18 research outputs found
A multipurpose Hopf deformation of the Algebra of Feynman-like Diagrams
We construct a three parameter deformation of the Hopf algebra
. This new algebra is a true Hopf deformation which reduces to
on one hand and to on the other, relating
to other Hopf algebras of interest in contemporary physics.
Further, its product law reproduces that of the algebra of polyzeta functions.Comment: 5 page
A Three Parameter Hopf Deformation of the Algebra of Feynman-like Diagrams
We construct a three-parameter deformation of the Hopf algebra \LDIAG. This
is the algebra that appears in an expansion in terms of Feynman-like diagrams
of the {\em product formula} in a simplified version of Quantum Field Theory.
This new algebra is a true Hopf deformation which reduces to \LDIAG for some
parameter values and to the algebra of Matrix Quasi-Symmetric Functions
(\MQS) for others, and thus relates \LDIAG to other Hopf algebras of
contemporary physics. Moreover, there is an onto linear mapping preserving
products from our algebra to the algebra of Euler-Zagier sums
Hopf Algebras in General and in Combinatorial Physics: a practical introduction
This tutorial is intended to give an accessible introduction to Hopf
algebras. The mathematical context is that of representation theory, and we
also illustrate the structures with examples taken from combinatorics and
quantum physics, showing that in this latter case the axioms of Hopf algebra
arise naturally. The text contains many exercises, some taken from physics,
aimed at expanding and exemplifying the concepts introduced
Recommended from our members
Hopf algebra structure of a model quantum field theory
Recent elegant work[1] on the structure of Perturbative Quantum Field Theory (PQFT) has revealed an astonishing interplay between analysis( Riemann Zeta functions), topology (Knot theory), combinatorial graph theory (Feynman Diagrams) and algebra (Hopf structure). The difficulty inherent in the complexities of a fully-fledged field theory such as PQFT means that the essential beauty of the relationships between these areas can be somewhat obscured. Our intention is to display some, although not all, of these structures in the context of a simple zero-dimensional field theory; i.e. a quantum theory of non-commuting operators which do not depend on spacetime. The combinatorial properties of these boson creation and annihilation operators, which is our chosen example, may be described by graphs [2, 3], analogous to the Feynman diagrams of PQFT, which we show possess a Hopf algebra structure[4]. Our approach is based on the partition function for a boson gas. In a subsequent note in these Proceedings we sketch the relationship between the Hopf algebra of our simple model and that of the PQFT algebra
Graduate School: Course Decriptions, 1972-73
Official publication of Cornell University V.64 1972/7
Commonwealth of Independent States aerospace science and technology, 1992: A bibliography with indexes
This bibliography contains 1237 annotated references to reports and journal articles of Commonwealth of Independent States (CIS) intellectual origin entered into the NASA Scientific and Technical Information System during 1992. Representative subject areas include the following: aeronautics, astronautics, chemistry and materials, engineering, geosciences, life sciences, mathematical and computer sciences, physics, social sciences, and space sciences