Validity of the effective potential method to study PT-symmetric field theories
| Autor: | Abouzeid M. Shalaby |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
010302 applied physics
Physics Field (physics) Truncation Pseudo-Hermitian Hamiltonians General Physics and Astronomy Potential method 02 engineering and technology 021001 nanoscience & nanotechnology 01 natural sciences Power law Hermitian matrix lcsh:QC1-999 Massless particle 0103 physical sciences Order (group theory) Boundary value problem Non-Hermitian models 0210 nano-technology lcsh:Physics Metric operators PT-symmetric theories Mathematical physics |
| Zdroj: | Results in Physics, Vol 13, Iss, Pp-(2019) |
| Popis: | We calculate the one loop effective potential for the class ( - ( i ϕ ) α ) of PT -symmetric and non-Hermitian field theories in 0 + 1 space-time dimensions. To test the method, we showed that for the massless Hermitian ϕ 4 theory, the method gives the exact power law behavior known from the literature. We show that this order of calculations goes beyond the truncation of the Schwinger-Dyson equations at the two-point green functions applied to the PT -symmetric ( - ϕ 4 ) theory in the literature. We found that the effective potential calculation represents good approximations of the vacuum energies of the class ( - ( i ϕ ) α ) compared to the numerical results. For the vacuum condensate, the method gives also accurate results for the absolute values but gives both positive as well as negative imaginary condensates for even α which again agrees with the prediction of the Schwinger-Dyson equations. Unlike other methods, the effective potential can be directly extended to higher dimensions as it offers a way to implement the PT -symmetric boundary conditions as well as there exist well known methods to regularize the theory at higher dimensions. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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