# ps02 - mass 2 The Lagrangian density of the 4 theory for a...

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Physics 651 – Problem Set 2 (due 9/15/03) Read PS 9 . 2 and 9 . 3 , to p.294. Optional (*) : read Chapter 8. 1. The typical collision energy in present high-energy scattering experiments is E 100 GeV, where 1 GeV = 10 9 eV is called one giga-electron-volt. Estimate the length scale corresponding to the resolution of such a high-energy collision, and compare it with the Compton wave length of a proton. A typical collision energy in atomic physics is E 1 eV. Estimate the length scale and the time scale in such an interaction. What are the energy/mass (known as the Planck scale/mass) and time scale of the Newton’s gravitational constant G ? Compare the Planck mass to the electron
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Unformatted text preview: mass. 2. The Lagrangian density of the 4 theory for a real scalar eld is L = 1 2 ( x ) ( x )-m 2 2 ( x ) 2- 4! ( x ) 4 Let Z[J] be the generating functional of all correlation functions, or Feynman di-agrams, of this theory. Write down the 0- and 2-point correlation functions up to the leading order, and the 4-point correlation function up to the 2 order. (Do not evaluate the integrals if they appear. We shall discuss them later.) Hint: It is very useful to draw the Feynman diagrams. 3. Problem 9.2 (a), (b) and (c). 1...
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