TY  - JOUR
A1  - Nehring, Benjamin
A1  - Zessin, Hans
T1  - A representation of the moment measures of the general ideal Boe gas
JF  - Mathematische Nachrichten
N2  - 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 loop integrals. This representation can be considered as a point process analogue of the old idea of Symanzik 15 that local times and self-crossings 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 Levy-measure belonging to some large class of measures containing that of the classical ideal Bose gas considered by Fichtner. It is well-known that the calculation of moments of higher order of point processes is notoriously complicated. See for instance Krickebergs 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.
KW  - Infinitely divisible point processes
KW  - integration by parts formula
KW  - random KMM-measure
KW  - permanental and determinantal point processes (MSC 2010) 35K55
KW  - 35K65
Y1  - 2012
U6  - https://doi.org/10.1002/mana.201000111
SN  - 0025-584X
VL  - 285
IS  - 7
SP  - 878
EP  - 888
PB  - Wiley-VCH
CY  - Weinheim
ER  -