From Osher Doctorow
The Quantum Lagrangian Densities from which elementary
particle masses are read off form additive scalar equations
with the slight complication that although the masses are
constant (or phase constant?) coefficients, the scalar
invariant variables are products of tensors or vectors or
variable scalars. The covariant and contravariant indices
"cancel" (balance) each other completely, thereby forming
scalar invariants.
The fact that they are scalar invariants suggests that they
are not products of observables or observable representa-
tions. Jacek Dobaczewski of Warsaw University Poland
in "Interactions, symmetry breaking, and effective fields
from quarks to nuclei (a primer in nuclear theory)," 2006-
05-11, www.fuw.edu.pl/~dobaczew/maub-42w/node9.html,
describes in fact how the terms of both the QED and QCD
Lagrangians are in various combinations Lorentz forces
or source terms in Maxwell equations corresponding to
electron current J^u or kinetic energy or other Lagrangian
densities respectively, etc.
The eminent Algebraic Physicist Rudolf Haag of Germany
generally has disliked Lagrangians and preferred Hamiltonian
or generalized Hamiltonian type structures, I think partly
because of intuitive product difficulties like the ones above.
However, Haag's statement that he "doesn't understand"
Lagrangians, taken in the context of this thread, suggests
that it might be wise to look for "non-standard" explanations
of things that we don't understand.
Osher Doctorow
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