|
|
|
N.D. Hari Dass |
|
Institute of Mathematical Sciences |
|
Chennai |
|
|
|
|
N.D. Hari Dass |
|
Institute of Mathematical Sciences |
|
Chennai |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Remarkably, if one plotted the angular momentum
of the state vs mass(or square of the mass) they all fell on families of
parallel straight lines. |
|
Nielsen, Nambu, Goto, Susskind in 1968 made the
astonishing suggestion that a relativistically rotating string had states
of excitation this spectrum! |
|
|
|
|
|
|
The relativity theory says that there is an
antiparticle for each particle. |
|
The antiparticle of u-quark with electric charge
2/3 is u-bar antiquark with charge
-2/3. |
|
The pion in this model is made up of u and d-bar
. |
|
|
|
|
If there were no forces between quarks (anti –
quarks) they would just fly apart without forming hadrons like protons,
pions, neutrons etc… |
|
The next important question is : what is the nature
of these forces? |
|
Are they attractive, repulsive … |
|
How do they vary with distance and what is their
dependence on the quark type? |
|
|
|
|
|
It turns out that fully consistency with the
hadrons requires that each quark type comes in 3 species which will
symbolically be denoted as red , blue and green . |
|
Observed hadrons only correspond to combinations
that are white. |
|
For example : proton is u(red), u(blue) and d(green). |
|
The analog of photons are gluons and they come
in 8 colours. |
|
|
|
|
|
QCD is a non-Abelian Gauge Theory. |
|
The gauge group is SU(3). |
|
The Quarks carry the fundamental representation
3. |
|
The Gluons, which transmit the forces between
quarks, carry the adjoint representation 8. |
|
3 has triality, 8 has no triality. |
|
The theory has defied analytical results despite
the best efforts for more than 25 years. |
|
It is an outstanding problem of theoretical
physics. |
|
|
|
|
|
|
|
|
|
|
First let us look at electrodynamics described
by Maxwell’s equations . |
|
|
|
|
Now we have 8 vector potentials and 8 scalar
potentials: |
|
|
|
|
|
|
|
It should be possible to release quarks by supplying sufficient energy to protons
and neutrons. |
|
But no quarks were liberated even in very high
energy collisions! |
|
|
|
|
|
|
“Mama Mia, if you don’t see something you should
be seeing, there must be a very deep reason”---- N. Testa |
|
The theory of Quarks must be such that they can never
be free! |
|
|
|
|
‘t Hooft, Mandelstam, Nambu: A thin flux tube connects
the quarks and keeps them from being liberated. |
|
This can happen to magnetic monopoles submerged
in a superconductor. |
|
Dual Superconductor Picture. |
|
Can this be proven in Quantum Chromodynamics
(QCD), the best candidate theory of Quarks and Gluons? |
|
|
|
|
|
Instead of charges consider magnetic monopoles: |
|
|
|
|
Discretise the space-time manifold. |
|
Continue from Minkowski signature to Euclidean
signature. |
|
The Quantum Field Theory is mapped exactly into Classical
Statistical Mechanics in Four spatial dimensions. |
|
Simulate that numerically. |
|
|
|
|
|
Due to a path breaking development in algorithms
it is now possible to measure extremely tiny quantities on the lattice. |
|
The flux tube is actually a string ! It is not
rigid but can actually fluctuate like a string. |
|
Even its states of excitations can be probed
numerically and they indeed look like hadronic states. |
|
|
|
|
|
|
If quarks are not too heavy, the flux tube can
snap. |
|
If quarks carry adjoint charge no flux tube
should be formed. |
|
|
|
|
What causes the flux tube formation? |
|
Colour Monopoles? |
|
Colour Vortices(Z3)? |
|
Instantons and topological charges? |
|