Abstract
We discuss diffeomorphism and gauge invariant theories in three dimensions motivated by the fact that some models of interest do not have a suitable action description yet. The construction is based on a canonical representation of symmetry generators and on building of the corresponding canonical action. We obtain a class of theories whose number of local degrees of freedom depends on the dimension of the gauge group and the number of the independent constraints. By choosing the latter, we focus on three special cases, starting with a theory with maximal local number of degrees of freedom and finishing with a theory with zero degrees of freedom (Chern-Simons).
Highlights
Building a suitable theory which would provide, through the principle of least action, a dynamical description of a physical system of interest, has been a long-standing problem in theoretical physics
Examples show that there are still many open problems in finding an appropriate action of gravity theories. This motivated us to employ a systematic way to construct a non-Abelian gauge theory which is invariant under general coordinate transformations, in pursuit of a simple description of an action invariant under two sets of local symmetries. It is well-known that gravity can be obtained as a Poincaregauge theory, where the fundamental field belongs to the representation of the Poincaregauge group
The main challenge of our method is to find a canonical representation of the constraints in terms of the canonical variables, a connection AaμðxÞ which transforms in the adjoint representation of the gauge group and the corresponding canonical momenta πμaðxÞ
Summary
Building a suitable theory which would provide, through the principle of least action, a dynamical description of a physical system of interest, has been a long-standing problem in theoretical physics. Examples show that there are still many open problems in finding an appropriate action of (relativistic or nonrelativistic) gravity theories This motivated us to employ a systematic way to construct a non-Abelian gauge theory which is invariant under general coordinate transformations, in pursuit of a simple description of an (effective) action invariant under two sets of local symmetries. With this respect, it is well-known that gravity can be obtained as a Poincaregauge theory, where the fundamental field belongs to the representation of the Poincaregauge group (see, for example, the textbook [13], and the references therein). V, pointing out open problems and possible future lines of research
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