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ajv
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In quantum field theory, a fundamental particle is an excitation in the underlying field, but what does that mean? Do fundamental particles have any physical existence according to QFT?
Ok, so according to QFT all fundamental particles are quanta of the underlying field. What is a "quanta"? Is it energy?Vanadium 50 said:Of course they have a physical existence. You're made of them. We can count them. We can move them around. What more do you want?
ajv said:Ok, so according to QFT all fundamental particles are quanta of the underlying field. What is a "quanta"? Is it energy?
Pretend we have a super powerful microscope that could see infinitely small things.bhobba said:QFT is more advanced than QM. QM can't really be expressed except using math, even though many popularisations attempt it with varying degrees of success, and also a lot of misconceptions. QFT is much much worse. As one mentor here says everything you have read about QFT outside a QFT textbook is likely wrong - and that even includes well respected non QFT textbooks - it really is that bad at the lay level.
That said, and running into that issue, its an extension of the harmonic oscillator of QM:
https://en.wikipedia.org/wiki/Quantum_harmonic_oscillator
Mathematically it can be described using creation and annihilation operators as well as the number operator. The interesting thing here is that its actually possible to formulate QM in terms of creation and annihilation operators - it one of a number of different formulations of QM:
http://susanka.org/HSforQM/[Styer]_Nine_Formulations_of_Quantum_Mechanics.pdf
Now heuristically here is what's going on. You write down the equations of a quantum field analogously to a classical field. You do a trick called a Fourier transform and low and behold the Fourier components are mathematically the same as the harmonic oscillator, hence you have creation and annihilation operators. Mathematically its exactly the same as the creation and annihilation formulation of QM. That's how particles come about in QFT.
As you can see its not trivial, but really its the best I can do to explain this advanced area in basic terms.
If you want to study the detail recently some good books have started to appear that can be tackled, admittedly with effort, after a basic course in QM
http://susanka.org/HSforQM/[Styer]_Nine_Formulations_of_Quantum_Mechanics.pdf
Sussliknds book is good enough preparation:
https://www.amazon.com/dp/0465062903/?tag=pfamazon01-20
While doable, be warned it will take time and attention to detail. But at the end you will have an understanding way beyond the lay level.
Thanks
Bill
ajv said:Pretend we have a super powerful microscope that could see infinitely small things. If we zoomed into an electron with an infinite magnification, according to QFT, what would we see? Would we see absolutely nothing?
bhobba said:Sussliknds book is good enough preparation:
https://www.amazon.com/dp/0465062903/?tag=pfamazon01-20
ajv said:Pretend we have a super powerful microscope that could see infinitely small things.
If we zoomed into an electron with an infinite magnification, according to QFT, what would we see? Would we see absolutely nothing?
FWIW it was and is Amazon for me, both text and link. Maybe time todo some scans?stevendaryl said:This is off-topic but very mysterious: In your original post, the link points to Walmart, but when I quote your post, it points instead to Amazon.
Lord Crc said:FWIW it was and is Amazon for me, both text and link. Maybe time todo some scans?
fxdung said:so they must have the size(the size of packet)
This is a subtle question. First of all one has to emphasize that the short answer to the question in the subject line is that the theoretical definition of an elementary particle is that it can be described by a local microcausal quantum field theory that induces an irreducible representation of the proper orthochronous Poincare group (see also #15).fxdung said:Is there any concept relationship between quantum field and wave function of particle?
A fundamental particle is a subatomic particle that is not composed of smaller particles. It is considered to be one of the basic building blocks of matter and cannot be broken down into simpler components.
According to Quantum Field Theory (QFT), a fundamental particle is a quantum excitation of a field. It is the smallest possible unit of a field and carries specific properties such as mass, charge, and spin.
Some examples of fundamental particles include electrons, quarks, photons, and neutrinos. These particles are considered to be the most basic constituents of matter and are described by QFT.
Fundamental particles are different from composite particles in that they cannot be broken down into smaller components. Composite particles, on the other hand, are made up of two or more fundamental particles.
Fundamental particles interact with each other through the exchange of other particles, such as photons or gluons. This interaction is described by the fundamental forces of nature, including electromagnetism, strong and weak nuclear forces, and gravity.