Lectio PraecursoriaTapio Salminen

19th August 2011

University of HelsinkiDepartment of Physics

NoncommutativeQuantum Field Theory:

Problemof Time

and SomeApplications

NoncommutativeQuantum Field Theory

Part 1

Science is about observing

predictingand

MicroscopeLength, l ~ 10-5 cmEnergy, E ~ 10-9 GeV

LHCl ~ 10-17cmE ~ 103GeV

Planck scalel ~ 10-33cmE ~ 1019GeV

Uncertainty of space-time coordinates:

or, equivalently:

Commutator

“Space-spacenoncommutativity”

“Time-spacenoncommutativity”

Noncommutative space(-time)

Part 2

Problem of Time

CausalityCommutative space-time

Cause

EffectFuture

Past

Now

CausalitySpace-space noncommutativity

Effect

Cause

Cause

EffectImpossibilityof making

predictions

CausalityTime-space noncommutativity

Part 3

and Some Applications

Commutative space-timeMagnetic monopole

Dipole Monopole

Quantization of electric and magnetic charge

Magnetic monopoleCommutative space-time

magnetic charge

electric charge

Observer-dependence introduced

Magnetic monopoleSpace-space noncommutativity

Noncommutative effect in the quantization condition

Magnetic monopoleSpace-space noncommutativity

Thank you