Build a basic model

- Introduce the particle electon, muon, quarks…
- Particles must follow the Dirac equation
- Laws of relativity
- Mass can converted to energy
- Particles can be created as long as charge and other quantum numbers are conserved
- Not allowed to produce a positive charge by itself but +1 and -1 okay since total is zero.
- Laws of QM are present
- Wave equation
- Interference by defining wf amplitudes
- Measurement based o the square of the amplitudes
- Introduce forces Ad Hoc
- E&M follows Maxwell equations
- Strong force QCD
- Weak can be combined with E&M è Electroweak
- Gravtity (unable to add QM) remains outside of the Stanard Model
- So weak on the subatomic scale that it can be neglected

Now you see which states are bound and are stable and interact and ………

In principle all of the real world physics should be derivable from this platform.

There are many more stories about extrapolating the underlying theory to the solution of an interesting problem,

Can we predict the where the charge of a proton is located based on the movement of the quarks ?

Can we predict the masses of the particles that we observe: proton, neutron, pion, kaon… ?

Can we predict yet unseen particles and how to look for them ?

The questions may be similar to extrapolation from atomic physic to chemistry and then to biology.

We can describe the hydrogen atom in a detailed and fairly complete way.

We can understand the overriding chemistry of the periodic table based on

What are the differences and similarities between quark-lepton particles and the interaction particles photon-gluon-W

Fermions è spin ½ and therefore don’t occupy same space. { We identify this characteristic a matter}

· Two tennis balls cannot be at the same place.

Bosonsè spin 1 particles and overlap

· Two words or sounds can be at the same place.

So we can write down a set of equations for all particles è **Free**** particle
solutions**

·
Then we add interactions

Feynman introduced a lovely pictorial representation of the particle world.

_{}

QED vertex

Electric and magnetic fields interact with moving charges.

A+BèC+D

Two electric charges can interact by creating a field and then the field interacts with the particle.

Given the verticies (INTERACTIONS)
all types of diagrams can be written down. No requirements on the exchanged
particle. Any particleconsistent with the **conserved quantities** can be exchanged.

Physics recognizes that some things are not changed == conserved, invariant..

SUMMARY

All particle satisfy a free particle equation

Introduce Ad Hoc the particles

Particles can interact

Introduce Ad Hoc the interactions

**Invariance,
transformations and symmetry.**

Define each one.

***********************************************************************

Einstein

And accelerating region cannot be distinguished from a gravitational field.

Elevator on earth

Elevator dragged through space in a rocket ship.

Noether’s Theorem:

An example of the early use of symmetry to constrain the
laws of physics is Noether’s theorem:

Every symmetry => conserved quantity.

•
Translation – conservation of momentum

•
Rotation – conservation of angular momentum

•
Time translation – Energy conservation

Space time curvature explains gravity, one of the fundamental forces.

Curvature is the process of twisting each point in space time by an amount.

This local variation
in the curvature results in a change in motion that is equivalent to a force.

LOCAL TRANSFORMATION

Curvature can be thought of as rotating your coordinate
system by different amounts as you move around your space.

Applying your Poincare
Transformations as a function of your position

Weyl tried to find a geometric
interpretation for the electric force. Added space
stretching.

setting the **GAUGE** (or
spacing).

Failed until the transformations were
applied to quantum states.

GLOBAL PHASE CHANGE implies conservation of electric charge.

LOCAL
PHASE CHANGE requires the introduction of electromagnetic
interactions.

Transformations determine the interactions.

Gravity == Poincare

QCD == SU3 (color)

QED == U1 (phase)

Electroweak == SU2xU1 (Weinberg Salam)

{u,d} {e, ν }

There has emerged a very elegant and compelling view of the
fundamental laws of nature.

The symmetries and associated transformations of our world
may serve as the starting point for our understanding.

The application of these ideas is riddled with mathematical
pitfalls and details that are quite complex.

Based on the success of SU2xU1 perhaps one should start with a larger group of transformations

Example

Poincare group (

Rotations

Translations

Boosts

SuperSymetry SU(5)

This divides into subgroups mentioned above SU(3), SU(2) ….

Excerpts from Brian Green’s web site http://superstringtheory.com/basics

&&&&&&

Einstein
took a very bold step, and reached out to some radical new mathematics called non-Euclidean geometry, where the Pythagorean rule is
generalized to include metrics with coefficients that depend on the spacetime coordinates in the form

where repeated indices imply a sum over all space and time
directions in the chosen coordinate system. Einstein extended the idea of Lorentz invariance to general coordinate
invariance, proposing that the values of physical observables should be
independent of a choice of coordinate system used to chart points in spacetime. He called this new theory the General
Theory of Relativity.

In Einstein's new theory, spacetime
can have curvature, like the surface of a beach ball
has curvature, compared to the flat top of a table, which doesn't. The
curvature is a function of the metric g_{ab} and its first and second
derivatives. In the Einstein equation

the spacetime curvature (represented by R_{mn} and R) is
determined by the total energy and momentum T_{mn} of the
"stuff" in the spacetime like the planets,
stars, radiation, interstellar dust and gas, black holes, etc.

The Einstein equation is not strictly a departure from
classical field theory, and the Einstein equation can be derived as the
solution to Euler-Lagrange equations that represent the stationary point, or extremum, of the action

&&&&&

But particles in string theory arise as excitations of the
string, and included in the excitations of a string in string theory is a
particle with **zero mass and two units
of spin**.

the particle that would carry the gravitational
force would have **zero mass and two
units of spin**. This has been known by theoretical physicists
for a long time. This theorized particle is called the **graviton**.

This led early string theorists to propose that string theory be
applied not as a theory of hadronic particles, but as
a theory of **quantum gravity. **

One can add a graviton to quantum field theory by hand, but the
calculations that are supposed to describe Nature become useless. This is
because, as illustrated in the diagram above, particle interactions occur at a
single point of spacetime, at zero distance between
the interacting particles. For gravitons, the mathematics behaves so badly at
zero distance that the answers just don't make sense. In string theory, the
strings collide over a small but finite distance, and the answers do make
sense.

This
doesn't mean that string theory is not without its deficiencies. But the zero
distance behavior is such that **we can
combine quantum mechanics and gravity**, and we can talk sensibly
about a string excitation that carries the gravitational force.

This
was a very great hurdle that was overcome for late 20th century physics, which
is why so many young people are willing to learn the grueling complex and
abstract mathematics that is necessary to study a quantum theory of interacting
strings.

In 26 spacetime dimensions, these extra unphysical states wind up disappearing from the spectrum. Therefore. bosonic string quantum mechanics is only consistent if the dimension of spacetime is 26.