THESIS
2019
viii, 35 pages : illustrations (some color) ; 30 cm
Abstract
In this thesis, we study the relation between the n-point correlation functions for a scalar
field on Minkowski space and the curvature perturbation in de Sitter space. With the
Schwinger-Keldysh formalism, we can write down the perturbation expansion for the correlation
functions, and each term in the expansion can be represented by a Feynman
diagram. We consider a scalar field theory on Minkowski space with direct couplings
only, and for the curvature perturbation we consider an effective field theory which contains
derivative couplings. For any given Feynman diagram, we found that the values of
that diagram for the two theories mentioned above are related by a differential operator
which depends only on the form of the couplings. We developed a systematic way for
constructin...[
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In this thesis, we study the relation between the n-point correlation functions for a scalar
field on Minkowski space and the curvature perturbation in de Sitter space. With the
Schwinger-Keldysh formalism, we can write down the perturbation expansion for the correlation
functions, and each term in the expansion can be represented by a Feynman
diagram. We consider a scalar field theory on Minkowski space with direct couplings
only, and for the curvature perturbation we consider an effective field theory which contains
derivative couplings. For any given Feynman diagram, we found that the values of
that diagram for the two theories mentioned above are related by a differential operator
which depends only on the form of the couplings. We developed a systematic way for
constructing these operators. With these operators, formulae for correlation functions in
Minkowski space can be translated into formulae for correlation functions in de Sitter
space. In particular, in this work, we will derive recursion relations with this method.
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