Related papers: Group-theoretic Approach for Symbolic Tensor Manip…
Index theorem is formulated in noncommutative geometry with finite degrees of freedom by using Ginsparg-Wilson relation. It is extended to the case where the gauge symmetry is spontaneously broken. Dynamical analysis about topological…
With the rapid progress in quantum hardware and software, the need for verification of quantum systems becomes increasingly crucial. While model checking is a dominant and very successful technique for verifying classical systems, its…
This document describes an attempt to develop a compiler-based approach for computations with symmetric tensors. Given a computation and the symmetries of its input tensors, we derive formulas for random access under a storage scheme that…
A prototype for an extensible interactive graphical term manipulation system is presented that combines pattern matching and nondeterministic evaluation to provide a convenient framework for doing tedious algebraic manipulations that so far…
Originally motivated by algebraic invariant theory, we present an algorithm to enumerate integer vectors modulo the action of a permutation group. This problem generalizes the generation of unlabeled graph up to an isomorphism. In this…
Abstract clones serve as an algebraic presentation of the syntax of a simple type theory. From the perspective of universal algebra, they define algebraic theories like those of groups, monoids and rings. This link allows one to study the…
We describe a logarithmic tensor product theory for certain module categories for a ``conformal vertex algebra.'' In this theory, which is a natural, although intricate, generalization of earlier work of Huang and Lepowsky, we do not…
Tensor contractions are ubiquitous in computational chemistry and physics, where tensors generally represent states or operators and contractions express the algebra of these quantities. In this context, the states and operators often…
We introduce the MathGR package, written in Mathematica. The package can manipulate tensor and GR calculations with either abstract or explicit indices, simplify tensors with permutational symmetries, decompose tensors from abstract indices…
We give an algorithm for finding the index of a positive outer automorphism of the free group, and prove the algorithm exits in a finite time.
The canonical tensor model, which is a tensor model in the Hamilton formalism, can be straightforwardly quantized and has an exactly solved physical state. The state is expressed by a wave function with a generalized form of the Airy…
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…
We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ``conformal vertex algebra'' or even more generally,…
We introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates…
Here we consider two algebras, a free unital associative complex algebra (denoted by ${\mathcal{B}}$) equiped with a multiparametric \textbf{\emph{q}}-differential structure and a twisted group algebra (denoted by ${\mathcal{A}(S_{n})}$),…
By a tensor we mean an element of a tensor product of vector spaces over a field. Up to a choice of bases in factors of tensor products, every tensor may be coordinatized, that is, represented as an array consisting of numbers. This note is…
We developed computer algebra tools for enumerating conjugacy classes of independent subsets and generating sets of symmetric groups up to $n=7$, and carried out an initial analysis of the obtained results.
The implicit signature k consists of the multiplication and the ({\omega}-1)-power. We describe a procedure to transform each {\kappa}-term over a finite alphabet A into a certain canonical form and show that different canonical forms have…
Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke…
Motivated by the recent rapid development of complexity theory applied to quantum mechanical processes we present the complete derivation of Nielsen's complexity of unitaries belonging to the representations of oscillator group. Our…