Related papers: E6Tensors: A Mathematica Package for E6 Tensors
We perform a complete analytical reduction of general one-loop Feynman integrals with five and six external legs for tensors up to rank R=3 and 4, respectively. An elegant formalism with extensive use of signed minors is developed for the…
In this paper we show how relativistic tensor dynamics and relativistic electrodynamics can be formulated in a biquaternion tensor language. The treatment is restricted to mathematical physics, known facts as the Lorentz Force Law and the…
Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes.…
Complicated mathematical equations involving products of tensors with permutation symmetries, frequently encountered in fields such as general relativity and quantum chemistry (e.g., equations in high-order coupled cluster theories),…
We study supersymmetric Sp(2N) gauge theories with matter in the antisymmetric tensor representation and F fundamentals. For F=6 we solve the theory exactly in terms of confined degrees of freedom and a superpotential. By adding mass terms…
Tensors are multiway arrays of data, and transverse operators are the operators that change the frame of reference. We develop the spectral theory of transverse tensor operators and apply it to problems closely related to classifying…
A tensor is a multidimensional array of numbers that can be used to store data, encode a computational relation and represent quantum entanglement. In this sense a tensor can be viewed as valuable resource whose transformation can lead to…
Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or…
A purely algebraic construction of super-energy tensors for arbitrary fields is presented in any dimensions. These tensors have good mathematical and physical properties, and they can be used in any theory having as basic arena an…
The system of tensor equations (TEs) has received much considerable attention in the recent literature. In this paper, we consider a class of generalized tensor equations (GTEs). An important difference between GTEs and TEs is that GTEs can…
We develop a method for finding the independent invariant tensors of a gauge theory. Our method uses a theorem relating invariant tensors and constant configurations in field space. We apply our method to an $SU(3)$ gauge theory with matter…
In this paper, we review some general formulations of exact renormalisation group equations and loop equations for tensor models and tensorial group field theories. We illustrate the use of these equations in the derivation of the leading…
Tensors play a pivotal role in the realms of science and engineering, particularly in the realms of data analysis, machine learning, and computational mathematics. The process of unfolding a tensor into matrices, commonly known as tensor…
Recently, many structured tensors are defined and their properties are discussed in the literature. In this paper, we introduce a new class of structured tensors, called exceptionally regular tensor, which is relevant to the tensor…
We provide explicit expressions of ABCD tensors for the most classical classes of spectral curves. And we discuss algorithmic implementation of Topological Recursion.
We present an index-based tensorial formulation for computing eigenvalues of charge operators acting on arbitrary tensor representations of unitary gauge groups. The construction follows directly from the action of Cartan generators on…
We describe generalizations of the manifestly E_{6(6)} covariant formulation of five-dimensional gauged maximal supergravity with regard to the structure of the vector and tensor fields. We indicate how the group-theoretical structures that…
The theory of first strain gradient elasticity (SGE) is widely used to model size and non-local effects observed in materials and structures. For a material whose microstructure is centrosymmetric, SGE is characterized by a sixth-order…
An algebraic representation of the Turing machines is given, where the configurations of Turing machines are represented by 4 order tensors, and the transition functions by 8 order tensors. Two types of tensor product are defined, one is to…
We give an introduction to the theory and to some applications of eigenvectors of tensors (in other words, invariant one-dimensional subspaces of homogeneous polynomial maps), including a review of some concepts that are useful for their…