Related papers: Hilbert's energy-momentum tensor extended
The requirements of conformal invariance for the two point function of the energy momentum tensor in the neighbourhood of a plane boundary are investigated, restricting the conformal group to those transformations leaving the boundary…
The canonical energy-momentum tensor is often considered as a purely academic object because of its gauge dependence. However, it has recently been realized that canonical quantities can in fact be defined in a gauge-invariant way provided…
Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives…
A new approach to analyze the properties of the energy-momentum tensor $T(z)$ of conformal field theories on generic Riemann surfaces (RS) is proposed. $T(z)$ is decomposed into $N$ components with different monodromy properties, where $N$…
We find the rules of the conformal transformation for the energetic quantities such as the Einstein energy-momentum complex, the Bergmann-Thomson angular momentum complex, the superenergy tensor, and the angular supermomentum tensor of…
We investigate stress-energy tensors constructed from the covariant derivatives of delta functions on a worldline. Since covariant derivatives are used all the components transform as tensors. We derive the dynamical equations for the…
We develop a variationally consistent mesoscopic extension of Cosserat elasticity motivated by the breakdown of compatibility in classical formulations. By admitting compatibility-breaking perturbations, the classical theory ceases to…
Following Kottler, \'E.Cartan, and van Dantzig, we formulate the Maxwell equations in a metric independent form in terms of the field strength $F=(E,B)$ and the excitation $H=({\cal D}, {\cal H})$. We assume a linear constitutive law…
In this paper we develop the Lagrangian and multisymplectic structures of the Heisenberg magnet (HM) model which are then used as the basis for geometric discretizations of HM. Despite a topological obstruction to the existence of a global…
The variational theory of the perfect fluid with an intrinsic hypermomentum is developed. The Lagrangian density of such fluid is stated and the equations of motion of the fluid and the evolution equation of the hypermomentum tensor are…
The 4-dimensionally covariant approach to multiconstituent Newtonian fluid dynamics presented in the preceding article of this series is developed by construction of the relevant 4-dimensional stress energy tensor whose conservation in the…
The usual prescription for constructing gauge-invariant Lagrangian is generalized to the case where a Lagrangian contains second derivatives of fields as well as first derivatives. Symmetric tensor fields in addition to the usual vector…
We associate determinant lines to objects of the extended abelian category built out of a von Neumann category with a trace. Using this we suggest constructions of the combinatorial and the analytic L^2 torsions which, unlike the work of…
In model building studies, it is important to check the energy conditions for the corresponding energy-momentum tensor determined by the gravitational field equations in order to single out physically reasonable models. In this process, one…
This is the first paper of a five part work in which we study the Lagrangian and Hamiltonian structure of classical field theories with constraints. Our goal is to explore some of the connections between initial value constraints and gauge…
A general affine connection has enough degrees of freedom to describe the classical gravitational and electromagnetic fields in the metric-affine formulation of gravity. The gravitational field is represented in the Lagrangian by the…
We examine the variational and conformal structures of higher order theories of gravity which are derived from a metric-connection Lagrangian that is an arbitrary function of the curvature invariants. We show that the constrained first…
The formulation of a dynamical theory of General Relativity, including matter, is viewed as a problem of coupling Einstein's theory of pure gravity, formulated as an action principle, to an independently chosen and well defined field theory…
In this proceeding, we review modified theories of gravity with a curvature-matter coupling between an arbitrary function of the scalar curvature and the Lagrangian density of matter. This explicit nonminimal coupling induces a…
We use a description based on differential forms to systematically explore the space of scalar-tensor theories of gravity. Within this formalism, we propose a basis for the scalar sector at the lowest order in derivatives of the field and…