# Quantum field theory questions?

• Nick V
In summary: QFT is an effective theory that can be replaced by other models in some situations, but in other situations it is the only theory that can explain certain phenomena. Is that about it?
Nick V
In QFM, what does it mean to say that an electron is just an excitation of the electron field? Does this apply to all particles? Does it mean to say that an electron is the quanta of the electron field?

Last edited:
I think that there is a vacuum ##|0\rangle## for the electrons, another for photons and so on. There is creation operator ##a^\dagger## for each field. The vacuum has a null occupation number(##a^\dagger a |0\rangle = zero##. You can call quantum the result of a creation operator on a vacuum (as the result has a number of 1)

naima said:
I think that there is a vacuum for the electrons, another for photons and so on. There is creation operator ##a^\dagger## for each field. The vacuum has a null occupation number. You can call quantum the result of a creation operator on a vacuum (as the result has a number of 1)
I don't really know what your saying. When Quantum field theory says that an electron is a excitation in the electron field, what does that mean? Does that mean that it is a quanta of the field or a particle of the field... what does excitation of the field mean?

You know that in an hydrogen atom an electron may be on his ground state (lower energy) he may be excited when a photon has been annihilated by the electron.
When we speak of fields we say that a field is in is ground state ##|0 \rangle## when its energy is minimum. its particle number is null. This field can interact with another field so that it is excited. it is no more on the ground state but in a state with a particle occupation number equal
to one. That is why we say the electron is an excitation of the electronic field
the word quanta is not important.

You need to become familiar with the quantisation of the Harmonic oscillator:
http://en.wikipedia.org/wiki/Quantum_harmonic_oscillator

It turns out when you quatitsise a field its mathematically similar with the creation and annihilation operators defined for the harmonic oscillator behaving the same as creating and destroying particles in a quantum field.

To fully understand it though you need to study the theory:
https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20

That text explains very carefully exactly what's going on.

Thanks
Bill

Last edited by a moderator:
bhobba said:
You need to become familiar with the quantisation of the Harmonic oscillator:
http://en.wikipedia.org/wiki/Quantum_harmonic_oscillator

It turns out when you quatitsise a field its mathematically similar with the creation and annihilation operators defined for the harmonic oscillator behaving the same as creating and destroying particles in a quantum field.

To fully understand it though you need to study the theory:
https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20

That text explains very carefully exactly what's going on.

Thanks
Bill

So electrons in atoms can be modeled as excitations of the electron field.. but why do we still discuss about whether electrons are particle or wave in the atoms.. why not just mention them as field excitations?

But then, is it possible this model of electron as field excitations can be replaced with other models.. meaning qft is just a temporary or effective field theory?

Last edited by a moderator:
Edward Wij said:
but why do we still discuss about whether electrons are particle or wave in the atoms.. why not just mention them as field excitations?

Advanced texts do not discuss if electrons are particles or waves - that's the domain of popularisations and beginning texts. It well known to be neither and that was decided ages ago when Dirac came up with his transformation theory at the end of 1926.

Edward Wij said:
But then, is it possible this model of electron as field excitations can be replaced with other models.. meaning qft is just a temporary or effective field theory?

Due to mathematical difficulty you do not use QFT to solve the usual problems of QM. QM is in fact a limit of QFT so while its correct to say electrons are excitations of an electron field a hammer is not usually chosen to crack a nut and for ordinary QM its a bit more vague - but mathematically easier.

Indeed the Effective Field Theory approach to renormaliation thinks of QFT as basically just effective.

I think you might find the following book interesting:
https://www.amazon.com/dp/0473179768/?tag=pfamazon01-20

Thanks
Bill

Last edited by a moderator:
vanhees71
bhobba said:
Advanced texts do not discuss if electrons are particles or waves - that's the domain of popularisations and beginning texts. It well known to be neither and that was decided ages ago when Dirac came up with his transformation theory at the end of 1926.
Due to mathematical difficulty you do not use QFT to solve the usual problems of QM. QM is in fact a limit of QFT so while its correct to say electrons are excitations of an electron field a hammer is not usually chosen to crack a nut and for ordinary QM its a bit more vague - but mathematically easier.

