Alternative derivation of the relativistic three-particle quantization condition
| Autor: | Tyler D. Blanton, Stephen R. Sharpe |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Physics
Nuclear Theory Unitarity 010308 nuclear & particles physics High Energy Physics - Lattice (hep-lat) FOS: Physical sciences 01 natural sciences Computer Science::Digital Libraries Nuclear Theory (nucl-th) High Energy Physics - Phenomenology Quantization (physics) High Energy Physics - Lattice High Energy Physics - Phenomenology (hep-ph) Amplitude 0103 physical sciences 010306 general physics Nuclear theory K matrix Mathematical physics |
| Zdroj: | Physical Review |
| Popis: | We present a simplified derivation of the relativistic three-particle quantization condition for identical, spinless particles described by a generic relativistic field theory satisfying a $\mathbb Z_2$ symmetry. The simplification is afforded by using a three-particle quasilocal K matrix that is not fully symmetrized, $\widetilde{\mathcal{K}}_{\rm df,3}^{(u,u)}$, and makes extensive use of time-ordered perturbation theory (TOPT). We obtain a new form of the quantization condition. This new form can then be related algebraically to the standard quantization condition, which depends on a fully symmetric three-particle K matrix, $\mathcal{K}_{\rm df,3}$. The new derivation is fully explicit, allowing, for example, a closed-form expression for $\mathcal{K}_{\rm df,3}$ to be given in terms of TOPT amplitudes. The new form of the quantization condition is similar in structure to that obtained in the "finite-volume unitarity" approach, and in a companion paper we make this connection concrete. Our simplified approach should also allow a more straightforward generalization of the quantization condition to nondegenerate particles, and perhaps also to more than three particles. Comment: 39 pages, 7 appendices, 11 figures; v2--added clarifications, corrected typos; v3--corrected additional typos, results unchanged; matches published version |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|