Related papers: Computer Algebra in Particle Physics
New notions are introduced in algebra in order to better study the congruences in number theory. For example, the <special semigroups> makes an important such contribution.
We study Smarandache sequences of numbers, and related problems, via a Computer Algebra System. Solutions are discovered, and some conjectures presented.
Particles have tremendous potential as astronomical messengers, and conversely, studying the universe as a whole also teaches us about particle physics. This thesis encompasses both of these research directions. Many models predict a…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
We give a definition of partition C*-algebras: To any partition of a finite set, we assign algebraic relations for a matrix of generators of a universal C*-algebra. We then prove how certain relations may be deduced from others and we…
Class field theory furnishes an intrinsic description of the abelian extensions of a number field that is in many cases not of an immediate algorithmic nature. We outline the algorithms available for the explicit computation of such…
Particle-in-cell merging algorithms aim to resample dynamically the six-dimensional phase space occupied by particles without distorting substantially the physical description of the system. Whereas various approaches have been proposed in…
We survey the development of Clifford's geometric algebra and some of its engineering applications during the last 15 years. Several recently developed applications and their merits are discussed in some detail. We thus hope to clearly…
Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…
We show that the time evolution of the wave function of a quantum mechanical many particle system can be implemented very efficiently on a quantum computer. The computational cost of such a simulation is comparable to the cost of a…
Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However, the lack of computationally efficient…
The advent of computers has allowed mathematicians to do increasingly more difficult computations that used to be practically impossible. Peer reviewers will seldom look at any code attached to a math paper, however. In this article, we…
This note is based on the plenary talk given by the second author at MACIS 2015, the Sixth International Conference on Mathematical Aspects of Computer and Information Sciences. Motivated by some of the work done within the Priority…
We study the plactic algebra and its action on bosonic particle configurations in the classical case. These particle configurations together with the action of the plactic generators can be identified with crystals of the quantum analogue…
Clifford algebras are used for definition of spinors. Because of using spin-1/2 systems as an adequate model of quantum bit, a relation of the algebras with quantum information science has physical reasons. But there are simple mathematical…
Generalised observables (POM observables) are necessary for representing all possible measurements on a quantum system. Useful algebraic operations such as addition and multiplication are defined for these observables, recovering many…
Machine learning models are poised to make a transformative impact on chemical sciences by dramatically accelerating computational algorithms and amplifying insights available from computational chemistry methods. However, achieving this…
These are expanded lecture notes of a series of expository talks surveying basic aspects of group cohomology and homology. They were written for someone who has had a first course in graduate algebra but no background in cohomology. You…
Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardware would have tremendous economic impact. Quantum computing…
Quantum computers are becoming real, and they have the inherent potential to significantly impact many application domains. We sketch the basics about programming quantum computers, showing that quantum programs are typically hybrid…