Some knowledge of statistical physics is also useful, but not required. In essence, quantum field theory is the formulation of quantum mechanics that allows one to describe processes that can change the number of particles involved. Because it turns out to very efficiently bake in a few core properties shared by all known physical laws, quantum field theory is also widely used even for systems whose total number of particles never changes. As the course will show, once relativity and quantum mechanics are combined it is a basic fact that all interactions necessarily change the number of particles.

## Photons and Atoms: Introduction to Quantum Electrodynamics

This is related to the reason why antiparticles must exist. See below for the course syllabus and more detailed course information.

The Electromagnetic Field 5. A handout with this information is distributed at the first lecture and will eventually be posted here. Lectures meet Mondays, Wednesdays and Thursdays from to Attendance to the lectures is certainly not compulsory, but if you come I do ask you to pay attention and not disrupt the class with personal conversation or social media.

I will do what I can to ensure that you do not have to gnaw your own arm off to stay awake. The course textbook is Quantum Field Theory in a Nutshell , by Zee, and has been ordered at the bookstore. I will likely use this only loosely and for assignments. It provides an alternative point of view to my lecture notes which I hope to be writing as the class progresses this year. A preliminary version of my notes is here. David Tong also has a good set of lecture notes though at a graduate level at his Cambridge University webpage.

Because I spend half my time at Perimeter Institute I may be hard to find in my office, so it is worth setting up any appointments in advance.

## A Brief Introduction to Quantum Electrodynamics | SpringerLink

I am happy to meet however, so either catch me in class or tell me there that you intend to meet me in my office. I usually do not just hang about the office unless I know students are coming by, so it is best to let me know in advance if you intend to stop in.

Otherwise, feel free to arrange another time with me on an individual basis. I will make a point of being in my office for scheduled appointments, sometimes coming in from off campus, so if you do set up an appointment, please show up! The course work involves completing a roughly weekly assignment. Electron-electron interactions were well-described, but photon-photon interactions were not.

Explaining phenomena like radioactive decay were entirely impossible within even Dirac's framework of relativistic quantum mechanics. Even with this enormous advance, a major component of the story was missing. The big problem was that quantum mechanics, even relativistic quantum mechanics, wasn't quantum enough to describe everything in our Universe. If you have a point charge and a metal conductor nearby, it's an exercise in classical physics alone to calculate the electric field and its strength at every point in space.

In quantum mechanics, we discuss how particles respond to that electric field, but the field itself is not quantized as well. This seems to be the biggest flaw in the formulation of quantum mechanics. Think about what happens if you put two electrons close to one another. If you're thinking classically, you'll think of these electrons as each generating an electric field, and also a magnetic field if they're in motion.

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Then the other electron, seeing the field s generated by the first one, will experience a force as it interacts with the external field. This works both ways, and in this way, a force is exchanged. This would work just as well for an electric field as it would for any other type of field: like a gravitational field. Electrons have mass as well as charge, so if you place them in a gravitational field, they'd respond based on their mass the same way their electric charge would compel them to respond to an electric field.

Even in General Relativity, where mass and energy curve space, that curved space is continuous, just like any other field.

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If two objects of matter and antimatter at rest annihilate, they produce photons of an extremely specific energy. If they produce those photons after falling deeper into a region of gravitational curvature, the energy should be higher. In General Relativity, the field carries energy away in waves: gravitational radiation. But, at a quantum level, we strongly suspect that just as electromagnetic waves are made up of quanta photons , gravitational waves should be made up of quanta gravitons as well.

## Photons and Atoms: Introduction to Quantum Electrodynamics

This is one reason why General Relativity is incomplete. Fields push on particles located at certain positions and change their momenta. But in a Universe where positions and momenta are uncertain, and need to be treated like operators rather than a physical quantity with a value, we're short-changing ourselves by allowing our treatment of fields to remain classical. The fabric of spacetime, illustrated, with ripples and deformations due to mass. A new theory must be more than identical to General Relativity; it must make novel, distinct predictions. As General Relativity offers only a classical, non-quantum description of space, we fully expect that its eventual successor will contain space that is quantized as well, although this space could be either discrete or continuous.

That was the big advance of the idea of quantum field theory , or its related theoretical advance: second quantization. All of a sudden, processes that weren't predicted but are observed in the Universe, like:. The major way this framework differs from quantum mechanics is that not merely the particles, but also the fields are quantized.

Although physicists typically think about quantum field theory in terms of particle exchange and Feynman diagrams, this is just a calculational and visual tool we use to attempt to add some intuitive sense to this notion. Feynman diagrams are incredibly useful, but they're a perturbative i.

But the motivation for quantizing the field is more fundamental than that the argument between those favoring perturbative or non-perturbative approaches. With quantum field theory and further advances in their applications, everything from photon-photon scattering to the strong nuclear force was now explicable. A diagram of neutrinoless double beta decay, which is possible if the neutrino shown here is its own antiparticle. This is an interaction that's permissible with a finite probability in quantum field theory in a Universe with the right quantum properties, but not in quantum mechanics, with non-quantized interaction fields.

The decay time through this pathway is much longer than the age of the Universe. At the same time, it became immediately clear why Einstein's approach to unification would never work. Motivated by Theodr Kaluza's work, Einstein became enamored with the idea of unifying General Relativity and electromagnetism into a single framework. In modern physics, the classical vacuum of tranquil nothingness has been replaced by a quantum vacuum with fluctuations of measurable consequence.

In The Quantum Vacuum, Peter Milonni describes the concept of the vacuum in quantum physics with an emphasis on quantum electrodynamics. He elucidates in depth and detail the role of the vacuum electromagnetic field in spontaneous emission, the Lamb shift, van der Waals, and Casimir forces, and a variety of other phenomena, some of which are of technological as well as purely scientific importance.