Related papers: The first acquaintance with the tensor
We explore alternative formulations of the analogy between viable Horndeski gravity and Eckart's first-order thermodynamics. We single out a class of identifications for the effective stress-energy tensor of the scalar field fluid that,…
We consider the standard gauge theory of Poincar\'{e} group, realizing as a subgroup of $GL(5. R)$. The main problem of this theory was appearing of the fields connected with non-Lorentz symmetries, whose physical sense was unclear. In this…
This is an intorduction to some of the basic methods and results of dense matter physics.It is aimed at readers interested in astrophysical and physical applications.
Eigenvectors of tensors, as studied recently in numerical multilinear algebra, correspond to fixed points of self-maps of a projective space. We determine the number of eigenvectors and eigenvalues of a generic tensor, and we show that the…
A theory of gravity with torsion is examined in which the torsion tensor is constructed from the exterior derivative of an antisymmetric rank two potential plus the dual of the gradient of a scalar field. Field equations for the theory are…
Lecture notes to a one-term course on operator algebras and their application in physics. Very brief and basic introduction to the subject of Banach- and C-star algebras complemented with their appearance in physics. The course is intended…
The content of this paper can be roughly organized into a three-level hierarchy of generality. At the first, most general level, we introduce a new language which allows us to express various categorical structures in a systematic and…
This is the first part in a two-part series of papers constructing a unitary structure for the modular tensor category (MTC) associated to a unitary rational vertex operator algebra (VOA).
Lichnerowicz's algebra of differential geometric operators acting on symmetric tensors can be obtained from generalized geodesic motion of an observer carrying a complex tangent vector. This relation is based upon quantizing the classical…
These lectures provide an introduction to the physics of particle colliders. Topics covered include a quantitative examination of the design and operational parameters of Large Hadron Collider, kinematics and observables at colliders, such…
We provide a brief overview of tensor models and group field theories, focusing on their main common features. Both frameworks arose in the context of quantum gravity research, and can be understood as higher-dimensional generalizations of…
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
Tensor type data are becoming important recently in various application fields. We determine a rank of a tensor T so that A+T is diagonalizable for a given 3-tensor A with 2 slices over the complex and real number field.
This friendly introduction to tropical geometry is meant to be accessible to first year students in mathematics. The topics discussed here are basic tropical algebra, tropical plane curves, some tropical intersections, and Viro's…
The systematic derivation of constants of the motion, based on Killing tensors and the gauge covariant approach, is outlined. Quantum dots are shown to support second-, third- and fourth-rank Killing tensors.
We demonstrated using an elementary method that the inertia tensor of a material point and the cross product of two vectors were only possible in a three or seven dimensional space. The representation matrix of the cross product in the…
Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…
[Taken from the "README" in the book] My goal with this book is to provide some kind of bridge for mathematics between the high-school-level and college-level for physics students. From my perspective, our job as physicists is to observe…
The current paper presents a new approach to multilinear dynamical systems analysis and control. The approach is based upon recent developments in tensor decompositions and a newly defined algebra of circulants. In particular, it is shown…
This educational article highlights the geometric and algebraic complexities that distinguish tensors from matrices, to supplement coverage in advanced courses on linear algebra, matrix analysis, and tensor decompositions. Using the case of…