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Determine the asymptotic behavior of Green's functions at high energies and momenta in quantum field theory using real-variable mathematical methods.

May 1, 1960Physical Review

High-Energy Behavior in Quantum Field Theory

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Determine the asymptotic behavior of Green's functions at high energies and momenta in quantum field theory using real-variable mathematical methods.
Defined a function class An of n real variables governed by specific asymptotic coefficients.
Mapped Feynman integrands with imaginary energies into the An class.
Proved multivariable integration theorems establishing conditions under which integrals converge and reduce from class An to An-k.
Proved that renormalized Feynman integrals strictly converge when asymptotic coefficient criteria are met.
Validated the Dyson-Salam renormalization procedure across all perturbation orders.
Established a general rule for calculating the high-energy asymptotic behavior of Green's functions to arbitrary orders.

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Implication

Theoretical study demonstrates convergence of renormalized Feynman integrals in quantum field theory, validating the Dyson-Salam renormalization procedure.

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Steven Weinberg (1960) studied this question.

synapsesocial.com/papers/6a1040bf068269ab45fa8339 https://doi.org/10.1103/physrev.118.838

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Implication

Theoretical study demonstrates convergence of renormalized Feynman integrals in quantum field theory, validating the Dyson-Salam renormalization procedure.

High-Energy Behavior in Quantum Field Theory

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Implication

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High-Energy Behavior in Quantum Field Theory

Key Points

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Implication

Cite This Study

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