The Feynman path integral, from the harmonic oscillator to quantum electrodynamics

The Feynman path integral, from the harmonic oscillator to quantum electrodynamics (2022)

Authors:
- Tonhon, Rafael Carlos Silva
- Mendes, Tereza Cristina da Rocha (Orientador)
USP affiliated author: TONHON, RAFAEL CARLOS SILVA - IFSC
School: IFSC
Subjects: INTEGRAIS DE FEYNMAN; MECÂNICA QUÂNTICA; SIMULAÇÃO (ESTATÍSTICA); MÉTODO DE MONTE CARLO; ELETRODINÂMICA QUÂNTICA
Language: Inglês
Abstract: The Feynman path-integral formulation of quantum mechanics is developed. The math- ematical framework is worked out from Schrödinger’s equation, illustrating the compati- bility of the two formulations. We introduce the sum over all paths, known as the kernel K, and discuss its implications for events occurring in succession. We compute the kernel for quadratic Lagrangians. Then, making use of imaginary time, we consider the discrete version of the kernel, known as the Euclidean path integral, and use it to solve the (quan- tum) harmonic and anharmonic oscillators through numerical Monte Carlo simulations. Lastly, we use the framework to quantize the electromagnetic field, as a motivation to discuss perturbation theory via Feynman diagrams.
Imprenta:
- Place of publication: São Carlos
- Date published: 2022

Tipo	Nome	Link
	Rafael Carlos Silva Tonho...	Direct link

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ABNT

TONHON, Rafael Carlos Silva. The Feynman path integral, from the harmonic oscillator to quantum electrodynamics. 2022. Trabalho de Conclusão de Curso (Graduação) – Instituto de Física de São Carlos, Universidade de São Paulo, São Carlos, 2022. Disponível em: https://bdta.abcd.usp.br/directbitstream/00086997-dc73-462f-a7be-80f6e0ab7dac/Rafael%20Carlos%20Silva%20Tonhon.pdf. Acesso em: 25 abr. 2024.
APA

Tonhon, R. C. S. (2022). The Feynman path integral, from the harmonic oscillator to quantum electrodynamics (Trabalho de Conclusão de Curso (Graduação). Instituto de Física de São Carlos, Universidade de São Paulo, São Carlos. Recuperado de https://bdta.abcd.usp.br/directbitstream/00086997-dc73-462f-a7be-80f6e0ab7dac/Rafael%20Carlos%20Silva%20Tonhon.pdf
NLM

Tonhon RCS. The Feynman path integral, from the harmonic oscillator to quantum electrodynamics [Internet]. 2022 ;[citado 2024 abr. 25 ] Available from: https://bdta.abcd.usp.br/directbitstream/00086997-dc73-462f-a7be-80f6e0ab7dac/Rafael%20Carlos%20Silva%20Tonhon.pdf
Vancouver

Tonhon RCS. The Feynman path integral, from the harmonic oscillator to quantum electrodynamics [Internet]. 2022 ;[citado 2024 abr. 25 ] Available from: https://bdta.abcd.usp.br/directbitstream/00086997-dc73-462f-a7be-80f6e0ab7dac/Rafael%20Carlos%20Silva%20Tonhon.pdf