Abstract
We show that the perturbative expansion of general gauge theories can be expressed in terms of gauge invariant variables to all orders in perturbations. In this we generalize techniques developed in gauge invariant cosmological perturbation theory, using Bardeen variables, by interpreting the passing over to gauge invariant fields as a homotopy transfer of the strongly homotopy Lie algebras encoding the gauge theory. This is illustrated for Yang-Mills theory, gravity on flat and cosmological backgrounds and for the massless sector of closed string theory. The perturbation lemma yields an algorithmic procedure to determine the higher corrections of the gauge invariant variables and the action in terms of these.
Highlights
Philosophically this seems to be quite different from fixing a gauge, our results establish an operational equivalence with gauge fixing
In this we generalize techniques developed in gauge invariant cosmological perturbation theory, using Bardeen variables, by interpreting the passing over to gauge invariant fields as a homotopy transfer of the strongly homotopy Lie algebras encoding the gauge theory
While a loss of manifest Lorentz invariance may be too much to ask for in particle physics applications, in cosmology the situation is different: there is a preferred time, so that the space/time split needed for the definition of Bardeen variables respects the symmetries of the FLRW backgrounds, making these variables ideally suited for cosmological perturbation theory
Summary
We illustrate the general approach for two simple theories: Maxwell’s theory and gravity linearized about flat space. We explain the formulation of these theories in terms of chain complexes, introduce gauge invariant variables and establish the notion of homotopy transfer
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