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We present a general algorithm constructing a discretization of a classical field theory from a Lagrangian. We prove a new discrete Noether theorem relating symmetries to conservation laws and an energy conservation theorem not based on any…
We calculate the energy-momentum tensor due to electromagnetic vacuum fluctuations between two parallel hyperplanes in more than four dimensions, considering both metallic and MIT boundary conditions. Using the axial gauge, the problem can…
We complete our study of the relativistic spatial distributions of the energy-momentum tensor inside polarized nucleons within the quantum phase-space formalism. In the present work, we focus on the components of the energy-momentum tensor…
A classical model of a stable particle of finite size is studied. The model parameters can be chosen such that the described particle has the mass and radius of a proton. Using the energy-momentum tensor (EMT), we show how the presence of…
We develop further the effective fluid theory of stationary branes. This formalism applies to stationary blackfolds as well as to other equilibrium brane systems at finite temperature. The effective theory is described by a Lagrangian…
Maxwell's macroscopic equations combined with a generalized form of the Lorentz law of force are a complete and consistent set of equations. Not only are these five equations fully compatible with special relativity, they also conform with…
We prove a conjectured relation between the energy-momentum and the displacement norm of superconformal defects. The proof completes earlier results, and shows that supersymmetry identifies two natural notions of brane tension in Anti-de…
In General Relativity, the issue of defining the gravitational energy contained in a given spatial region is still unresolved, except for particular cases of localized objects where the asymptotic flatness holds for a given spacetime. In…
Brane models at low energy are described by an effective action involving gravity and two moduli fields associated with the brane positions. The scalar-tensor nature of the effective theory and the coupling to matter are explicitly spelt…
The kinematics of pre-Maxwell electrodynamics is examined and interpretations of these fields is found through an examination of the associated Lorentz force and the structure of the energy-momentum tensor.
Motivated by a special consideration in quantum measurement, we present a new improved energy-momentum tensor. The new tensor differs from the traditional canonical and symmetric ones, and can be derived as Nother current from a Lagrangian…
One has not any conventional energy-momentum conservation law in Lagrangian field theory, but relations involving different stress-energy-momentum tensors associated with different connections. It is not obvious how to choose the true…
We study braneworlds in six-dimensional Einstein-Gauss-Bonnet gravity. The Gauss-Bonnet term is crucial for the equations to be well-posed in six dimensions when non-trivial matter on the brane is included (the also involved induced gravity…
Differential conservation laws in Lagrangian field theory are usually related to symmetries of a Lagrangian density and are obtained if the Lie derivative of a Lagrangian density by a certain class of vector fields on a fiber bundle…
This paper is aimed to elaborate the problem of energy-momentum in General Relativity. In this connection, we use the prescriptions of Einstein, Landau-Lifshitz, Papapetrou and M\"{o}ller to compute the energy-momentum densities for two…
We discuss general properties of the conservation law associated with a local symmetry. Using Noether's theorem and a generalized Belinfante symmetrization procedure in 3+1 dimensions, a symmetric energy-momentum (pseudo) tensor for the…
This course provides a self contained introduction to the general theory of relativistic brane models, of the category that includes point particle, string, and membrane representations for phenomena that can be considered as being confined…
We analyze the general covariant energy-momentum tensor of the gravitational system in genreal five-dimensional cosmological brane-world models. Then through calculating this energy-momentum for the cosmological generalization of the…
We investigate the energy of a theory with a unit vector field (the "aether") coupled to gravity. Both the Weinberg and Einstein type energy-momentum pseudotensors are employed. In the linearized theory we find expressions for the energy…
Using the stress energy tensor, we establish some monotonicity formulae for vector bundle-valued p-forms satisfying the conservation law, provided that the base Riemannian (resp. K\"ahler) manifolds poss some real (resp. complex)…