Phase space structure and short distance behavior of local quantum field theories

In this article a general relation between the short distance structure of quantum field theories and their phase space properties is exemplified by the simple class of generalized free fields. As is known, theories with decent phase space properties, resulting from a finite or moderately increasing infinite particle spectrum, always have non-trivial scaling (short distance) limits [cf. D. Buchholz and R. Verch, Rev. Math. Phys. 10, 775 (1998)]. But, whereas in the finite particle case the phase space properties of the limit theories comply with strong nuclearity conditions, they violate in the infinite particle case even rather mild compactness assumptions. These results provide further evidence to the effect that relevant information on the short distance structure of a theory can be obtained by phase space analysis. (C) 2002 American Institute of Physics.