M. Cobal, PIF 2006/7
Em interactions
M. Cobal, PIF 2006/7
Electromagnetic Interactions
M. Cobal, PIF 2006/7
Some Examples
M. Cobal, PIF 2006/7
M. Cobal, PIF 2006/7
Electromagnetic Interactions Dimensionless coupling constant specifying strenght of interaction between charged particles and photons
Fine structure costant: (it determines spin-orbit splitting in atomic spectra) Em fields have vector transformation properties. Photon is a vector particle → spin parity JP = 1- In the example seen, the photoelectric cross section (or matrix elements squared) is proportional to a first order process The Rutherford scattering is a second order process
1371
≅α
α
t
Photoelectric effect: absorption (or emission) of a photon by an electron (for an electron bound in an atom to ensure momentum Conservation.
M. Cobal, PIF 2006/7
e-
e+
µ+
µ-
( )
=
ssememem
34~
22πααα
σ
Other examples at higher orders:
−+−+ → µµee
M. Cobal, PIF 2006/7
Self Energy Corrections
M. Cobal, PIF 2006/7
Electron line: represents a”bare” electron Real observable particles: “bare” particles “dressed” by these virtual processes (“self-energy” terms) which contribute to the mass and charge. No limitation on the momentum k of these virtual particles → logarithmically divergent term As a consequence the theoretically calculated “bare” mass or charge (m0, e0) becomes infinite
∫ kdk
Divergent terms of this type are present in all QED calculations.
QED: quantum field theory to compute cross sections for em processes
renormalisability
Gauge invariance
α α e
M. Cobal, PIF 2006/7
“Bare” mass or charge are replaced by physical values e,m as determined from the experiment. A consequence of renormalization procedure: Coupling constants (such α) are not constants: depends on log of measurements energy scale
1/αEM
αE
M (0) =
1/1
37
.03
59
89
5(6
1)
Renormalization
M. Cobal, PIF 2006/7
Running of α
M. Cobal, PIF 2006/7
α runs
M. Cobal, PIF 2006/7
Gauge Invariance
M. Cobal, PIF 2006/7
M. Cobal, PIF 2006/7
Magnetic moment of the electron
M. Cobal, PIF 2006/7