2013/10/02 by J. S. Dowker, Dowker, J. S.
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #gr-qc #hep-th #math-ph #math.DG #math.MP #math.SP
paper · pdf · doi:10.48550/arxiv.1310.0759
11 pages, 7 figures. Multiplicative anomalies corrected and listed as polynomials. The Dirichlet-to-Robin operator introduced
arxiv created 2013/10/10 · arxiv updated 2013/10/14
The functional determinants of the GJMS scalar operators, P2k, on even-dimensional spheres are computed via Barnes multiple gamma functions relying on the numerical availability of the digamma function. For the critical k=d/2 case, it is necessary to calculate the Stirling moduli. The multiplicative anomalies are given as odd polynomials in k and it is emphasised that that the Dirichlet--to--Robin factorisation, P2l+1, gives the same results as P2k if k=l+1/2.The results are presented as graphs and show a series of extrema in the effective action as k is varied in the reals. For odd dimensions these extrema occur at integer k.