Geometric Amplitudes: A Covariant Functional Approach for Massless Scalar Theories
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| Format: | Preprint |
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2026
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| _version_ | 1866911613999644672 |
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| author | Delgado, Antonio Martin, Adam Wang, Runqing |
| author_facet | Delgado, Antonio Martin, Adam Wang, Runqing |
| contents | Functional geometry is a framework using concepts from geometry to understand the invariance of amplitudes in quantum field theory under a large class of field redefinitions, including those involving derivatives. It is inspired by recursion relations among correlation functions, where higher-point functions depend iteratively upon smaller correlators. Previous work has shown that, with suitable modifications, these correlation functions become covariant under field redefinitions, provided they are evaluated at the physical ``on-shell" point. In this paper, we show how to further modify correlation functions in massless scalar field theories to achieve ``off-shell" covariance. We investigate the conditions required for the framework to work and discuss the geometric interpretation of this construction -- which prioritizes the covariant transformation of observables under field redefinitions over the role of a metric tensor and its derivatives. While analogous modifications may exist for massive theories, we show that framework developed here does not extend straightforwardly to that case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_20099 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometric Amplitudes: A Covariant Functional Approach for Massless Scalar Theories Delgado, Antonio Martin, Adam Wang, Runqing High Energy Physics - Theory Functional geometry is a framework using concepts from geometry to understand the invariance of amplitudes in quantum field theory under a large class of field redefinitions, including those involving derivatives. It is inspired by recursion relations among correlation functions, where higher-point functions depend iteratively upon smaller correlators. Previous work has shown that, with suitable modifications, these correlation functions become covariant under field redefinitions, provided they are evaluated at the physical ``on-shell" point. In this paper, we show how to further modify correlation functions in massless scalar field theories to achieve ``off-shell" covariance. We investigate the conditions required for the framework to work and discuss the geometric interpretation of this construction -- which prioritizes the covariant transformation of observables under field redefinitions over the role of a metric tensor and its derivatives. While analogous modifications may exist for massive theories, we show that framework developed here does not extend straightforwardly to that case. |
| title | Geometric Amplitudes: A Covariant Functional Approach for Massless Scalar Theories |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.20099 |