Physics – Mathematical Physics
Scientific paper
2012-03-07
Physica Scripta 82 038115 (2010)
Physics
Mathematical Physics
8 pages/(4 pages published version), 1 Figure. arXiv admin note: text overlap with arXiv:1011.0524
Scientific paper
In this paper, we present a Hopf algebra description of a bosonic quantum model, using the elementary combinatorial elements of Bell and Stirling numbers. Our objective in doing this is as follows. Recent studies have revealed that perturbative quantum field theory (pQFT) displays an astonishing interplay between analysis (Riemann zeta functions), topology (Knot theory), combinatorial graph theory (Feynman diagrams) and algebra (Hopf structure). Since pQFT is an inherently complicated study, so far not exactly solvable and replete with divergences, the essential simplicity of the relationships between these areas can be somewhat obscured. The intention here is to display some of the above-mentioned structures in the context of a simple bosonic quantum theory, i.e. a quantum theory of non-commuting operators that do not depend on space-time. The combinatorial properties of these boson creation and annihilation operators, which is our chosen example, may be described by graphs, analogous to the Feynman diagrams of pQFT, which we show possess a Hopf algebra structure. Our approach is based on the quantum canonical partition function for a boson gas.
Blasiak Pawel
Duchamp Gerard E. H.
Horzela Andrzej
Penson Karol A.
Solomon Allan I.
No associations
LandOfFree
A generic Hopf algebra for quantum statistical mechanics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A generic Hopf algebra for quantum statistical mechanics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A generic Hopf algebra for quantum statistical mechanics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-393768