Particles before symmetry

Abstract

The Standard Model of particle physics is standardly formulated in terms of principal fibre bundles and their associated representations -- what may be called a symmetry-first approach. This paper develops an alternative geometry-first formulation in which the fundamental objects are Hermitian vector bundles equipped with compatible covariant derivatives, and symmetry groups arise as automorphism groups rather than being postulated. Working entirely in this framework, I give new derivations of two central mechanisms of the Standard Model. First, the Higgs mechanism: mass acquisition for gauge bosons is identified with the extrinsic curvature of a sub-bundle singled out by the Higgs vacuum, requiring no appeal to symmetry breaking, Goldstone's theorem, or gauge fixing. Second, the Yukawa mechanism: fermion mass terms are constructed as fibrewise contractions determined by the inner-product and orientation structures of the fundamental bundles, eliminating a centraliser ambiguity that arises in the standard representation-theoretic treatment. I also show that charge quantisation follows from the discrete algebraic structure of tensor powers of the fundamental line bundle -- a derivation that applies even when the relevant automorphism group is non-compact. Finally, I identify the structural conditions under which the symmetry-first and geometry-first formulations are genuinely equivalent, showing that the Standard Model satisfies these conditions but that theories based on exceptional Lie groups do not.