{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# ps3 - Physics 509 Relativistic Quantum Field Theory Problem...

This preview shows pages 1–2. Sign up to view the full content.

Physics 509: Relativistic Quantum Field Theory Problem Set 3 Due Friday, 14 October 2011 Reading: Peskin 2.4, 3.1-3.2, 4.1-4.4 11. Anharmonic SHO and Feynman Diagrams I Consider, as usual, the anharmonic oscillator L = 1 2 ˙ φ 2 - 1 2 m 2 φ 2 - λ 4! φ 4 , where λ is a small, positive coupling constant. Write H = H 0 + V , where H 0 is the free ( λ = 0) part of the Hamiltonian, and V is the anharmonic perturbation. Let | 0 be the ground state of H 0 with energy E 0 , while | Ω is the ground state of H with energy E Ω . a) Show that as T (1 - i ε ) for ε an infinitesimal positive quantity, we have 0 | e - iHT | 0 = Ze - iE Ω T , (1) where Z = | 0 | Ω | 2 is the wavefunction renormalization. Also show that in the same limit 0 | T e - i T/ 2 - T/ 2 dt V I ( t ) | 0 = Ze - i ( E Ω - E 0 ) T . (2) b) Using the result in (2) and your ability to calculate SHO Green’s functions (Feynman diagrams), find the shift in the ground state energy E Ω - E 0 due to interactions and the wavefunction renormalization Z up to O ( λ 2 ).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}