Chapter5_11 - time allowed by the uncertainty principle The...

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PHY3063 R. D. Field Department of Physics Chapter5_11.doc University of Florida QED and the Quantum Vacuum Q em γ e - e - e - e - Q em Momentum-Space time p 1 p 2 p 3 p 4 ~ ~ Space-like virtual photon Q em γ p 1 p 2 Vertex (QED) p 1 = p 2 +q q ~ ~ ~ ~ ~ ~ 4-Momentum Space: At a vertex additive quantum numbers are conserved and the 4-momentum is conserved , but particles may or may not be on their mass shell . 2 2 2 ~ m p p E p = = r r (“on shell” = “real” particle) 2 2 2 ~ m p p E p = r r (“on shell” = “virtual” particle) The invariant mass of a “virtual” particle can by positive ( i.e. time-like) or negative ( i.e. space-like). The Quantum Vacuum: The uncertainty principle makes the vacuum a very complicated object! The vacuum is an object with zero energy. But there is an uncertainty in the zero and everything that is not forbidden by other conservation laws happens for short times t h/ E , where the E is the energy of the state. The energy E is borrowed from the uncertainty principle, but it can only be borrowed for the
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Unformatted text preview: time allowed by the uncertainty principle. The vacuum we live in is full there “virtual” states being “born” and then “dying”. The “classical vacuum” containing nothing does not exist! Real particles moving through the quantum vacuum interact with the virtual states and are affected by the vacuum. If you add energy to the vacuum a virtual state can absorb it and thereby become “real”, since energy and momentum can now be conserved. For example, it is possible to collide two photons and produce an electron-positron pair, γ + γ → e + + e-, and you can produce a proton-antiproton pair by annihilating and electron-positron pair, p p e e + → + − + . e + e-Time Space ∆ t ~ h/(2m e c 2 ) QED = Quantum Electrodynamics Feynman Diagram e-+ e-→ e-+ e-Virtual particle-antiparticle pair!...
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