  United States: N. p., 2011. 
        Web.  doi:10.1063/1.3582756.

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                    Iliev, Bozhidar Z. A Mathematical Base for Fibre Bundle Formulation of Lagrangian Quantum Field Theory.  United States.  https://doi.org/10.1063/1.3582756

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                    Iliev, Bozhidar Z. 2011.  
        "A Mathematical Base for Fibre Bundle Formulation of Lagrangian Quantum Field Theory".  United States.  https://doi.org/10.1063/1.3582756.

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@article{osti_21513181,

  title        = {A Mathematical Base for Fibre Bundle Formulation of Lagrangian Quantum Field Theory},

  author       = {Iliev, Bozhidar Z},

  abstractNote = {The paper contains a differential-geometric foundations for an attempt to formulate Lagrangian (canonical) quantum field theory on fibre bundles. In it the standard Hilbert space of quantum field theory is replace with a Hilbert bundle; the former playing a role of a (typical) fibre of the letter one. Suitable sections of that bundle replace the ordinary state vectors and the operators on the system's Hilbert space are transformed into morphisms of the same bundle. In particular, the field operators are mapped into corresponding field morphisms.},

  doi          = {10.1063/1.3582756},

  url          = {https://www.osti.gov/biblio/21513181},
  journal      = {AIP Conference Proceedings},

  issn         = {0094-243X},

  number       = 1,

  volume       = 1340,

  place        = {United States},

  year         = {Thu Apr 07 00:00:00 EDT 2011},

  month        = {Thu Apr 07 00:00:00 EDT 2011}

}

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