For instance, two very prominent features of noncommutative field theory, the alleged violation of unitarity and the ultraviolet-infrared mixing property turn out to be artefacts of the formalism employed in most of the literature on the subject - a formalism which - in ordinary quantum field theory - makes sense due to the remarkable theorem of Osterwalder and Schrader, but does not seem to be a suitable approach in a noncommutative setting.
To understand what the underlying structural reasons for this apparent breakdown of the formalism are, and how the problem can be solved, is currently one of our most active lines of research. Confronting these features of noncommutative field theories with ordinary quantum field theory, insight regarding the latter can be gained.
Mathematically, these investigations require methods of applied combinatorial algebra as well as applied functional analysis keywords: Hopf algebras, microlocal analysis.
Journal of Noncommutative Geometry
Algebraic String Quantization Another field of research we pursue is the quantization of strings in an approach based on the so-called invariant charges. In this approach, the shape of a string's 'worldsheet' a surface which is immersed in a higher dimensional vector space , is encoded in terms of a set of functionals which are independent of the surface's parametrization.
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This set is endowed with a natural Poisson structure and deforming the resulting Poisson algebra into an associative algebra yields a reparametrization invariant quantization of string theory. The chart shows the evolution of the average number of times documents published in a journal in the past two, three and four years have been cited in the current year.
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Evolution of the total number of citations and journal's self-citations received by a journal's published documents during the three previous years. Journal Self-citation is defined as the number of citation from a journal citing article to articles published by the same journal. Evolution of the number of total citation per document and external citation per document i.
International Collaboration accounts for the articles that have been produced by researchers from several countries. The chart shows the ratio of a journal's documents signed by researchers from more than one country; that is including more than one country address.
Not every article in a journal is considered primary research and therefore "citable", this chart shows the ratio of a journal's articles including substantial research research articles, conference papers and reviews in three year windows vs. Ratio of a journal's items, grouped in three years windows, that have been cited at least once vs.
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Quantum Groups and Noncommutative Geometry | Mathematics Area - SISSA
Year SJR 0. Citations per document. Year International Collaboration