Abstract
Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and lack of excitation of some degrees of freedom, of the Noether currents associated with physical symmetries leads to emergent gauge symmetries in specific situations. An example of a relativistic field theory of a vector field is worked out in detail in order to make explicit how this mechanism works and to clarify the physics behind it. The interplay of these ideas with well-known results of importance to the emergent gravity program, such as the Weinberg-Witten theorem, are discussed.
Highlights
Expect that this paradigm has chances of being feasible, though the difficulties to overcome cannot be underestimated [3]
For the sake of this introductory discussion, probably the most convenient way to stress the different nature of gauge and physical symmetries is the well-known feature that gauge symmetries indicate redundancies in the field-theoretical description of a given system, as it can be made explicit through the occurrence of first-class constraints in its Hamiltonian formulation
Working with particular theories has led us to consider a general definition of emergent gauge symmetries that might be applicable to a large class of systems
Summary
Local and global symmetries are classified quite intuitively by the form they are labeled. The classification of gauge and physical symmetries in terms of Noether charges is valid for both finite- and infinite-dimensional systems. Following these definitions, local symmetries are not necessarily gauge symmetries in field theory, as we show . The Noether current associated with a local symmetry (2.5), defined using a one-parameter group of transformations βθ with β ∈ R for a given function θ(x), is given by. Only the limiting case α = 0 leads in eq (2.9) to non-trivial charges, but these are the same charges obtained from the Noether current associated with the global symmetries (2.6), corresponding to the electric charge of the system. The Noether current (2.8) is trivial in the sense that it does not contain any physical information of the system which is not already contained in the Noether current (2.6) associated with global transformations
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