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Home > Art, Film & Photography > Noncommutative Geometry: Spectral Triple, Noncommutative Quantum Field Theory, Connection, Jlo Cocycle, Noncommutative Residue
Noncommutative Geometry: Spectral Triple, Noncommutative Quantum Field Theory, Connection, Jlo Cocycle, Noncommutative Residue

Noncommutative Geometry: Spectral Triple, Noncommutative Quantum Field Theory, Connection, Jlo Cocycle, Noncommutative Residue


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About the Book

Chapters: Spectral Triple, Noncommutative Quantum Field Theory, Connection, Jlo Cocycle, Noncommutative Residue, Noncommutative Measure and Integration. Source: Wikipedia. Pages: 30. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Noncommutative geometry, or NCG, is a branch of mathematics concerned with the possible spatial interpretations of algebraic structures for which the commutative law fails, that is, for which xy does not always equal yx. Although one could technically construct geometries by simply removing this condition (commutativity), the results are typically trivial or uninteresting. The most common usage of the term, therefore, refers to what is properly called differential noncommutative geometry, a subject which was developed extensively by French mathematician Alain Connes. The challenge of NCG theory is to get around the lack of commutative multiplication, which is a requirement of previous geometric theories of algebraic structures. In mathematics, there is a close relationship between spaces, which are geometric in nature, and the numerical functions on them. In general, such functions will form a commutative ring. For instance, one may take the ring C(X) of continuous complex-valued functions on a topological space X. In many important cases (e.g., if X is a compact Hausdorff space), we can recover X from C(X), and therefore it makes some sense to say that X has commutative geometry. For other cases and applications, including mathematical physics and functional analysis, non-commutative rings arise as the natural candidates for a ring of functions on some non-commutative "space." "Non-commutative spaces," however defined, cannot be too similar to ordinary topological spaces, as these are known to correspond to commutative rings in many important cases. For this rea...More: http: //booksllc.net/?id=29591


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Product Details
  • ISBN-13: 9781157178606
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • Sub Title: Spectral Triple, Noncommutative Quantum Field Theory, Connection, Jlo Cocycle, Noncommutative Residue
  • Width: 229 mm
  • ISBN-10: 115717860X
  • Publisher Date: 15 Sep 2010
  • Binding: Paperback
  • Spine Width: 2 mm
  • Weight: 59 gr


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