Three ways to solve critical \(\phi^4\) theory on \(4 - \epsilon\) dimensional real projective space: perturbation, bootstrap, and Schwinger-Dyson equation. (English) Zbl 1385.81032
Summary: In this paper, we solve the two-point function of the lowest dimensional scalar operator in the critical \(\phi^4\) theory on \(4 - \epsilon\) dimensional real projective space in three different methods. The first is to use the conventional perturbation theory, and the second is to impose the cross-cap bootstrap equation, and the third is to solve the Schwinger-Dyson equation under the assumption of conformal invariance. We find that the three methods lead to mutually consistent results but each has its own advantage.
MSC:
| 81T10 | Model quantum field theories |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
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