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Solving differential equation by using Dyson series
WebNote that the differential equation ( 8.45 ), plus the initial condition ( 8.47 ), are equivalent to the following integral equation: This expansion is known as the Dyson series [ 34 ]. where the superscript refers to a first-order term in the expansion, et cetera. It follows from Equations ( 8.50) and ( 8.53) that. In scattering theory, a part of mathematical physics, the Dyson series, formulated by Freeman Dyson, is a perturbative expansion of the time evolution operator in the interaction picture. Each term can be represented by a sum of Feynman diagrams. This series diverges asymptotically, but in quantum … See more This leads to the following Neumann series: Here we have $${\displaystyle t_{1}>t_{2}>\cdots >t_{n}}$$, so we can say that the fields are See more One can then express the state vector at time t in terms of the state vector at time t0, for t > t0, Then, the inner … See more • Schwinger–Dyson equation • Magnus series • Peano–Baker series • Picard iteration See more how much is rtb
4 - From Dyson
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