Related papers: Matrix regularization for tensor fields
A possible avenue towards the covariant formulation of the bosonic Matrix Theory is explored. The approach is guided by the known covariant description of the bosonic membrane. We point out various problems with this particular…
In this article, we introduce the $k$-th collineation variety of a third order tensor. This is the closure of the image of the rational map of size $k$ minors of a matrix of linear forms associated to the tensor. We classify such varieties…
This paper presents a regularized Newton method (RNM) with generalized regularization terms for unconstrained convex optimization problems. The generalized regularization includes quadratic, cubic, and elastic net regularizations as special…
We propose a new method for low-rank approximation of Moore-Penrose pseudoinverses (MPPs) of large-scale matrices using tensor networks. The computed pseudoinverses can be useful for solving or preconditioning of large-scale overdetermined…
A proposal for the matrix model formulation of the M-theory on a space with a boundary is given. A general machinery for modding out a symmetry in M(atrix) theory is used for a Z_2 symmetry changing the sign of the X_1 coordinate. The…
Many problems can be formulated as recovering a low-rank tensor. Although an increasingly common task, tensor recovery remains a challenging problem because of the delicacy associated with the decomposition of higher order tensors. To…
After a brief review of recent rigorous results concerning the representation theory of rational chiral conformal field theories (RCQFTs) we focus on pairs (A,F) of conformal field theories, where F has a finite group G of global symmetries…
To alleviate the bias generated by the l1-norm in the low-rank tensor completion problem, nonconvex surrogates/regularizers have been suggested to replace the tensor nuclear norm, although both can achieve sparsity. However, the…
In this paper, we present a unified analysis of matrix completion under general low-dimensional structural constraints induced by {\em any} norm regularization. We consider two estimators for the general problem of structured matrix…
Regularization of quantum field theories (QFT's) can be achieved by quantizing the underlying manifold (spacetime or spatial slice) thereby replacing it by a non-commutative matrix model or a ``fuzzy manifold'' . Such discretization by…
In this paper, some tensor commutation matrices are expressed in termes of the generalized Pauli matrices by tensor products of the Pauli matrices.
We define tensors, corresponding to cubic polynomials, which have the same exponent $\omega$ as the matrix multiplication tensor. In particular, we study the symmetrized matrix multiplication tensor $sM_n$ defined on an $n\times n$ matrix…
We show that in the presence of the torsion tensor $S^k_{\phantom{k}ij}$, the quantum commutation relation for the four-momentum, traced over spinor indices, is given by $[p_i,p_j]=2i\hbar S^k_{\phantom{k}ij}p_k$. In the Einstein--Cartan…
We construct $N$-complexes of non completely antisymmetric irreducible tensor fields on $\mathbb R^D$ which generalize the usual complex $(N=2)$ of differential forms. Although, for $N\geq 3$, the generalized cohomology of these…
We generalize a regularization method of Stumpf 1984 in the case of non-linear spinor field models to fourth order theories and to non-scalar interactions. The involved discrete symmetries can be connected with C,P,T transformations.
We introduce a new class of states for bosonic quantum fields which extend tensor network states to the continuum and generalize continuous matrix product states (cMPS) to spatial dimensions $d\geq 2$. By construction, they are Euclidean…
In this paper, we revisit implicit regularization from the ground up using notions from dynamical systems and invariant subspaces of Morse functions. The key contributions are a new criterion for implicit regularization---a leading…
In this text we review a few structural properties of matrix models that should at least partly generalize to random tensor models. We review some aspects of the loop equations for matrix models and their algebraic counterpart for tensor…
This thesis studies matrix field theories, which are a special type of matrix models. First, the different types of applications are pointed out, from (noncommutative) quantum field theory over 2-dimensional quantum gravity up to algebraic…
A general form of the polarization matrix valid for any type of electromagnetic radiation (plane waves, multipole radiation etc.) is defined in terms of a certain bilinear form in the field-strength tensor. The quantum counterpart is…