Riassunto esame Fisica teorica II, Prof. Rapuano Federico, libro consigliato Quantum Field Theory, Franz Mandl

Fisica teorica II

Lezione 23/11/22

Siamo quindi riusciti ad avere una teoria delle perturbazioni covariante, siamo riusciti anche ad esprimere le particelle come eccitazioni dei campi. Abbiamo quindi una teoria quantistica e relativistica perfettamente consistente. Con questi strumenti siamo in grado di arrivare a qualcosa di misurabile, la sezione d'urto.

Ora abbiamo visto solo diagrammi albero, arriveremo anche a discutere i loop e a calcolare le divergenze causate da momenti non fissati K. La teoria che spiega questi fenomeni è la QED. Iniziamo studiando un caso particolare: lo scattering in un campo esterno. In generale posso separare il campo EM in una parte quantizzata (che abbiamo già trattato) ed una parte classica.

A^μ(x) = A^qμ(x) + A^cμ(x)

E⁻ e⁻

Supponiamo di fare scattering su nucleo e che questo sia talmente pesante che non risente dello scattering e non subisce rinculo (ecco cos'è X sul nucleo).

p = p'

D'altra parte il principio di indeterminazione ci dice che: ΔvΔx ≈ ¹/_M ⇨ il nucleo ha M grande quindi il rinculo va giù come 1/M. Il nucleo produce quindi un campo classico esterno che non risente dello scattering. È quindi statico.

La prima obiezione da fare è che avevamo detto che al primo ordine in un processo di scattering avevamo termini che non davano contributi ad S poiché non conservavano il 4-momento. Questo adesso non è più vero perché il fotone ora è una particella virtuale con         elettroni sono ancora sul loro     shell mentre il          più. La conservazione qui è quindi possibile.

Sfi ≠ 0

Inoltre se  − ∞ è sempre più affidabile una trattazione classica del campo utilizziamo quindi: la trattazione Coulombiana. Posso quindi scrivere il campo classico:

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