Resolution of Inconsistency in the Double-Scaling Limit

Carl M. Bender, Moshe Moshe, Sarben Sarkar

The conventional double-scaling limit of a quartic quantum field theory is inconsistent because the critical coupling constant is negative. Thus, at the critical coupling the Lagrangian appears to define a quantum theory whose energy is complex. Worse yet, the functional integral for 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. The partition function is calculated explicitly in the double-scaling limit of an zero-dimensional O(N)-symmetric quartic model.
High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph)

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