Related papers: Lectures on Symmetric Tensor Categories
Recently, Zhao and Yang introduced centrosymmetric tensors. In this paper, we further introduce skew centrosymmetric tensors and centrosymmetric Cauchy tensors, and discuss properties of these three classes of structured tensors. Some…
This paper studies nuclear norms of symmetric tensors. As recently shown by Friedland and Lim, the nuclear norm of a symmetric tensor can be achieved at a symmetric decomposition. We discuss how to compute symmetric tensor nuclear norms,…
This is the second part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part II), we develop logarithmic formal…
These notes were prepared for a series of intensive lectures delivered at Hokkaido University, Nagoya University, Kyoto University, and Kyushu University. We begin with a brief review of higher-form symmetries, anomalies, and discrete gauge…
In this series of lectures presented at the CIMPA Winter School on Discrete Integrable Systems in Pondicherry, India, in February, 2003 we give a review of the application of Lie point symmetries, and their generalizations to the study of…
Recently, several discussions on the possible observability of 4-vector potential have been published in literature. Furthermore, several authors recently claimed existence of the helicity=0 electromagnetic field. We re-examine the theory…
The following notes derive from review lectures on closed string field theory given at the Galileo Galilei Institute for Theoretical Physics in March 2019.
The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important tool in attempting to overcome this…
This $Physics$ viewpoint considers recent work by Tilloy and Cirac [Phys. Rev. X 9, 021040 (2019), arXiv:1808.00976]; those authors overcame several past limitations in the generalization of tensor networks to the continuum and proposed a…
These lectures are a brief introduction to scattering amplitudes. We begin with a review of basic kinematical concepts like the spinor helicity formalism, followed by a tutorial on bootstrapping tree-level scattering amplitudes. Afterwards,…
The series of three lectures given at Tel-Aviv University in 1992: 1. Tensor categories. 2. Quantum groups. 3. Topological (quantum) field theories. Published as the preprint IAS 897-92 of Tel-Aviv University and The Mortimer and Raymond…
A symmetric tensor may be regarded as a partially symmetric tensor in several different ways. These produce different notions of rank for the symmetric tensor which are related by chains of inequalities. By exploiting algebraic tools such…
We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed…
Knop constructed a tensor category associated to a finitely-powered regular category equipped with a degree function. In recent work with Harman, we constructed a tensor category associated to an oligomorphic group equipped with a measure.…
We survey recent developments in a novel kind of generalized global symmetry, the non-invertible symmetry, in diverse spacetime dimensions. We start with several different but related constructions of the non-invertible Kramers-Wannier…
This paper is an introduction to Homological Mirror Symmetry, derived categories, and topological D-branes aimed mainly at a mathematical audience. In the paper we explain the physicists' viewpoint of the Mirror Phenomenon, its relation to…
As a step towards the structure theory of Lie algebras in symmetric monoidal categories we establish results involving the Killing form. The proper categorical setting for discussing these issues are symmetric ribbon categories.
The symmetry-constrained response tensors on transport, optical, and electromagnetic effects are of central importance in condensed matter physics because they can guide experimental detections and verify theoretical calculations. These…
In the paper a concept of a double symmetry is introduced, and its qualitative characteristics and rigorous definitions are given. We describe two ways to construct the double-symmetric field theories and present an example demonstrating…
Lorentzian manifolds with vanishing second covariant derivative of the Riemann tensor are studied. Their existence, classification and explicit local expression are considered. Related issues and open questions are briefly commented.