منابع مشابه
Non-commutative worlds
Abstract. This paper presents a mathematical view of aspects of physics, showing how the forms of gauge theory, Hamiltonian mechanics and quantum mechanics arise from a non-commutative framework for calculus and differential geometry. This work is motivated by discrete calculus, as it is shown that classical discrete calculus embeds in a non-commutative context. It is shown how various processe...
متن کاملNon-Commutative Worlds - A Summary
Aspects of gauge theory, Hamiltonian mechanics and quantum mechanics arise naturally in the mathematics of a non-commutative framework for calculus and differential geometry. This paper consists in two sections. This first section sketches our results in this domain in general. The second section gives a derivation of a generalization of the Feynman-Dyson derivation of electromagnetism using ou...
متن کاملNon-commutative Gröbner Bases for Commutative Algebras
An ideal I in the free associative algebra k〈X1, . . . ,Xn〉 over a field k is shown to have a finite Gröbner basis if the algebra defined by I is commutative; in characteristic 0 and generic coordinates the Gröbner basis may even be constructed by lifting a commutative Gröbner basis and adding commutators.
متن کاملNon-commutative automorphisms of bounded non-commutative domains
We establish rigidity (or uniqueness) theorems for nc automorphisms which are natural extensions of clasical results of H. Cartan and are improvements of recent results. We apply our results to ncdomains consisting of unit balls of rectangular matrices.
متن کاملDirected prime graph of non-commutative ring
Prime graph of a ring R is a graph whose vertex set is the whole set R any any two elements $x$ and $y$ of $R$ are adjacent in the graph if and only if $xRy = 0$ or $yRx = 0$. Prime graph of a ring is denoted by $PG(R)$. Directed prime graphs for non-commutative rings and connectivity in the graph are studied in the present paper. The diameter and girth of this graph are also studied in the pa...
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ژورنال
عنوان ژورنال: New Journal of Physics
سال: 2004
ISSN: 1367-2630
DOI: 10.1088/1367-2630/6/1/173