document: Another remarkable feature of the quantum field treatment can be revealed from the investigation of the vacuum state. For a classical field, vacuum is realized by simply setting the potential to zero resulting in an unaltered, free evolution of the particle's plane wave (|ψI〉=|ψIII〉=|k0〉). In the quantized treatment, vacuum is represented by an initial Fock state |n0=0〉 which still interacts with the particle and yields as final state |ΨIII〉 behind the field region(19)|ΨI〉=|k0〉⊗|0〉⇒|ΨIII〉=∑n=0∞t0n|k−n〉⊗|n〉 with a photon exchange probability(20)P0,n=|t0n|2=1n!e−Λ2Λ2n The particle thus transfers energy to the vacuum field leading to a Poissonian distributed final photon number. Let's consider, for example, a superconducting resonant circuit as source of the field. The magnetic field along the axis of a properly shaped coil is well approximated by the rectangular form. A particle with a magnetic dipole moment passing through the coil then interacts with the circuit and excites it with a measurable loss of kinetic energy even if the circuit is initially uncharged and there is classically no field it can couple to. The phenomenon that vacuum in quantum field theory does not mean to “no influence” as known from Casimir forces or Lamb shift is clearly visible here as well.
doc_bio_tags: O O O O O B I I O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B I B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O B I I O O O O O O B I O O O O O B I I O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B I I I I O O O O O O
extractive_keyphrases: casimir forces or lamb shift magnetic field particle properly shaped coil quantized treatment quantum field treatment superconducting resonant circuit vacuum
abstractive_keyphrases: particle's plane wave vacuum state