Analisis Penampang Lintang Hamburan Bhabha Dalam Elektrodinamika Kuantum

Yafi, Izzudin Ali (2025) Analisis Penampang Lintang Hamburan Bhabha Dalam Elektrodinamika Kuantum. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Hamburan Bhabha merupakan salah satu proses interaksi partikel elementer dalam ranah elektrodinamika kuantum. Dalam proses ini, elektron dan positron di keadaan awal terhambur dan menjadi elektron positron di keadaan akhir (e+ + e− → e+ + e−). Penelitian ini dilakukan dengan pertama melakukan prosedur kuantisasi kedua pada medan Klein-Gordon, Dirac, dan medan elektromagnetik. Dalam kuantisasi kedua, medan dipromosikan menjadi operator dan memenuhi relasi komutasi atau antikomutasi pada waktu yang sama. Medan-medan tersebut diekspansikan dalam ekspansi Fourier yang setiap mode ekspansinya merupakan osilator harmonik dan koefisien ekspansinya merupakan operator kreasi dan anihilasi. Perhitungan relasi komutasi atau antikomutasi pada waktu yang berbeda membawa kita pada konsep propagator, yang menyatakan penciptaan partikel di suatu titik disertai dengan penjalaran ke titik lain dan dimusnahkan di titik lain tersebut. Interaksi antar medan dirumuskan dengan mendefinisikan matriks S dan perhitungan disederhanakan menggunakan teorema Wick. Menggunakan ekspansi matriks S untuk interaksi elektromagnetik, elektrodinamika kuantum kemudian dirumuskan dengan menggambarkan semua diagram Feynman yang muncul pada ekspansi matriks S orde pertama dan kedua. Dari diagram-diagram tersebut, terdapat dua diagram yang menyatakan proses hamburan Bhabha. Dengan menentukan amplitudo Feynman kedua diagram, formula penampang lintang diferensial hamburan Bhabha dapat ditentukan. Dari formula tersebut, didapat bahwa penampang lintang diferensial menjadi infinit pada sudut hambur yang sangat kecil (θ ≈ 0). Perilaku ini mencerminkan jangkauan interaksi elektromagnetik yang infinit.
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Bhabha scattering is one of the elementary particle interaction processes in the realm of quantum electrodynamics. In this process, an electron and a positron in the initial state scatter and become an electron and a positron in the final state (e+ +e− → e+ +e−). This study is conducted by first performing second quantization on the Klein-Gordon, Dirac, and electromagnetic fields. In second quantization scheme, the fields are promoted to operators that satisfy commutation or anticommutation relations at equal times. These fields are expanded in Fourier series, where each mode of expansion acts as a harmonic oscillator and the expansion coefficients become creation and annihilation operators. The calculation of commutation or anticommutation relations at different times leads to the concept of the propagator, which describes the creation of a particle at one point, its propagation to another point, and annihilation at that point. The interaction between fields is formulated by defining the S-matrix, and calculations are simplified using Wick’s theorem. Using the S-matrix expansion for electromagnetic interactions, quantum electrodynamics is then formulated by representing all Feynman diagrams arising from the first- and second-order expansions of the S-matrix. Among these diagrams, there are two diagrams that correspond to the Bhabha scattering process. By determining the Feynman amplitudes of both diagrams, the formula for the differential cross section of Bhabha scattering can be derived. From this formula, it is found that the differential cross section becomes infinite at very small scattering angles (θ ≈ 0). This behavior reflects the infinite range of electromagnetic interactions.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Diagram Feynman, Elektrodinamika kuantum, Hamburan, Penampang lintang, Cross section, Feynman diagram, Scattering, Quantum electrodynamics.
Subjects:	Q Science > Q Science (General) > Q180.55.M38 Mathematical models Q Science > QC Physics > QC20.7.F67 Fourier transformations Q Science > QC Physics > QC631.D29 Electrodynamics.
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Physics > 45201-(S1) Undergraduate Thesis
Depositing User:	Izzudin Ali Yafi
Date Deposited:	24 Jul 2025 08:34
Last Modified:	24 Jul 2025 08:34
URI:	http://repository.its.ac.id/id/eprint/121480

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