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An Introduction to Quantum Field Theory

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Re: An Introduction to Quantum Field Theory

#11

Post by danbruc »

toxikitty wrote: post #5
danbruc wrote: post #3

Are quantum fields actual elements of reality or just a convenient mathematical tool to deal with many particle systems? One of the questions I am struggling to find a satisfying answer for for quite some time. Depends on whom you ask? We can't tell because both ways of thinking are completely equivalent? Fields are real! No, they are just a tool! Are there issues with real fields forming a preferred reference frame?…

It depends on what constitutes 'an element of reality'. Are photons an element of reality? Depending on the field of science/engineering and the specific application, one might choose to work with electromagnetic fields, photons or a combination of both. In the QFT framework, a photon is merely a quanta of the electromagnetic field. So photon based or EM field based approaches are just two ways of dealing with proble…

Compare it with temperature. If you run next to fast atom and you touch it, it doesn't actually feel hot. So temperature is not really a fundamental thing in nature but a higher level abstraction of the different moments of a large collection of particles. Temperature also becomes meaningless and the whole concept breaks down if you have only one or a few particles. It is of course a useful concept nonetheless.

So I could probably reformulate the question as whether fields are an abstraction of particles or particles are an abstraction of fields.

Re: An Introduction to Quantum Field Theory

#12

Post by toxikitty »

peterfirefly wrote: post #8
timelined wrote: post #4

This is a pretty good introduction. I highly recommend Feynman's book "QED: The Strange Theory of Light and Matter" as an excellent in-depth work that does not sacrifice accuracy for the sake of making difficult ideas understandable. It is both very clear to the layperson and accurate to the physics.

It would be nice to have a version that uses complex numbers and linear algebra instead of spinning arrows. A little bit more math would make it easier to connect with the "grown up" version of the theory.

Anthony Zee's book on QFT (http://www.kitp.ucsb.edu/members/PM/zee/QuantumFieldTh.html) might be what you're looking for.

It starts off with a spring mattress analogy (like the one in the linked article, but with more math) and goes on to more advanced material from there. I remember it requiring little background besides LinAl and multivariable calc.

Re: An Introduction to Quantum Field Theory

#13

Post by danbruc »

xlm1717 wrote: post #9
danbruc wrote: post #3

Are quantum fields actual elements of reality or just a convenient mathematical tool to deal with many particle systems? One of the questions I am struggling to find a satisfying answer for for quite some time. Depends on whom you ask? We can't tell because both ways of thinking are completely equivalent? Fields are real! No, they are just a tool! Are there issues with real fields forming a preferred reference frame?…

The way I've understood it is, particles are localized excitations of fields. You know of the Higgs boson. It is the excitation of the Higgs field, which exists through all space. Similarly, an electron is an excitation of the electron field (not electromagnetic field), which exists through all space. Every single electron is a localized excitation of the same, single field. I don't know how to answer the relativisti…

I understand that, but is it just a neat mathematical model to treat particles as excitations of fields because it makes calculations especially easy or is there really a field out there?

Re: An Introduction to Quantum Field Theory

#14

Post by w0000t »

mudil wrote: post #7

Ether is back! Well, somewhat. Now it's in the form of Higgs field. Unlike ether, Higgs field does not interact with uniformly moving particles, only those that are accelerating. Here's a great book I just recently listened: http://www.amazon.com/The-Black-Hole-War-Mechanics/dp/031601... It's by Leonard Susskind from Stanford. The thoughts experiments in the book are just terrific. Loved it.

I wouldn't call it Ether, since that would imply some absolute reference frame.

Re: An Introduction to Quantum Field Theory

#16

Post by w0000t »

xlm1717 wrote: post #9
danbruc wrote: post #3

Are quantum fields actual elements of reality or just a convenient mathematical tool to deal with many particle systems? One of the questions I am struggling to find a satisfying answer for for quite some time. Depends on whom you ask? We can't tell because both ways of thinking are completely equivalent? Fields are real! No, they are just a tool! Are there issues with real fields forming a preferred reference frame?…

The way I've understood it is, particles are localized excitations of fields. You know of the Higgs boson. It is the excitation of the Higgs field, which exists through all space. Similarly, an electron is an excitation of the electron field (not electromagnetic field), which exists through all space. Every single electron is a localized excitation of the same, single field. I don't know how to answer the relativisti…

http://physics.stackexchange.com/a/186203

Re: An Introduction to Quantum Field Theory

#17

Post by yk »

danbruc wrote: post #13
xlm1717 wrote: post #9

Earlier quoted context omitted.

