## Physics from SymmetryThis is a textbook that derives the fundamental theories of physics from symmetry. It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived. As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations. |

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### Contents

2 | |

3 | |

2
Special Relativity | 11 |

Part II
Symmetry Tools | 23 |

3
Lie Group Theory | 24 |

4
The Framework | 91 |

Part III The Equations of Nature | 111 |

5
Measuring Nature | 112 |

10
Classical Mechanics | 227 |

11
Electrodynamics | 233 |

12
Gravity | 239 |

13
Closing Words | 245 |

Part V Appendices | 246 |

A
Vector calculus | 249 |

B
Calculus | 256 |

C
Linear Algebra | 267 |

6
Free Theory | 117 |

7
Interaction Theory | 127 |

Part IV Applications | 171 |

8
Quantum Mechanics | 172 |

9
Quantum Field Theory | 205 |

D Additional Mathematical
Notions | 271 |

273 | |

276 | |

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### Common terms and phrases

1st edition analogous angular momentum appendix arbitrary basis boost bosons called chapter charge conjugation chiral components compute conserved quantity constant coordinate system corresponding cos(p defined definition denotes derived in Sec describe Dirac equation Dirac spinor doublet eigenstate eigenvalues eigenvectors electron energy equation of motion example exponential free spin function Hamiltonian Hermitian Higgs interaction internal symmetry irreducible representations ISBN isospin Lagrangian last section Lie algebra Lie group linear Lorentz group Lorentz invariant Lorentz transformations mass terms massless mathematical matrix means measurement Minkowski notation object operator parity transformations photon Physics from Symmetry Poincare group quantum field theory quantum mechanics quarks quaternions rewrite right-chiral spinor rotation sin(x solution spacetime special relativity spin 1 fields spin 12 Take note tensor tion transforming according Undergraduate Lecture Notes unit complex numbers vector space Weyl spinor write x-axis z-axis zero