Abstract
We provide a new formulation of non-relativistic diffeomorphism invariance. It is generated by localising the usual global Galilean symmetry. The correspondence with the type of diffeomorphism invariant models currently in vogue in the theory of fractional quantum Hall effect has been discussed. Our construction is shown to open up a general approach of model building in theoretical condensed matter physics. Also, this formulation has the capacity of obtaining Newton–Cartan geometry from the gauge procedure.
Highlights
There has been a spate of papers in the literature [1, 2, 3, 4] which use the non relativistic diffeomorphism invariance to analyse the motion of two dimensional trapped electrons which is directly connected with the theory of Fractional Quantum Hall Effect (FQHE)
One has to consider the general form (42) as the effective 3-d diffeomorhism invariant theory if one adopts the approach of constructing the nonrelativistic diffeomorphism invariant model by systematic localisation of Galilean symmetry
We have discussed a method of localisation of the global Galilean invariance of a general field theoretic model
Summary
There has been a spate of papers in the literature [1, 2, 3, 4] which use the non relativistic diffeomorphism invariance to analyse the motion of two dimensional trapped electrons which is directly connected with the theory of Fractional Quantum Hall Effect (FQHE). In these theories gauge invariance and nonrelativistic diffeomorphism invariances are introduced separately It would be very nice if these symmetries emerge systematically from some basic principles. The starting point is a nonrelativistic field theory invariant under global Galilean transformations with constant values of the translation, rotation and boost parameters. Anticipating the emergence of nonrelativistic diffeomorphism invariance in space we construct a set of coordinate axis at every spatial point which are trivially connected with the global coordinate system. This connection is subsequently shown to be non trivial. Apart from restoring Galilean invariance this localisation, subject to a further restriction, introduces diffeomorphism in 3-d space as we shall see
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