Abstract
We study, using the example of general covariance, to what extent a would-be non-abelian extension of free field abelian gauge theory can be helped by a field redefinition; answer – not much! However, models resulting from dimensional reduction also include non-gauge fields needing to be integrated out, thereby offering a wider choice of redefinitions whose effects may indeed change the situation.
Highlights
We study, using the example of general covariance, to what extent a would-be non-abelian extension of free field abelian gauge theory can be helped by a field redefinition; answer – not much! models resulting from dimensional reduction include non-gauge fields needing to be integrated out, thereby offering a wider choice of redefinitions whose effects may change the situation
A pervasive feature in attempts to construct nonabelian gauge theories that are seen to be inconsistent is that the first – abelian invariant quadratic – action term exists, as does the cubic one, taken as the product “ J μ Aμ” of the conserved abelian invariant current and the putative gauge field, abelian invariant
We study a concrete and important case: a would-be Einstein action, say from dimensional reduction, where exactly this occurs; we will show that the action cannot generally be made consistent by the only valid procedure
Summary
We study, using the example of general covariance, to what extent a would-be non-abelian extension of free field abelian gauge theory can be helped by a field redefinition; answer – not much! models resulting from dimensional reduction include non-gauge fields needing to be integrated out, thereby offering a wider choice of redefinitions whose effects may change the situation. We study, using the example of general covariance, to what extent a would-be non-abelian extension of free field abelian gauge theory can be helped by a field redefinition; answer – not much!
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