Speaker
Description
Within the physics literature, there are multiple definitions of the energy-momentum tensor for Lagrangian field theories. The most common expressions are the ``canonical'' Noether formula, Hilbert's definition in terms of metric tensor derivatives, and Belinfante/Rosenfeld's improvement procedure. These definitions are not generally equivalent, but converge to the same result in cases such as the Klein-Gordon Lagrangian. However, alterations of the scalar field Lagrangian can differentiate the results of the different methods. This suggests that the equivalences of some of these definitions are coincidences, emerging from being applied to simple Lagrangians. In this talk, we will discuss results related to general scalar field Lagrangians which depend on first and second derivatives of the fields, and how they can be used to help specify a particular energy-momentum tensor definition. Using methods found in the mathematics literature involving quasi-symmetries and how they affect the calculation of Noether currents, a method is presented that can resolve uniqueness issues when defining said conserved quantities, and is more general as it works in arbitrary coordinate systems and on manifolds with curvature. Additionally, constraints are placed on to what degree tracelessness of an energy-momentum tensor can imply conformal symmetry of the field theory.