---
Carl Bender
---
PT symmetry and the double-scaling limit in quantum field theory
---
The conventional double-scaling limit of an
O(N)-symmetric quartic quantum field theory
is inconsistent because the critical coupling
constant is negative. Thus, at the critical
coupling the Lagrangian defines a quantum
theory with an
upside-down potential whose energy appears
to be unbounded below. Worse yet, the integral
representation of the partition function
of the theory does not exist. It is shown
that one can avoid these difficulties if
one approaches this correlated limit in a
PT-symmetric fashion.
---