Abstract
We reconsider the fundamental work of Fichtner 2 and exhibit the permanental structure of the ideal Bose gas again, using a new approach which combines a characterization of infinitely divisible random measures (due to Kerstan, Kummer and Matthes 4, 6 and Mecke 9, 10) with a decomposition of the moment measures into its factorial measures due to Krickeberg 5. To be more precise, we exhibit the moment measures of all orders of the general ideal Bose gas in terms of certain βloopβ integrals. This representation can be considered as a point process analogue of the old idea of Symanzik 15 that local times and selfβcrossings of the Brownian motion can be used as a tool in quantum field theory.
Behind the notion of a general ideal Bose gas there is a class of infinitely divisible point processes of all orders with a LΓ©vyβmeasure belonging to some large class of measures containing that of the classical ideal Bose gas considered by Fichtner.
It is wellβknown that the calculation of moments of higher order of point processes is notoriously complicated. See for instance Krickebergβs calculations for the Poisson or the Cox process in 5.
Relations to the work of Shirai, Takahashi 12 and Soshnikov 14 on permanental and determinantal processes are outlined.