Re: Mass and strong interaction.

DW wrote:
> I am just curious whether we can trace the origin of
> mass back to the interaction of elementary particles.

Yes.

If you start a quantum field theory out with a Lagrangian that has no
mass terms, it will acquire such terms in the higher order radiative
corrections.

For fermions, for instance, labelling fermions as y' and y; gauge
bosons as B; and contractions by []; then the graph corresponding to
[y(u) y'(v)] [B(u) B(v)] e^2 y(v) y'(u)
gives you an effective mass term proportional to e^2.

In this context, it's of interest to note that for the Leptons, the
trace Tr(M_L) of the mass matrix M_L is, to a high degree of accuracy,
just
Tr(M_L) = v e^2
where v is the Higgs vacuum potential.

Scharf et. al. took the general idea one step further in the mid to
late 1990's. Implementing a 2nd quantized version of gauge invariance,
called perturbative gauge invariance:
[Q, T[exp(iA)]] = del_{nu} T[d_Q^{nu}(A(x)) exp(iA)]
with Q being an appropriately defined coboundary operator; they managed
in formulating a already-renormalized definition of the T[] operator
which when applied to the formal solution
S = T[exp(i H_I)]
starting from a general interactive Hamiltonian H_I, gives you (in the
case of a massive SU(2)xU(1) gauge theory) EXACTLY the right
constraints found in the Standard Model, and (as counter-terms) even
derives a Higgs field out of the blue with the right expression for the
potential.

Though their method starts out with a massive field in the initial
Lagrangian, I don't see any obstacle against removing it from the
initial Lagrangian and deriving it as one of the instances of a
universal Lagrangian which envelopes the standard model as one of its
instances.

.

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