PT-symmetric interpretation of double-scaling

Abstract

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 replaces the original theory by its PT-symmetric analog. For a zero-dimensional O(N)-symmetric quartic vector model the partition function of the PT-symmetric analog is calculated explicitly in the double-scaling limit.

11 pages, 2 figures

References in corpus (8)

• Making Sense of Non-Hermitian Hamiltonians
• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• An Equivalent Hermitian Hamiltonian for the non-Hermitian -x^4 Potential
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• Reflectionless Potentials and PT Symmetry
• Families of particles with different masses in PT-symmetric quantum field theory
• Quasi-hermitian Quantum Mechanics in Phase Space
• PT symmetry and large-N models

Cited by in corpus (4)

• $\mathcal{P}\mathcal{T}$-symmetric $-g{\phi }^4$ theory
• Towards perturbative renormalization of ${\varphi }^2(i\varphi {)}^{\epsilon }$ quantum field theory
• Double-Scaling Limit of the O(N)-Symmetric Anharmonic Oscillator
• Non-Convergent Perturbation Theory and Misleading Inferences about Parameter Relationships: the Case of Superexchange