Concatenating Variational Principles and the Kinetic Stress-Energy-Momentum Tensor
We show how to "concatenate" variational principles over dierent 
bases into one over a single base, thereby providing a unied Lagrangian 
treatment of interacting systems. As an example we study a Klein{ 
Gordon eld interacting with a mesically charged particle. We employ 
our method to give a novel group-theoretic derivation of the kinetic 
stress-energy-momentum tensor density corresponding to the particle.
Stress-Energy-Momentum Tensors and the Belinfante-Rosenfeld Formula
We present a new method of constructing a stress-energy-momentum tensor 
for a classical field theory based on covariance considerations and Noether theory. 
The stress-energy-momentum tensor T ^μ 
_ν that we construct is defined using 
the (multi)momentum map associated to the spacetime diffeomorphism group. 
The tensor T ^μ 
_ν is uniquely determined as well as gauge-covariant, and depends 
only upon the divergence equivalence class of the Lagrangian. It satisfies 
a generalized version of the classical Belinfante-Rosenfeld formula, and hence 
naturally incorporates both the canonical stress-energy-momentum tensor and 
the “correction terms” that are necessary to make the latter well behaved. Furthermore, 
in the presence of a metric on spacetime, our T^(μν) coincides with the 
Hilbert tensor and hence is automatically symmetric.
Natural bundles have finite order
LET A. DENOTE the category of n-dimensional smooth (= C”) manifolds, with smooth embeddings ‘as morphisms, and let 9 denote the category whose objects are smooth fiber bundles r: E+ B and whose morphisms are smooth bundle maps. (That is, a morphism of rr,: E, + B, to 7~~: Ez+Bz is a smooth map If: E, + E2 such that for each x E B, the fiber (EI)X = P,-‘(X) is mapped diffeomorphically onto the fiber (E,), over some point y = h(x) in Bz. The map h: B,+& is automatically smooth and we say that H COLV~S h.)