Double scaling limit of a broken symmetry quantum field theory
Jul, 2000
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Abstract:
The Ising limit of a conventional Hermitian parity-symmetric scalar quantum field theory is a correlated limit in which two bare Lagrangian parameters, the coupling constant and the {\it negative} mass squared , both approach infinity with the ratio held fixed. In this limit the renormalized mass of the asymptotic theory is finite. Moreover, the limiting theory exhibits universal properties. For a non-Hermitian -symmetric Lagrangian lacking parity symmetry, whose interaction term has the form , the renormalized mass diverges in this correlated limit. Nevertheless, the asymptotic theory still has interesting properties. For example, the one-point Green's function approaches the value independently of the space-time dimension for . Moreover, while the Ising limit of a parity-symmetric quantum field theory is dominated by a dilute instanton gas, the corresponding correlated limit of a -symmetric quantum field theory without parity symmetry is dominated by a constant-field configuration with corrections determined by a weak-coupling expansion in which the expansion parameter (the amplitude of the vertices of the graphs in this expansion) is proportional to an inverse power of . We thus observe a weak-coupling/strong-coupling duality in that while the Ising limit is a strong-coupling limit of the quantum field theory, the expansion about this limit takes the form of a conventional weak-coupling expansion. A possible generalization of the Ising limit to dimensions is briefly discussed.Note:
- 27 pages, 2 figures
- field theory: scalar
- field theory: Euclidean
- any-dimensional
- spontaneous symmetry breaking
- effective action: expansion
- scaling
- correlation function
- Schroedinger equation
- Ising model
- parity: invariance
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