Infrared finite scattering theory: Amplitudes and soft theorems
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2024
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| _version_ | 1866917825021476864 |
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| author | Prabhu, Kartik Satishchandran, Gautam |
| author_facet | Prabhu, Kartik Satishchandran, Gautam |
| contents | Any non-trivial scattering with massless fields in four spacetime dimensions will generically produce an out-state with memory. Scattering with any massless fields violates the standard assumption of asymptotic completeness -- that all "in" and "out" states lie in the standard (zero memory) Fock space -- and therefore leads to infrared (IR) divergences in the standard $S$-matrix amplitudes. In this paper we define an infrared finite scattering theory which assumes only (1) the existence of in/out algebras and (2) that Heisenberg evolution is an automorphism of these algebras. The resulting "superscattering" map $\$$ allows for transitions between different in/out memory states and agrees with the standard $S$-matrix when it is defined. We construct $\$$-amplitudes by defining (3) a "generalized asymptotic completeness" which accommodates states with memory in the space of asymptotic states and (4) a complete basis of improper states which generalize the usual $n$-particle momentum basis to account for states with memory. Using only general properties of $\$$, we prove an analog of the Weinberg soft theorems in quantum gravity and QED which imply that all $\$$-amplitudes are well-defined in the infrared. We comment on how one must generalize this framework to consider $\$$-amplitudes for theories with collinear divergences (e.g., massless QED and Yang-Mills theories). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_18637 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Infrared finite scattering theory: Amplitudes and soft theorems Prabhu, Kartik Satishchandran, Gautam High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics Any non-trivial scattering with massless fields in four spacetime dimensions will generically produce an out-state with memory. Scattering with any massless fields violates the standard assumption of asymptotic completeness -- that all "in" and "out" states lie in the standard (zero memory) Fock space -- and therefore leads to infrared (IR) divergences in the standard $S$-matrix amplitudes. In this paper we define an infrared finite scattering theory which assumes only (1) the existence of in/out algebras and (2) that Heisenberg evolution is an automorphism of these algebras. The resulting "superscattering" map $\$$ allows for transitions between different in/out memory states and agrees with the standard $S$-matrix when it is defined. We construct $\$$-amplitudes by defining (3) a "generalized asymptotic completeness" which accommodates states with memory in the space of asymptotic states and (4) a complete basis of improper states which generalize the usual $n$-particle momentum basis to account for states with memory. Using only general properties of $\$$, we prove an analog of the Weinberg soft theorems in quantum gravity and QED which imply that all $\$$-amplitudes are well-defined in the infrared. We comment on how one must generalize this framework to consider $\$$-amplitudes for theories with collinear divergences (e.g., massless QED and Yang-Mills theories). |
| title | Infrared finite scattering theory: Amplitudes and soft theorems |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2402.18637 |