A note on tree factorization and no particle production. (English) Zbl 1522.81174
Summary: We prove factorization of the generating functional of connected tree diagrams by exploring that it is the Legendre transform of the action. This theorem is then applied to the example of a local relativistic interacting field theory in 2D with a single massive real scalar field that has no derivative couplings and no classical tadpole. In the process we streamline the proof that the assumption of no particle production leads to either the sin(h)-Gordon or the Bullough-Dodd model.
MSC:
| 81T10 | Model quantum field theories |
| 81U05 | \(2\)-body potential quantum scattering theory |
| 12D05 | Polynomials in real and complex fields: factorization |
| 81R12 | Groups and algebras in quantum theory and relations with integrable systems |
| 44A15 | Special integral transforms (Legendre, Hilbert, etc.) |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
References:
| [1] | Elvang, H.; Huang, Y-T, Scattering Amplitudes in Gauge Theory and Gravity (2015), Cambridge: Cambridge University Press, Cambridge · Zbl 1332.81010 |
| [2] | Travaglini, G., The SAGEX review on scattering amplitudes (2022) |
| [3] | Arefeva, I.; Korepin, V., Scattering in two-dimensional model with Lagrangian \(####\), Pisma Zh. Eksp. Teor. Fiz./JETP Lett., 20, 680 (1974) |
| [4] | Dorey, P., Exact S-matrices (1998) |
| [5] | Gabai, B.; Mazac, D.; Shieber, A.; Vieira, P.; Zhou, Y., No particle production in two dimensions: recursion relations and multi-Regge limit, J. High Energy Phys., JHEP02(2019)094 (2019) · Zbl 1411.81111 · doi:10.1007/JHEP02(2019)094 |
| [6] | Bercini, C.; Trancanelli, D., Supersymmetric integrable theories from no particle production, Phys. Rev. D, 97 (2018) · doi:10.1103/PhysRevD.97.105013 |
| [7] | Dorey, P.; Polvara, D., Tree level integrability in 2d quantum field theories and affine Toda models, J. High Energy Phys., JHEP02(2022)199 (2022) · Zbl 1522.81485 · doi:10.1007/JHEP02(2022)199 |
| [8] | Dodd, R. K.; Bullough, R. K., Polynomial conserved densities for the Sine-Gordon equations, Proc. R. Soc. A, 352, 481 (1977) · doi:10.1098/rspa.1977.0012 |
| [9] | Braden, H. W.; Sasaki, R., Affine Toda perturbation theory, Nucl. Phys. B, 379, 377 (1992) · doi:10.1016/0550-3213(92)90601-7 |
| [10] | Braden, H. W.; Corrigan, E.; Dorey, P. E.; Sasaki, R., Affine Toda field theory and exact S-matrices, Nucl. Phys. B, 338, 689 (1990) · Zbl 1029.81504 · doi:10.1016/0550-3213(90)90648-W |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
