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How mathematicians view physics
Posted:
Nov 2, 2013 3:26 AM


Conservation of angular momentum Space rotation symmetry
Conservation of energy (First law of thermodynamics) Time translation symmetry
Newton's 1st Law of Motion Conservation of momentum (space translation symmetry)
Newton's 2nd Law of Motion Definition of force
Newton's 3rd Law of Motion Conservation of momentum (space translation symmetry)
Second law of thermodynamics Statistical definition of the arrow of time
Special relativity Spacetime rotation symmetry
General relativity General covariance, LeibnizMach principle, principle of equivalence
Quantum time evolution equation (timedependent Schrödinger equation) Global gauge invariance
Quantum operator differential forms Global gauge invariance
Quantum operator commutation rules Global gauge invariance
Quantization of action Global gauge invariance
Quantization rules for angular momenta Global gauge invariance
Maxwell's equations of electromagnetism Local gauge invariance under U(1)
Quantum Lagrangians for particles in presence of electromagnetic field Local gauge invariance under U(1)
Conservation of electric charge Global gauge invariance under U(1)
Masslessness of photon Local gauge invariance under U(1)
Conservation of weak isospin Global gauge invariance under SU(2)
Electroweak Lagrangian Mixing of U(1) and S(2) local gauge symmetries (spontaneous symmetry breaking)
Conservation of color charge Global gauge invariance under SU(3)
Strong interaction Lagrangian Local gauge invariance under SU(3)
Masslessness of gluon Local gauge invariance under SU(3)
Structure of the vacuum (Higgs particles) Spontaneous symmetry breaking
Doublet structure of quarks and leptons Conservation of weak isospin (global gauge invariance under SU(2)
Masses of particles Higgs mechanism (spontaneous symmetry breaking)
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