FromQuantumMechanicsto
Lagrangian Densities
Just as there is no derivation of quantum mechanics
from classical mechanics, there is no derivation of
relativistic field theory from quantum mechanics. The
route from one to the other is based on physically
re
The
Theelectromagnetic(EM)field
servesasamodelforparticlefields
=chargedensity,J =currentdensity
4vectorrepresentationofEMfield
A is the vector potential
istheelectrostaticpotential;
c=speedoflight
HowEandBarerelatedto
DerivationofE
Wave
Waveequationsfo
Standard
StandardModelRequires
TreatmentofParticlesasFields
Hamiltonian, H=E, not Lorentz invariant.
QM not a relativistic theory.
Lagrangian, TV, used in particle physics.
Creation and annihilation must be described.
Relativistic Quantum Field theor
Ei
Eightfold Way (old model)
GELL MANN - NISHIJIMA FORMULA
RELATING CHARGE TO ISOSPIN
Q = I3 + (B + S)
B = baryon number, S = strangeness
Q = charge (in units of e, the electronic charge)
Y = B + S was called hypercharge.
I3
= z component of
ISOSPIN
Iso
I
the
the forces
electromagnetic (photon)
weak ( W+ W- Z0)
strong (8 gluons)
gravitational ( graviton not yet observed)
all have spin = 1 (or 2 for graviton)
they are bosons
some
some particle
physics
physics puzzles
While we have learned a great deal in
t
Physics
Physics 357/457
Spring 2011
(Chapter 1: getting started)
the elementary particles
the forces
the model
how can we understand it?
Elementary
Elementary particle:
an entity not able to be further decomposed
tit
with a unique set of properties
mass,
Gauge
GaugeInvarianceand
ConservedQuantities
Noether's theorem was proven by German
mathematician, Emmy Noether in 1915 and
published in 1918. Noether's theorem has become
a fundamental tool of quantum field theory and
has been called "one of the most imp