Related papers: The stress-energy tensor for biharmonic maps

We study the quantum stress tensor correlation function for a massless scalar field in a flat two-dimensional spacetime containing a moving mirror. We construct the correlation functions for right-moving and left-moving fluxes for an…

We give several construction methods and use them to produce many examples of proper biharmonic maps including biharmonic tori of any dimension in Euclidean spheres (Theorem 2.2, Corollaries 2.3, 2.4, and 2.6), biharmonic maps between…

We prove that multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard. Our list here includes: determining the feasibility of a system of bilinear equations, deciding whether a 3-tensor…

A variational derivative of a Lagrangian with regard to the metric tensor is used in classical field models to define Hilbert's energy-momentum tensor for a matter field. In solid-state physics, constitutive relationships between…

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…

Conformal harmonic maps from a 4-dimensional conformal manifold to a Riemannian manifold are maps satisfying a certain conformally invariant fourth order equation. We prove a general existence result for conformal harmonic maps, analogous…

Furthering the development of Da Lio-Gianocca-Rivi\`ere's Morse stability theory (arXiv:2212.03124) that was first applied to harmonic maps between manifolds and later extended to the case of Willmore immersions (arXiv:2306.04608-04609), we…

Based on the covariant variation formalism, two versions of the symmetric effective stress-energy tensor of the electromagnetic field in a dynamo-optically active relativistic media are reconstructed in the framework of the tetrad and…

We apply the energy-momentum tensor which is coordinate independent to calculate the energy content of the axisymmetric solutions. Our results are compared with what have been obtained before within the framework of Einstein general…

This paper presents a nonconforming finite element approximation of the space of symmetric tensors with square integrable divergence, on tetrahedral meshes. Used for stress approximation together with the full space of piecewise linear…

We present a comprehensive analysis of the implications of conformal invariance for 3-point functions of the stress-energy tensor, conserved currents and scalar operators in general dimension and in momentum space. Our starting point is a…

In this short pedagogical note we clarify some subtleties concerning the symmetries of the coefficients of a Riemann-Cartan connection and the symmetries of the coefficients of the contorsion tensor that has been a source of some confusion…

We analyze the renormalized stress-energy tensor (RSET) of a massless quantum scalar field in time-dependent gravitational backgrounds. Starting from its formal expression obtained within the covariant perturbative expansion to lowest order…

The Abraham--Minkowski momentum controversy is the outwardly visible symptom of an inconsistency in the use of the energy-momentum tensor in the case of a plane quasimonochromatic field in a simple linear dielectric. We show that the Gordon…

We consider two hypothesis testing problems for low-rank and high-dimensional tensor signals, namely the tensor signal alignment and tensor signal matching problems. These problems are challenging due to the high dimension of tensors and…

This note provides an explicit proof of the equivalence of the Belinfante's energy-momentum tensor and the metric energy-momentum tensor for general mixed tensor-spinor fields.

By considering Hadamard vacuum states, we first construct the two-point functions associated with Stueckelberg massive electromagnetism in de Sitter and anti-de Sitter spacetimes. Then, from the general formalism developed in [A. Belokogne…

Vacuum expectation value of the stress-energy-momentum tensor for scalar and spinor fields is obtainted on the homogeneous space with $G$-invariant metrics using the orbits of coadjoint representation of Lie group and the generalized…

We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel-Robinson type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a…

We use computational algorithms recently developed by us to study completely four index divergence free quadratic in Riemann tensor polynomials in GR. Some results are new and some other reproduce and/or correct known ones. The algorithms…