Lecture: April 1, 2020

The Matter Of Antimatter: Answering The Cosmic Riddle Of Existence: Brian Green and then Discussion with Brian Greene as a the moderator

Quantum Field Theory (QFD) – The Ultimate Theory of Quantum Particles

Firstly, trying to picture electron as a wave causes lot of headaches... These waves are clearly not ordinary waves – they are not like ripples on the surface of water... Despite all this, Schodinger¨ wave theory or its relativisic version, Dirac theory, has been very successful. However, at end of 1920, physicist realized that it told only part of the truth...

(a) It only describes how particles move. It cannot handle physics when particles are created and destroyed, as happens when a radioactive element decays or when electron and positron annihilate each other, creating photons....

(b) Recall the g- factor :

e e ~ Magnetic moment of an electron is µ = g m S = g m 2 .

Dirac theory predicted g = 2. This was good to explain all the spilling of energies.

Shelter island conference in 1947 Organizer was Robert Oppenheimer. The cost of the conference was about 890 dollars. All well known physicists were invited...

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Physicist Rabi’s precise measurement of g-factor showed that g is ONLY APPROXIMATELY equal to 2. He found the g value to be equal to g = 2.00244 He know the precise error bars of his experiment and was certain that g equal to 2 is only an approximation. This led to the notion of Quantum Fields. (1920)s: Particles are described by Wave Equations. This cannot describe creation and annihilation of particles (1930)s : Particles are described by Fields: Quantum Field Theory– It can describe creation-annihilation of particles.

In this description, instead of talking about particles, one talks about quantum fields. That is, when you think of electrons, you think about some field associated with it that pervades the entire space, like the electric, the magnetic field or the gravitational field.

QFD treats particles as excited states, also called quanta, of their underlying fields, which are in a sense more fundamental than the basic particles.

2 WHAT IS QED ???

Richard Feynman called it “the jewel of physics” for its extremely accurate predictions of quantities like the the g-factor of the electron. This explained the fine structure of H-spectrum known as and the Lamb shift . In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons .

However, as Feynman points out, it fails totally to explain why particles such as the electron have the masses they do. “There is no theory that adequately explains these numbers. We use the numbers in all our theories, but we don’t understand them – what they are, or where they come from. I believe that from a fundamental point of view, this is a very interesting and serious problem.

FEYNMAN DIAGRAM

Interactions between particles can be visually represented by Feynman diagrams. Creation and destruction of particles is adding or removing quanta from the field. Earlier versions of quantum field theory had lot of problems... like infinity occurs due to electrons interacting with its own electromagnetic field... Then physicists realized that this problem can be solved and theory provides a new way to understand forces between two particles... like repulsion between two electrons.

In 1932, Bethe and Fermi suggested that repulsion between two electrons is due to exchange of photons between two electrons. These photon cannot be observed and are called virtual photons.

This is wonderful... photon is not only simply the quantum particle of light or electromagnetic waves, it is the ”carrier” of the electromagnetic force.

3 Quantuam Electro Dynamics or QED

Three physicists independently developed the complete theory of QED – the quantum electrodynamics. They are two American physicists Richard Feynman and Julian Schwinger and Japanese physicist Sin-Itiro Tomonaga. Interestingly, these theories that on the surface looked very different were shown to be equivalent by Freeman Dyson. These 3 physicists shared Nobel prize in 1965.

Let us understand this using Feynman’s way ... Imagine two electrons interacting, shown with the Feynman diagram... The wavy line shows the exchange of photons between this. This is a way to describe the

4 interaction between two electrons. Electron also interacts with its own electromagnetic field. This corresponds to electron absorbing a photon. if you take this second diagram and calculate the magnetic moment of the electron, it gives the g-factor equal to 2. Now comes the real magic: If we add more photons, it increases the value of this g-factor. More photons you add, bigger the g gets, but this increase occurs at higher decimal places. Roughly, to with every decimal place, you add another photon... Well, this way, you can predict g to as many decimal places as you like. Here is the ultimate test of the theory: g = 2.00231930436182... measured in the experiment. And every decimal place is predicted correctly by the theory...

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