## How is Quantum Field Theory Possible?Quantum field theory (QFT) combines quantum mechanics with Einstein's special theory of relativity and underlies elementary particle physics. This book presents a philosophical analysis of QFT. It is the first treatise in which the philosophies of space-time, quantum phenomena, and particle interactions are encompassed in a unified framework. Describing the physics in nontechnical terms, and schematically illustrating complex ideas, the book also serves as an introduction to fundamental physical theories. The philosophical interpretation both upholds the reality of the quantum world and acknowledges the irreducible cognitive elements in its representation. The interpretation is based on an analysis of our ways of thinking as the are embedded in the logical structure of QFT. The author argues that philosophical categories are significant only if they play active and essential roles in our knowledge and hence constitute part of the theories in actual use. Thus she regards physical theories as primary, extracts their categorical structure, and uses it to rethink key philosophical questions. Among the questions this book tries to answer are: What are the quantum properties independent of measurements? How do we refer to individual things in a continuous field? How do theories relate to objects? What are the general conditions of the world and of our ways of thinking that make possible our knowledge of the microscopic realm, which is so intangible and counterintuitive? As a penetrating analysis of vital themes in contemporary science, the book will engage the interest of students and professionals in physics and philosophy alike. |

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### Contents

Introduction | 3 |

2 The Categorical Framework of Objective Knowledge | 11 |

Nonrelativistic quantum mechanics | 16 |

4 The Quantum Measurement Problem | 22 |

Relativity and symmetry | 26 |

6 Symmetries in Physics | 32 |

7 The Principles of Relativity and Local Symmetry | 38 |

Quantum field theory | 43 |

21 The Referential Structure of Field Theory | 152 |

Field Quanta | 157 |

Quantum MultipleParticle Systems | 160 |

Explicit relations and the causal order interacting fields | 166 |

25 Permanence Endurance and the Concepts of Time | 169 |

26 How are Regular Successions of Events Possible? | 175 |

Phase and Potential | 183 |

Connection and Parallel Transport | 187 |

9 Fields Quantum Fields and Field Quanta | 47 |

10 Interacting Fields and Gauge Field Theories | 54 |

Object of experiences quantum stateobservablesstatistics | 61 |

12 The Form of Observation and the Reality of Quantum States | 70 |

Eigenvalue and Probability | 78 |

Observables | 85 |

15 The General Concept of Objects in Physical Theories | 89 |

16 The Illusion of the Observer | 104 |

17 The mentalism of YesNo Experiments | 113 |

The event structure and the spatiotemporal structure local fields | 119 |

Events or Local Fields | 122 |

20 The Basic SpatioTemporal Structure of the Physical World | 133 |

Renormalization | 189 |

Epilogue | 194 |

Measure and probability quantity quality modality | 197 |

Individual and Collective Qualities | 203 |

A3 Individual Statistical and Probabilistic Statements | 206 |

Fiber bundle and interaction dynamics | 214 |

The cosmic and the microscopic an application | 223 |

NOTES | 229 |

265 | |

273 | |

### Common terms and phrases

absolute abstract amplitude argued Born postulate called causal characteristics classical mechanics complex conceptual structure conventional coordinate systems curve defined definite differentiable distinction dynamical eigenstates eigenvalues Einstein electromagnetic field elements empirical entities equation explicit relation fiber bundle formal framework function fundamental G-orbit gauge field theories geometry global Hilbert space idea identity independent individual interaction field interpretation invariant ip(x Kant kind Lagrangian Leibniz local symmetry logical magnitudes manifold mathematical matter field meaning metric metric tensor momentum notion objective world observable operators parameter particles phase philosophical physical significance physical theories physicists Poincare group position possible potential predicates primitive principal fiber bundle principle probability problem property type qualities quantity quantum field theory quantum mechanics quantum system quantum theories real numbers representations represented sense space-time spatial spatio-temporal structure special relativity specific spin statements statistical substantival substantive symmetry group tangent space temporal things tion variables various vector