The role of gauge invariance
in physics is analogous to an equivalence class in mathematics.
I think that the treatment of the scalar multiplet actions in the present work may contain clues to supergravity, both considering the extra gauge invariances
and the extra factors of [lambda] in the action.
Baranov, (Mis-)handling Gauge Invariance
in the Theory of the Quantum Hall Effect.
Tyutin, "Gauge invariance
in field theory and statistical physics in operator formalism," 1975, https://arxiv.org/abs/ 0812.0580.
Just the same situation comes about in the weak interaction , where the obstructive role of reference systems stimulates the appearance of auxiliary "principles" like gauge invariance
with its artificial group structure that can only explain the already known results of experiments rather than predict them.
This is a consequence of gauge invariance
of [W.sub.L] before symmetry breaking.
Thirdly, even if the first two points were met, physics does not admit local gauge invariance
for all predicates, but only for a very limited number, so it could not be the solution to the general philosophical problem.
In particular, if the couplings to up and down quarks are different the mediator does not couple to the left handed quark doublet but to its two components separately, thus breaking gauge invariance
. Similarly, the t-channel model of (10) is not gauge invariant unless the scalar mediator [[??].sup.i.sub.L] is charged and transforms as (2, -1/2) under SU[(2).sub.L] x U[(1).sub.Y].
Also, the lagrangian can still be completely massless (as in the Higgs scenario), preserving attractive features such as gauge invariance
that would be broken by explicit mass terms, the generation of mass being a secondary physical phenomenon.
In QED it has been known for quite a long time that manifest covariance and manifest gauge invariance
are competing aspects of a generating functional construction.
For example, in the Standard Model, due to its chiral nature, a Higgs field is introduced in order to manifest gauge invariance
. Once the Higgs field acquires a VEV the mass term only respects the symmetry of the resulting group which is U[(1).sub.EM].
The principle of local gauge invariance
is at the heart of standard model of particle physics, where there is a stunning degree of agreement between theory and experiment.