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Generating Contact Terms for Scalar Field Interactions with Polynomial Rings

Kerdijk, Amy (2024) Generating Contact Terms for Scalar Field Interactions with Polynomial Rings. Master's Thesis / Essay, Physics.


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Mandelstam polynomials in scattering amplitudes correspond to contact contributions, and emerge from taking derivative terms in the Lagrangian. Equivalence relations between polynomials can be observed by employing the equations of motion, momentum conservation, and Gram constraints, which is powerful since they can serve as substitutes to finding corresponding redundancies in the Lagrangian, which are instead found with integration by parts and field redefinitions. The objective of this work is to study the use of polynomial rings to generate possible n-point contact terms in d-dimensions up to these equivalences, along with the representations in which Mandelstam invariants live. Contact contributions live in a polynomial ring, modded out by an ideal generated by momentum conservation and Gram conditions. Without Gram conditions, this becomes a study of the representations of the symmetric group acting on a set of unordered pairs, which describes the behaviour of Mandelstam invariants. In 4-point amplitudes in particular, elementary symmetric polynomials can be used as generators instead, such that there are a different number of independent polynomials at each order in the Mandelstam variables.

Item Type: Thesis (Master's Thesis / Essay)
Supervisor name: Roest, D. and Mazumdar, A.
Degree programme: Physics
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 18 Jan 2024 13:15
Last Modified: 18 Jan 2024 13:15

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