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Tuesday 1st of March, 2022

On-Shell Covariance of Quantum Field Theory Amplitudes


Scattering amplitudes in quantum field theory are independent of the field parameterization, which has a natural geometric interpretation as a form of `coordinate invariance.' Amplitudes can be expressed in terms of Riemannian curvature tensors, which makes the covariance of amplitudes under non-derivative field redefinitions manifest. We present a generalized geometric framework that extends this manifest covariance to all allowed field redefinitions. Amplitudes satisfy a recursion relation that closely resembles the application of covariant derivatives to increase the rank of a tensor. This allows us to argue that (tree-level) amplitudes possess a notion of `on-shell covariance,' in that they transform as a tensor under any allowed field redefinition up to a set of terms that vanish when the equations of motion and on-shell momentum constraints are imposed. We highlight a variety of immediate applications to effective field theories.
Comments: 6 pages
Subjects: High Energy Physics - Theory (hep-th); High Energy Physics - Phenomenology (hep-ph)
Cite as: arXiv:2202.06965 [hep-th]
  (or arXiv:2202.06965v1 [hep-th] for this version)

    Submission history

From: Xiaochuan Lu [view email
[v1] Mon, 14 Feb 2022 19:00:01 UTC (135 KB)


Geometry-Kinematics Duality

We propose a mapping between geometry and kinematics that implies the classical equivalence of any theory of massless bosons -- including spin and exhibiting arbitrary derivative or potential interactions -- to a nonlinear sigma model (NLSM) with a momentum-dependent metric in field space. From this kinematic metric we construct a corresponding kinematic connection, covariant derivative, and curvature, all of which transform appropriately under general field redefinitions, even including derivatives. We show explicitly how all tree-level on-shell scattering amplitudes of massless bosons are equal to those of the NLSM via the replacement of geometry with kinematics. Lastly, we describe how the recently introduced geometric soft theorem of the NLSM, which universally encodes all leading and subleading soft scalar theorems, also captures the soft photon theorems.
Comments: 5 pages
Subjects: High Energy Physics - Theory (hep-th); High Energy Physics - Phenomenology (hep-ph)
Report number: CALT-TH 2022-006
Cite as: arXiv:2202.06972 [hep-th]
  (or arXiv:2202.06972v1 [hep-th] for this version)

Submission history

From: Andreas Helset [view email
[v1] Mon, 14 Feb 2022 19:00:03 UTC (25 KB)

discussion on both papers led by Manuel Pérez-Victoria