Related papers: The universal 'energy' operator
Although the super-energy Bel-Robinson tensor gives a desirable gravitational energy-momentum in a small sphere region, the angular-momentum is vanishing. Intuitively, it should be non-zero. Our present work shows that indeed the angular…
We consider T(x), a tensor of arbitrary rank that is symmetric in all of its indices and conserved in the sense that the divergence on any one index vanishes. Our conjecture is that all integral moments of this tensor will vanish if the…
Potential functions can be used as generating potentials of relevant geometric structures for a Riemannian manifold such as the Riemannian metric and affine connections. We study wether this procedure can also be applied to tensors of rank…
We study an energy functional on the universal spinor bundle over a closed $n$-dimensional spin manifold $M$. The critical points of this functional, which is modelled on the total torsion functional of $G_2$-structures in seven dimensions,…
The main contribution of this note is to establish a framework to extend results of tensor functions over specific field to general field. As a consequence of this framework, we extend the existing work to more general settings: \emph{(1)}…
The tensor and exterior squares of a completely continuous non-negative linear operator $A$ acting in the ideal space $X(\Omega)$ are studied. The theorem representing the point spectrum (except, probably, zero) of the tensor square $A…
The exponent $\sigma(T)$ of a tensor $T\in\mathbb{F}^d\otimes\mathbb{F}^d\otimes\mathbb{F}^d$ over a field $\mathbb{F}$ captures the base of the exponential growth rate of the tensor rank of $T$ under Kronecker powers. Tensor exponents are…
We construct the energy-momentum tensor of the O(N) linear sigma model explicitly in the large N limit using the exact renormalization group (ERG) formalism. The energy-momentum tensor is obtained as a cutoff dependent functional of N…
Within the Lagrange formalism we show that the gauge invariant total energy-momentum tensor for gravitational interactions is zero. If the equations of motion are satisfied the energy tensor is conserved.
We consider the one-loop renormalization of dimension four composite operators and the energy-momentum tensor in noncommutative \phi^4 scalar field theory. Proper operator bases are constructed and it is proved that the bare composite…
Completely positive graphs have been employed to associate with completely positive matrices for characterizing the intrinsic zero patterns. As tensors have been widely recognized as a higher-order extension of matrices, the…
Here we present our actual point of view on the canonical superenergy tensors.
A tensor space is a vector space equipped with a finite collection of multilinear forms. The length of a tensor space is its length as a representation of its symmetry group. Infinite dimension tensor spaces of finite length are special,…
An $N = 1$ supersymmetric version of two dimensional dilaton gravity coupled to matter is considered. It is shown that the linear dilaton vacuum spontaneously breaks half the supersymmetries, leaving broken a linear combination of left and…
The question of which functions acting entrywise preserve positive semidefiniteness has a long history, beginning with the Schur product theorem [Crelle 1911], which implies that absolutely monotonic functions (i.e., power series with…
We consider the Dirac equation in flat Minkowski 3-space and rewrite it as the Maxwell equation in Minkowski 4-space with torsion. The torsion tensor is defined as the dual of the electromagnetic vector potential. Our model clearly…
Nonnegative tensor factorization has applications in statistics, computer vision, exploratory multiway data analysis and blind source separation. A symmetric nonnegative tensor, which has a symmetric nonnegative factorization, is called a…
A set of new tensors of purely geometric origin have been investigated, which form a hierarchy. A tensor of a lower rank plays the role of the potential for the tensor of one rank higher. The tensors have interesting mathematical and…
Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address…
We show a tensorial-computational way to find out conditions that must fulfil an m-rank tensor in arbitrary dimension in order to be algebraically the energy-momentum tensor of some field. We apply in this paper our method to three 2-rank…