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26231 results in Theoretical Physics and Mathematical Physics

Page 5 of 1312

  • 7 - The Euler–Lagrange Equations

  • 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 148-155
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  • Summary

    The Euler–Lagrange equations for causal variational principles are derived, and their general structure is discussed.

  • 15 - Functional Analytic Methods in Spacetime

  • 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 279-295
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  • Summary

    A functional analytic method is developed, which gives rise to a canonical decomposition of the Dirac solution space into two subspaces, even in a time-dependent situation.

  • Contents

  • 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 vii-xii
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  • 2 - Mathematical 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 21-58
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  • Summary

    We summarize some mathematical preliminaries that we believe are important for studying causal fermion systems.

  • 13 - Methods of Hyperbolic Partial Differential 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 243-267
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  • Summary

    The well-posedness of the Cauchy problem for linear symmetric hyperbolic systems is proven, and consequences are worked out.

  • 1 - What is This Book About?

  • Marco Fabbrichesi, Italian National Institute of Nuclear Physics
  • Book:
    The Standard Model
    Published online:
    22 January 2026
    Print publication:
    23 October 2025, pp 1-5

  • Summary

    The theory called the Standard Model represents the state of the art of our understanding of the physics of elementary particles and their interactions. It is, as explained in the following chapters, a gauge theory, that is, a theory in which the interactions among the matter constituents are determined by gauge invariance and carried by gauge bosons. Everything else in physics (except perhaps gravitational phenomena at very high energies), as well as everything in the Universe, from chemistry to biology, is but an application (admittedly, very convoluted in most cases) of this model.

  • 3 - Elements of Operator Theory

  • 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 59-67
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  • Summary

    We introduce some material from functional analysis that will be needed later in this book.

  • 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 91-92
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  • 10 - Positive Functionals

  • 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 190-198
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  • Summary

    Positive functionals arising from causal variational principles are derived and discussed.

  • 8 - The Linearized Field Equations

  • 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 156-170
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  • Summary

    The linearized field equations for causal variational principles are derived, and their general structure is discussed.

  • 10 - Things That Go Bump in the Night

  • 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 309-335

  • Summary

    Even though the physics of coupled two-state systems is something we learn about in a first class on quantum mechanics, it is still a fascinating subject and, as a matter of fact, important in the study of particle physics.

  • 6 - Strong Interactions

  • 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 172-214

  • Summary

    The strong interactions are described in the Standard Model by the gauge theory of the color group SU(3)c. Matter is made of “colored” quarks interacting through the exchange of gluons, the gauge fields associated with the color group. The theory is called QCD by analogy to QED, with the electric charge replaced by the color (chromo) charges.

  • Preface

  • 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 xiii-xiv
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  • 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 351-352
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Page 5 of 1312