Related papers: Matrices de commutation tensorielle: de l'\'equati…
We define and study the probability current and the Hamiltonian operator for a fully general set of Dirac matrices in a flat spacetime with affine coordinates, by using the Bargmann-Pauli hermitizing matrix. We find that with some weak…
A binary tensor consists of $2^n$ entries arranged into hypercube format $2 \times 2 \times \cdots \times 2$. There are $n$ ways to flatten such a tensor into a matrix of size $2 \times 2^{n-1}$. For each flattening, $M$, we take the…
Properties of six-component electromagnetic field solutions of a matrix form of the Maxwell equations, analogous to the four-component solutions of the Dirac equation, are described. It is shown that the six-component equation, including…
We develop a formalism to treat higher order (nonlinear) metric perturbations of the Kerr spacetime in a Teukolsky framework. We first show that solutions to the linearized Einstein equation with nonvanishing stress tensor can be decomposed…
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…
We express Maxwell's equations as a single equation, first using the divergence of a special type of matrix field to obtain the four current, and then the divergence of a special matrix to obtain the Electromagnetic field. These two…
Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…
The polarization operator (tensor) for planar charged fermions in constant uniform magnetic field is calculated in the one-loop approximation of the 2+1 dimensional quantum electrodynamics (QED$_{2+1}$) with a nonzero fermion density. We…
A generalized vector particle theory with the use of an extended set of Lorentz group irredicible representations, including scalar, two 4-vectors, and antisymmetric 2-rang tensor, is investigated. Initial equations depend upon four complex…
We study the three-dimensional $SU(2)$ principal chiral model (PCM) using different tensor renormalization group methods based on the triad and anisotropic decomposition of the tensor. The tensor network representation is formulated based…
Tensor and matrix formulations of Dirac-K\"ahler equation for massive and massless fields are considered. The equation matrices obtained are simple linear combinations of matrix elements in the 16-dimensional space. The projection…
A Green-function formalism for the Kondo lattice model is presented, which is designed to be combined with the dynamical mean-field theory. With use of Wick's theorem only for conduction electrons, dynamical quantities are represented in…
Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex…
The process tensor framework to open quantum systems provides the most general description of multi-time correlations in non-Markovian quantum dynamics. A compressed representation of a process tensor in terms of matrix product operators…
The interaction energy of a given distribution of electric charges and currents with an electromagnetic external field is expressed by the Cartesian components of the multipole tensors of this distribution. Special attention is paid to the…
The solution of linear non-autonomous ordinary differential equation systems (also known as the time-ordered exponential) is a computationally challenging problem arising in a variety of applications. In this work, we present and study a…
The Tucker decomposition expresses a given tensor as the product of a small core tensor and a set of factor matrices. Apart from providing data compression, the construction is useful in performing analysis such as principal component…
We present a numerically stable re-formulization of the transfer matrix method (TMM). The iteration form of the traditional TMM is transformed into solving a set of linear equations. Our method gains the new ability of calculating accurate…
In the framework of tensor spaces, we consider orthogonalization kernels to generate an orthogonal basis of a tensor subspace from a set of linearly independent tensors. In particular, we experimentally study the loss of orthogonality of…
A macroscopic description of thermoelectric phenomena involves several tensorial transport coefficients. Textbook microscopic Kubo formulas for them are plagued with ambiguities in the definitions of the current operators and the…