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