I'd like to extend my gratitude to APCTP Pohang for hosting me and to IISER Pune for granting me the opportunity to work on my thesis abroad.

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… amplitude and resolving the color structures systematically while utilising the efficiency of the off-shell recursions for generating higher loop amplitudes.

Finally I'd like to thank my collaborators Hojin and Kanghoon for their patient guidance and efforts.

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and obtain cross-sections for 2-to-2 and 2-to-4 processes in leading order from the 1-loop and 3-loop 2-to-2 "doubled" amplitudes. We look forward to implementing this for gauge theories starting with pure Yang–Mills as the true benefits of such a method are that we bypass squaring the...

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… after amputation. We then use the Cutkosky rules algebraically (enabled by the LTE) to obtain cross sections for various multiplicity processes in leading order (but in theory, we may obtain cross-section contributions at any order). Here, we use the φ⁴ theory as a proof of concept...

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This "doubling" prescription is equivalent to the Schwinger–Keldysh formalism, moreover the amplitudes in this prescription are equivalent to the imaginary part of the amplitudes in the regular theory. From here, we generate off-shell currents at high loops which translate to amplitudes…

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We use the quantum off-shell recursion framework (arxiv.org/abs/2202.08133) alongside a form of the optical theorem, the Largest Time Equation (LTE). And for that we derive the action formalism for LTE, which essentially doubles the field content in the regular theory.

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Human Sadness by The Voidz
Soothsayer by Buckethead