Effective field calculations of the energy spectrum of the PT-symmetric (-x{sup 4}) potential
- Physics Department, Faculty of Science, Mansoura University (Egypt)
In this work, we show that the traditional effective field approach can be applied to the PT-symmetric wrong sign (-x{sup 4}) quartic potential. The importance of this work lies in the possibility of its extension to the more important PT-symmetric quantum field theory while the other approaches which use complex contours are not willing to be applicable. We calculated the effective potential of the massless -x{sup 4} theory as well as the full spectrum of the theory. Although the calculations are carried out up to first order in the coupling, the predicted spectrum is very close to the exact one taken from other works. The most important result of this work is that the effective potential obtained, which is equivalent to the Gaussian effective potential, is bounded from below while the classical potential is bounded from above. This explains the stability of the vacuum of the theory. The obtained quasiparticle Hamiltonian is non-Hermitian but PT symmetric and we showed that the calculation of the metric operator can go perturbatively. In fact, the calculation of the metric operator can be done even for higher dimensions (quantum field theory) which, up until now, cannot be calculated in the other approaches either perturbatively or in a closed form due to the possible appearance of field radicals. Moreover, we argued that the effective theory is perturbative for the whole range of the coupling constant and the perturbation series is expected to converge rapidly (the effective coupling g{sub eff}=(1/6))
- OSTI ID:
- 21260180
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 79, Issue 6; Other Information: DOI: 10.1103/PhysRevD.79.065017; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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