- #1
VietBrian
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Hello everyone :) I'm reading the book QFT - L. H. Ryder, and I don't understand clearly what are the generating functional Z[J] and vacuum-to-vacuum boundary conditions? Help me, please >"<
[itex]Z \left[ 0 \right]=0[/itex]
The generating functional in quantum field theory (QFT) is a mathematical tool that allows us to calculate the probabilities of different particle interactions and processes. It is a functional of the external sources in the theory and is used to derive the Green's functions and correlation functions.
The generating functional is related to Feynman diagrams as it provides a way to organize and calculate the amplitudes associated with each Feynman diagram. The functional is used to sum over all possible Feynman diagrams and obtain the total amplitude for a given process.
Vacuum-to-vacuum boundary conditions are a set of conditions that describe the behavior of the fields in the vacuum state in QFT. These conditions ensure that the vacuum state remains unchanged under time evolution and that the vacuum energy is zero.
Vacuum-to-vacuum boundary conditions are important in QFT because they provide a framework for calculating physical observables. They help us understand the behavior of the fields in the vacuum state and how they evolve over time. These conditions also play a crucial role in renormalization and the cancellation of divergences in QFT calculations.
Vacuum-to-vacuum boundary conditions are typically implemented in QFT calculations by using the path integral formalism. This involves summing over all possible field configurations that satisfy the boundary conditions and calculating the amplitude for each configuration. The total amplitude is then obtained by integrating over all possible field configurations. Alternatively, these conditions can also be imposed through the use of counterterms in perturbative calculations.