The way I've understood it is, particles are localized excitations of fields. You know of the Higgs boson. It is the excitation of the Higgs field, which exists through all space. Similarly, an electron is an excitation of the electron field (not electromagnetic field), which exists through all space. Every single electron is a localized excitation of the same, single field. I don't know how to answer the relativisti…

I understand that, but is it just a neat mathematical model to treat particles as excitations of fields because it makes calculations especially easy or is there really a field out there?

Depends, if you are a realist, then there is a field; if you are a anti-realist then the electron is not real but only a convenient shorthand in the first place.

Compare http://plato.stanford.edu/entries/scientific-realism/ (and references therein)

Re: An Introduction to Quantum Field Theory

#18

Post by toxikitty »

danbruc wrote: post #11
toxikitty wrote: post #5

Earlier quoted context omitted.

It depends on what constitutes 'an element of reality'. Are photons an element of reality? Depending on the field of science/engineering and the specific application, one might choose to work with electromagnetic fields, photons or a combination of both. In the QFT framework, a photon is merely a quanta of the electromagnetic field. So photon based or EM field based approaches are just two ways of dealing with proble…

Compare it with temperature. If you run next to fast atom and you touch it, it doesn't actually feel hot. So temperature is not really a fundamental thing in nature but a higher level abstraction of the different moments of a large collection of particles. Temperature also becomes meaningless and the whole concept breaks down if you have only one or a few particles. It is of course a useful concept nonetheless. So I…

AFAIK the particles vs fields discussion is not the same as temperature vs fields.

At the risk of straying into quantum info territory:

- given all possible information about a collection of particles, you could compute the temperature. However, knowing the temperature doesn't allow you to determine info about particles uniquely (you can write down a density matrix, and not assign a pure state).

- the above doesn't hold for the case of particles and fields. Given a set of field frequencies and amplitudes, you could describe the positions of particles and probabilities of observing them. Given positions and probabilities of observing particles, you could compute the frequencies and amplitudes of the associated field.

We can describe any given set of particles (however big or small, however fast or slow) in terms of fields, and vice versa.

I like this comment :

When I studied quantum mechanics, my professor advised that I avoid the question "which is more fundamental?" and replace it with "which is more useful?".

From this stackoverflow link (http://physics.stackexchange.com/questions/122570/which-is-m...)

My QFT knowledge is rusty, so please correct me if I'm wrong.

Re: An Introduction to Quantum Field Theory

#20

Post by MisterMashable »

danbruc wrote: post #3

Are quantum fields actual elements of reality or just a convenient mathematical tool to deal with many particle systems? One of the questions I am struggling to find a satisfying answer for for quite some time. Depends on whom you ask? We can't tell because both ways of thinking are completely equivalent? Fields are real! No, they are just a tool! Are there issues with real fields forming a preferred reference frame?…

Quantum Field Theory is really just ordinary Quantum Mechanics. It is necessary to use fields instead of "wave equations" because the number of particles can vary when the energy of a system exceeds a certain threshhold. (e.g. a single photon having an energy equal to or higher than the E=mc^2 energy of two electrons can transmute into an electron-positron pair. 1 particle transforms into 2. This is very common in high energy processes.)

Quantum fields are REAL because certain phenomena like solitons, vortices, monopoles and quark confinement can only be understood properly in the full field context. Quantum field theory cannot describe these phenomena in terms of Feynman diagrams. Feynmann diagrams and scattering cross sections/lifetimes were once considered fundamental and fields were believed to be a tool to derive them. Physicists now understand (the competent ones) that Fields are more fundamental than the diagrams. The Fields are also real in the sense that the do much more than just represent particle states, field symmetries are fundamental symmetries of nature, e.g. the strong force has SU(3) symmetry, electroweak SU(2)xU(1) etc.

Steven Weinberg gives a very strong argument for the necessity of fields in his vol. 1 QFT book. It's very technical but a brief summary is... QM + relativity + cluster decomposition principal (which more or less says the results of distant experiments should be unrelated) --> fields

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