| 研究課題/領域番号 |
18K13533
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| 研究機関 | 東京大学 |
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研究代表者 |
Melia Thomas 東京大学, カブリ数物連携宇宙研究機構, 特任助教 (30814909)
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| 研究期間 (年度) |
2018-04-01 – 2021-03-31
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| キーワード | Effective field theory / Operator bases |
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| 研究実績の概要 |
A major step towards achieving the objective of this proposal has been achieved: the construction of an operator basis in the case of distinguishable particles. This was based on the approach outlined in (A) and (B) and (C) of the proposal plan. However, it has revealed new and beautiful mathematical structures that control the operator basis, that were not anticipated. Specifically, this research has uncovered a new example of a particular mathematical duality - Howe duality - in physics. A key step in this understanding was the identification of a ‘physical manifold’ upon which all observables have to live - a Stiefel manifold - and relating operator construction to harmonic analysis of this manifold. This presents a genuinely new way of understanding the approach of EFT - that of a power spectrum analysis.
The Stiefel manifold is closely related to the Grassmann manifold, that proliferates the modern study of four-dimensional scattering amplitudes. This led to an interesting application of the mathematical results in an unanticipated setting: Monte Carlo generation of phase space for high-precision calculations in quantum chromodynamics. The insight here was that using variables of a particular chart on the Grassmannian leads to a simple parameterisation of the regions of phase space where singular (infra-red divergent) contributions to the calculation live.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
1: 当初の計画以上に進展している
理由
Uncovered a new layer of mathematical structure that enables a shift in perspective and provides a connection to the framework of harmonic analysis (although of a more complicated manifold than the sphere).
This structure also ensures that space-time dimensions 2,3 and 4 are all described in essentially the same way, allowing for a universal treatment.
Have revealed unanticipated connections to the area of Monte Carlo generation for high-precision QCD calculations.
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| 今後の研究の推進方策 |
The plans are unchanged, and will proceed along those outlined in the original proposal. The new unanticipated mathematical structure uncovered will naturally be explored in the process of this, and will play a role in achieving the goal of the proposal.
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| 次年度使用額が生じた理由 |
Travel for conferences that occur within next fiscal year
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