## Conceptual Developments of 20th Century Field TheoriesThis book gives a broad synthesis of conceptual developments of twentieth-century field theories, from the general theory of relativity to quantum field theory and gauge theory. The author gives a historico-critical exposition of the conceptual foundations of the theories revealing a pattern to the evolution of these conceptions. Theoretical physicists and students of theoretical physics will find in this book an account of the foundational problems of their discipline that will help them understand the internal logic and dynamics of their subject. In addition the book will provide professional historians and philosophers of science, and especially philosophers of physics, with a conceptual basis for further historical, cultural and sociological analysis of the theories discussed. The book also contains much material for philosophical (metaphysical, methodological and semantical) reflection. Finally, the scientifically qualified general reader will find in this book a deeper analysis of contemporary conceptions of the physical world than can be found in popular accounts of the subject. |

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### Contents

Introduction | 1 |

Metaphysics | 5 |

Causality | 7 |

Ontology | 10 |

History and the history of science | 14 |

An outline of the main story | 15 |

The rise of classical field theory | 24 |

The continuous medium | 27 |

Interaction | 177 |

Renormalization | 185 |

The quantum field programme QFP | 210 |

Failed attempts | 212 |

Various attitudes toward renormalizability | 214 |

The axiomatic approach | 217 |

The Smatrix theory | 220 |

The PCAC hypothesis and current algebra | 229 |

The mechanical ether field theory | 30 |

The electromagnetic field theory | 40 |

The geometrical programme for fundamental interactions | 45 |

Einsteins route to the gravitational field | 47 |

Guiding ideas | 48 |

The special theory of relativity STR | 53 |

The geometrical interpretation of STR | 58 |

The introduction of gravitational fields the principle of equivalence | 60 |

The general theory of relativity GTR | 65 |

The field and geometry | 66 |

The field and spacetime general covariance | 69 |

Matter versus spacetime and the field Machs principle | 74 |

The consistency of GTR the genesis of relativistic cosmology | 82 |

The geometrical programme GP | 90 |

The geometrical programme strong and weak versions | 99 |

Further developments | 103 |

Topological investigations singularities horizons and black holes | 112 |

The quantum field programme for fundamental interactions | 123 |

The rise of quantum theory | 125 |

The quantization of radiation | 128 |

The birth of matrix mechanics | 133 |

The duality of matter individuality and quantum statistics | 136 |

The birth of wave mechanics | 138 |

Uncertainty and complementarity | 139 |

The formation of the conceptual foundations of quantum field theory | 144 |

Interpretations of the wave function | 145 |

Quantization | 152 |

The quantization of fields | 158 |

The vacuum | 173 |

Anomalies | 246 |

The renormalization group | 255 |

Swings of the pendulum | 261 |

The gauge field programme for fundamental interactions | 269 |

The route to gauge fields | 271 |

The gauge principle of fixing forms of interactions | 273 |

Early attempts | 275 |

The formation of the conceptual foundations of gauge field theories | 280 |

Mechanisms for shortrange interactions II asymptotic freedom | 290 |

Renormalizability | 296 |

Global features | 305 |

Open questions | 310 |

The gauge field programme GFP | 320 |

Further extensions | 327 |

GFP as a synthesis of GP and QFP | 332 |

Stagnation and a new direction effective field theories | 339 |

Ontological synthesis and scientific realism | 355 |

Frameworks opposed to the incommensurability thesis | 358 |

Structural properties of ontologies | 359 |

Conceptual revolutions via ontological synthesis | 362 |

Conceptual revolutions and scientific realism | 366 |

Conceptual revolutions and scientific rationality | 368 |

The rise of intrinsic local and dynamic geometry | 371 |

Homotopy classes and homotopy groups | 375 |

Bibliography | 377 |

420 | |

426 | |

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### Common terms and phrases

assumption asymptotic atom axial charge classical concept coupling covariant current algebra cutoff Dirac divergence dynamical effects Einstein electrodynamics electromagnetic field electron energy entities ether existence fermion Feynman field equations field programme field theory finite force formulation framework fundamental fundamental interactions gauge field gauge invariance gauge theory Gell-Mann geometrical structures geometry gravitational field hadrons Heisenberg hypothesis idea inertial interpretation isospin Lagrangian laws Lorentz Mach's mass massless mathematical matter meson metric momentum motion non-Abelian gauge theories non-renormalizable observable ontology parameters PCAC phenomena physical reality physicists pion Poincare potential principle properties quantization quantum field quantum mechanics quantum theory quarks radiation relations relativistic relativity renormalizability renormalization group S-matrix scale invariance Schrodinger Schwinger self-energy singularity solution space spacetime strong interactions structures of spacetime suggested tensor theoretical tion transformation vacuum vector Veltman wave function weak interactions Yang-Mills theory