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26333 results in Theoretical Physics and Mathematical Physics

Page 9 of 1317

  • 5 - Hidden Gauge Freedom

  • from Part I - Where the Model is Explained
  • Marco Fabbrichesi, Italian National Institute of Nuclear Physics
  • Book:
    The Standard Model
    Published online:
    22 January 2026
    Print publication:
    23 October 2025, pp 148-171

  • Summary

    It is time to face the elephant in the room. Beautiful though they are, the gauge bosons of the weak interactions are massless and cannot be the mediators of the weak interactions. They do not reproduce Fermi’s interaction at low energy. They make the weak interactions long range while they are most definitely not.

  • 12 - Measure-Theoretic Methods

  • from Part III - Mathematical Methods and Analytic Constructions
  • Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
  • Book:
    Causal Fermion Systems
    Published online:
    15 November 2025
    Print publication:
    23 October 2025, pp 215-242
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  • Summary

    The existence of minimizers is proven using measure-theoretic tools.

  • 5 - A Brief Introduction to Causal Fermion Systems

  • from Part II - Causal Fermion Systems: Fundamental Structures
  • Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
  • Book:
    Causal Fermion Systems
    Published online:
    15 November 2025
    Print publication:
    23 October 2025, pp 93-134
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  • Summary

    We define and explain the basic objects and structures of a causal fermion system.

  • 1 - Physical Preliminaries

  • from Part I - Physical and Mathematical Background
  • Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
  • Book:
    Causal Fermion Systems
    Published online:
    15 November 2025
    Print publication:
    23 October 2025, pp 3-20
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  • Summary

    We summarize some basics on quantum mechanics and relativity theory as needed in order to understand the physical content and context of the theory of causal fermion systems.

  • 14 - Energy Methods for the Linearized Field Equations

  • from Part III - Mathematical Methods and Analytic Constructions
  • Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
  • Book:
    Causal Fermion Systems
    Published online:
    15 November 2025
    Print publication:
    23 October 2025, pp 268-278
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  • Summary

    The initial-value problem for the linearized field equations is developed.

  • 4 - Spinors in Curved Spacetime

  • from Part I - Physical and Mathematical Background
  • Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
  • Book:
    Causal Fermion Systems
    Published online:
    15 November 2025
    Print publication:
    23 October 2025, pp 68-90
    • Chapter
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  • Summary

    A brief introduction to spinors in curved spacetime is given in a formulation as a U(2,2) gauge theory.

  • Appendix: - The Spin Coefficients

  • Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
  • Book:
    Causal Fermion Systems
    Published online:
    15 November 2025
    Print publication:
    23 October 2025, pp 388-390
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  • Summary

    The spin coefficients are computed in detail.

  • Subject Index

  • Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
  • Book:
    Causal Fermion Systems
    Published online:
    15 November 2025
    Print publication:
    23 October 2025, pp 402-407
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  • 22 - Connection to Quantum Field Theory

  • from Part IV - Applications and Outlook
  • Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
  • Book:
    Causal Fermion Systems
    Published online:
    15 November 2025
    Print publication:
    23 October 2025, pp 379-387
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  • Summary

    An outlook is given on how to get a connection between the causal action principle and the dynamics of quantum fields.

  • Part I - Physical and Mathematical Background

  • Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
  • Book:
    Causal Fermion Systems
    Published online:
    15 November 2025
    Print publication:
    23 October 2025, pp 1-2
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  • 8 - Quantum Chromodynamics at Work

  • from Part II - Where the Model is Put to Use
  • Marco Fabbrichesi, Italian National Institute of Nuclear Physics
  • Book:
    The Standard Model
    Published online:
    22 January 2026
    Print publication:
    23 October 2025, pp 247-284

  • Summary

    Strong interactions are, well, strong. You have hadrons interacting and breaking up into a huge number of other hadrons. It is hard to understand what is going on. Physicists stumbled along during the 1960s trying out many ideas (the key words here are current algebra, analytic S-matrix, Regge trajectories and string theory) without much real understanding.

  • 9 - Surface Layer Integrals and Conservation Laws

  • from Part II - Causal Fermion Systems: Fundamental Structures
  • Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
  • Book:
    Causal Fermion Systems
    Published online:
    15 November 2025
    Print publication:
    23 October 2025, pp 171-189
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  • Summary

    Surface layer integrals are introduced as an adaptation of surface integrals to causal fermion systems and causal variational principles. Conservation laws are derived and formulated in terms of surface layer integrals.

  • 17 - Methods of Scattering Theory

  • from Part III - Mathematical Methods and Analytic Constructions
  • Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
  • Book:
    Causal Fermion Systems
    Published online:
    15 November 2025
    Print publication:
    23 October 2025, pp 309-319
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  • Summary

    The mass oscillation property is proved in Minkowski space using methods of scattering theory.

  • 4 - Gauge Fields

  • from Part I - Where the Model is Explained
  • Marco Fabbrichesi, Italian National Institute of Nuclear Physics
  • Book:
    The Standard Model
    Published online:
    22 January 2026
    Print publication:
    23 October 2025, pp 123-147

  • Summary

    The Lagrangian for the charge and neutral currents of the Standard Model contains fermion fields, what we call matter – leptons and quarks – and their interaction with spin-1 fields. These spin-1 fields are the W-, Z- and γ-bosons. As will become clear as I proceed, these fields are at the very center of the definition of the Standard Model as a gauge theory.

  • 9 - Finding Things Out

  • from Part II - Where the Model is Put to Use
  • Marco Fabbrichesi, Italian National Institute of Nuclear Physics
  • Book:
    The Standard Model
    Published online:
    22 January 2026
    Print publication:
    23 October 2025, pp 285-308

  • Summary

    “Marvelous is the working of our world!” N. Gogol, Nevsky Prospect, 1835 Should this have been the first chapter? Where to start from in teaching the Standard Model? The data painfully collected by experiments are the basis of everything – but they would be mute were it not for our models and theories. On the other hand, it seems that our brain is not very good at working all by itself. It needs the gentle prodding of experimental data, of finding out how (real) things are. Without external inputs, our mind is easily led astray, going round in circles (often of narrower and narrower radius).

  • 16 - Fourier Methods

  • from Part III - Mathematical Methods and Analytic Constructions
  • Felix Finster, Universität Regensburg, Germany, Sebastian Kindermann, Comenius Gymnasium Deggendorf, Germany, Jan‐Hendrik Treude, Universität Konstanz, Germany
  • Book:
    Causal Fermion Systems
    Published online:
    15 November 2025
    Print publication:
    23 October 2025, pp 296-308
    • Chapter
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  • Summary

    Fourier methods for the analysis are developed and used for the analysis of the kernel of Green’s operators, the causal fundamental solution and the kernel of the fermionic projector.

Page 9 of 1317