{"id":608,"date":"2022-09-22T11:04:54","date_gmt":"2022-09-22T10:04:54","guid":{"rendered":"https:\/\/pulpscience.de\/?p=608"},"modified":"2022-09-22T20:43:47","modified_gmt":"2022-09-22T19:43:47","slug":"what-is-quantum-field-theory","status":"publish","type":"post","link":"https:\/\/pulpscience.de\/de\/2022\/09\/22\/what-is-quantum-field-theory\/","title":{"rendered":"What is Quantum Field Theory?"},"content":{"rendered":"
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Quantum Field Theory (QFT) is a unified language, a toolbox, a set of techniques for modern theoretical physicists. And it has had tremendous success with it’s, in my eyes, brightest achievement being the standard model of particle physics, but also the explanation of superconductivity, Hall effect and others. Important things!<\/p>\n

So what is it?
\nFirst, we have to go through some words again.
\nWhat is a field? Imagine a hilly landscape with a coordinate grid beneath it. The ‘field’ in this case could be the height of each point above the ground (i.e. a number). An arrow (a vector, really) at each point pointing in the wind’s direction would also be a field. More abstractly speaking, a field assigns to each point in space (and possibly time) a value, like a number, vector or something else.
\nA QFT now just naturally incorporates quantum fluctuations and, thus, describes quantum fields.
\nAn absurdly short attempt to explain quantum fluctuations (stay tuned for a possible post on quantum mechanics): Due to nature’s inherent property of uncertainty, i.e. the inability to determine the position and velocity of a particle with perfect precision, this uncertainty carries over to our field of the QFT. So we call this ‘uncertainty’ a quantum fluctuation, as it randomly changes the content, like the height or arrow, of the field. You can really imagine it as a hilly landscape that randomly fluctuates, but only on a very small scale.<\/p>\n

Regarding the particles we are comprised of. The key to QFT is to treat particles as if they were excitations of quantum fields (read: “peaks in the landscape”). The mathematics underlying this proclamation are a bit dry, so let us jump to the technique by which physicists try to describe nature using wobbly fields: path integrals.
\nPath integrals are a real nightmare for mathematicians and as of today, I am not sure ‘why’ they work at all, but they do.<\/p>\n

Imagine a double slit experiment. A particle, two passable slits, and a detector on the other side. A classical particle (like a tennis ball) passes through either slit. A quantum particle however interferes with itself and leaves a nice interference pattern.
\nRichard Feynman asked what would happen if we considered all possible paths the particle could go, yes all. And then add the paths in a weighted average. This idea was simply revolutionary.
\nCarrying out the maths, one makes some observations:<\/p>\n