2023/03/08 by van Nuland, Teun D. H., Sukochev, Fedor, Zanin, Dmitriy · 1 citation
#46L87 #58B34 #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.2303.04686
We explicitly compute the local invariants (heat kernel coefficients) of a conformally deformed non-commutative d-torus using multiple operator integrals. We derive a recursive formula that easily produces an explicit expression for the local invariants of any order k and in any dimension d. Our recursive formula can conveniently produce all formulas related to the modular operator, which before were obtained in incremental steps for d∈\2,4\ and k∈\0,2,4\. We exemplify this by writing down some known (k=2, d=2) and some novel (k=2, d≥ 3) formulas in the modular operator.