Christian G rard, Fumio Hiroshima, Annalisa Panati and Akito Suzuki
Infrared divergence of a scalar quantum field on a pseudo Riemann manifold
(476K, latex)

ABSTRACT.  A scalar quantum field model 
defined on a pseudo Riemann manifold 
is considered. 
The model is unitarily transformed to the one with a variable mass. 
By means of a Feynman-Kac-type formula, 
it is shown that 
 when the variable mass is short range, the Hamiltonian 
has no ground state. 
Moreover 
the infrared divergence 
 of the expectation values of the number of bosons in the ground state is discussed.