# Quantum Field Theory 

Hi I've learned a lot of physics over the years ... Some of it was dry (introductory optics was booooring) but most of it was pretty cool. One of the single most interesting topics I studied however, was a physical theory called 'quantum field theory', whose aim was to unite the worlds of quantum mechanics with the idea of fields and of special relativity to create a really powerful set of tools for describing phenomena at the smallest scales.

#### What's a field?

In physics, a field is simply an entity which can be described by a number (or series of numbers) distributed in space. For example, we can consider the temperature across a room as being what is known as a 'scalar field' (scalar = 1 number to describe the field at each point in the room) or we can consider the wind across a country as a 'vector field' (vector = (x,y,z) direction of the wind, for example drawn by an arrow, at each point across the country). Fields crop up a whole lot in physics, and in fact the study of them mathematically is known as 'field theory'.

Further to this, there is a distinction in physics between what are known as 'classical' or 'quantum' field theories. Classical field theories include the theory of electromagnetism, or of general relativity (gravity). They are denoted 'classical' by the fact that they describe classical or pre-quantum physics, not that they are necessarily any simpler or don't still provide fertile research ground.

The whole aim of a classical field theory, is to describe mathematically the properties of a given field (or set of fields) and how they interact with matter. For example, electromagnetic field theory provides a description of how electric and magnetic fields interacting with objects which possess charge, such as electrons and protons. General relativistic field theories describe how objects with mass interact with one another and create changes in the gravitational field through their distortion of spacetime.

So, that's a field theory, but what make 'quantum' field theories so interesting?

#### What's a quantum field?

The description of the behaviour of very small objects in the universe is  often accomplished by using the tools of quantum mechanics. Quantum mechanics tells us that the world of the very small (atoms, nuclei, electrons, protons, quarks etc) is a world in which the normal rules of motion do not apply. For example, electrons are both waves and particles at the same time and they can be in two places at once. What became clear through the 20th century however, was that quantum mechanics was not providing a complete picture of behaviour at very small scales for a variety of phenomena.

For example, the electromagnetic (EM) field around a point charge, for example the electron, was a bit of a conundrum. Physicists like Jordan, Heisenberg and Born had developed a method for creating a quantum field theory for the free EM field in the mid 1920s (think photons). This was an excellent start but it didn't have the concept of interactions in it, so if you plopped an electron into your system you couldn't really say much about it.

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