electroweak phase transition

Before the electroweak phase transition of the Universe, all weak bosons are massless just like the photons, and with the temperatures well above TeV, the Higgs-particle hasn’t given any mass to the charged leptons yet. Would there be a way of distinguishing electrons, muons and taus?

physics bonus question: In quantum mechanics, what property of the Hamiltonian operator is responsible for the conservation of probability?

maths bonus question: Can you show that \(\exp(A)\) is unitary if \(A\) is anti-Hermitean, \(A^+=-A\), where \(A^+\) is the complex-conjugated, transposed matrix \(A\)?