The path-integral is a formulation of quantum mechanics equivalent to the standard one, offering a new point oh view of the subject which is more intuitive than the usual approach. In this work we firstly present the Dirac orginal idea and then we describe how Feynman developed it. Therefore we apply the path-integral approach to the case of a scalar field theory, introducing the concept of generating functional. Finally we illustrate two alternative representations of the generating functional, dual to the Schwinger formalism, discussing how they lead to a realation with the Hermite polynomials. We also introduce the Schwinger-Dyson equation and express it through the representations introduced.

The generating functional for scalar field theories

Ricci, Lorenzo
2016/2017

Abstract

The path-integral is a formulation of quantum mechanics equivalent to the standard one, offering a new point oh view of the subject which is more intuitive than the usual approach. In this work we firstly present the Dirac orginal idea and then we describe how Feynman developed it. Therefore we apply the path-integral approach to the case of a scalar field theory, introducing the concept of generating functional. Finally we illustrate two alternative representations of the generating functional, dual to the Schwinger formalism, discussing how they lead to a realation with the Hermite polynomials. We also introduce the Schwinger-Dyson equation and express it through the representations introduced.
2016-09
22
path-integral, scalar field, Schwinger-Dyson equation, Hermite polynomials
File in questo prodotto:
File Dimensione Formato  
Tesi_L_Ricci.pdf

accesso aperto

Dimensione 2.28 MB
Formato Adobe PDF
2.28 MB Adobe PDF Visualizza/Apri

The text of this website © Università degli studi di Padova. Full Text are published under a non-exclusive license. Metadata are under a CC0 License

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12608/28415