Traces for Star Products*)
نویسندگان
چکیده
منابع مشابه
Traces of Matrix Products
Given two noncommuting matrices, A and B, it is well known that AB and BA have the same trace. This extends to cyclic permutations of products of A’s and B’s. It is shown here that for 2 × 2 matrices A and B, whose elements are independent random variables with standard normal distributions, the probability that Tr(ABAB) > Tr(AB) is exactly 1 √ 2 .
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The notion of associative infinite product is applied to traces, resulting in an alternative approach to introducing infinite traces. Four different versions of product are explored, two of them identical to known definitions of infinite trace.
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These notes, based on the mini-course given at the PQR2003 Euroschool held in Brussels in 2003, aim to review Kontsevich’s formality theorem together with his formula for the star product on a given Poisson manifold. A brief introduction to the employed mathematical tools and physical motivations is also given.
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We relate the Bohr-Sommerfeld conditions established in λ-microlocal analysis to formal deformation quantization of symplectic manifolds by classifying star products adapted to some Lagrangian sub-manifold L, i.e. products preserving the classical vanishing ideal IL of L up to IL-preserving equivalences.
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The infinite matrices in Witten’s vertex are easy to diagonalize. It just requires some SL(2,R) lore plus a Watson-Sommerfeld transformation. We calculate the eigenvalues of all Neumann matrices for all scale dimensions s, both for matter and ghosts, including fractional s which we use to regulate the difficult s = 0 limit. We find that s = 1 eigenfunctions just acquire a p term, and x gets rep...
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ژورنال
عنوان ژورنال: Progress of Theoretical Physics Supplement
سال: 2001
ISSN: 0375-9687
DOI: 10.1143/ptps.144.92