Indeed the Effective Field Theory approach to renormaliation thinks of QFT as basically just effective.

I think you might find the following book interesting:
https://www.amazon.com/dp/0473179768/?tag=pfamazon01-20

Thanks
Bill

I bought the book you suggested above and reading it since yesterday. But it says qft didn't solve the mystery of the double slit too. Quoting in the book:

"Field collapse: Field collapse is not an easy concept to accept- perhaps more difficult than the concept of a field. Here I have been working hard, trying to convince you that fields are a real property of space - indeed, the only reality - and now I am asking you to believe that this field quantum, spread out as it may be, suddenly disappears into a tiny absorbing atom. Yet it is the process that can be visualized without inconsistency. In fact, if a photon is an entity that lives and dies as a unit, field collapse must occur. A quantum cannot split and put half its energy in one place and half in another, or live here and die there. That would violate the basic quantum principle. While QFT does not provide an explanation for when or why collapse occurs, somne day we may have a theory that does. In any case, field collapse is necessary and has been demonstrated experimentally."

Bill, Is this why the double slit experimental are not explained using QFT.. because field collapse is just as inexplanable as particles passing both slits? Also I think most physicists don't attribute any physical existence of the quantum fields.. and field collapse if real needs instantaneously faster than light signaling.. this is almost like saying the wave function was real.. only this time the quantum fields are real but fields collapse superluminally. What is your thoughts of this?

Last edited by a moderator:
Well I think we need to be clear what explain means. With the assumption the field changes on observation then the double slit is explained. Did you expect the explanation not to assume some things? Any explanation does that.

It doesn't explain the measurement 'problem' (postulate is probably a better description than problem - but its pretty standard so I will stick with it) which any observation in QM has - but in general QM merely accepts it as a primitive of the theory.

In modern times decoherence is used to elucidate better the measurement postulate which has a number of parts. It explains a number of those parts such as a preferred basis - it doesn't explain the so called problem of outcomes which colloquially is why do we get any outcomes at all, or more technically how an improper mixed state becomes a proper one. Exactly what that issue is, is explained here (sorry that its rather technical but we are getting into deep waters here):
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

If I remember correctly that book you got also mentions decoherence - but doesn't give any details. This may help at your level:
http://www.ipod.org.uk/reality/reality_decoherence.asp

Thanks
Bill

Last edited by a moderator:
bhobba said:
Well I think we need to be clear what explain means. With the assumption the field changes on observation then the double slit is explained. Did you expect the explanation not to assume some things? Any explanation does that.

It doesn't explain the measurement 'problem' (postulate is probably a better description than problem - but its pretty standard so I will stick with it) which any observation in QM has - but in general QM merely accepts it as a primitive of the theory.

In modern times decoherence is used to elucidate better the measurement postulate which has a number of parts. It explains a number of those parts such as a preferred basis - it doesn't explain the so called problem of outcomes which colloquially is why do we get any outcomes at all, or more technically how an improper mixed state becomes a proper one. Exactly what that issue is, is explained here (sorry that its rather technical but we are getting into deep waters here):
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

If I remember correctly that book you got also mentions decoherence - but doesn't give any details. This may help at your level:
http://www.ipod.org.uk/reality/reality_decoherence.asp

Thanks
Bill

Bill. Have you actually read the book you recommended days ago (the "Fields color theory escaped Einstein"? I finished reading it and it's a very unusual book with a different interpretation of QFT and even special relativity. For example. There is a passage inside that says:

"While I hope you can accept, as did FitzGerald and Lorentz, that length contraction happens because the field equations require it, it would be nice to have some intuitive insight into the phenomenon. We must recognize that even if the molecular configuration of an object appears to be static, the component fields are always interacting with each other. The EM field interacts with the matter fields and vice versa, the strong field interacts with with the nucleon fields, etc. These interactions are what holds the object together. Now if the object is moving very fast, this communication among fields will become more difficult because the fields, on the average, will have to interact through greater distances. Thus the object in motion must somehow adjust itself so that the same interaction among fields can occur. How can it do this? The only way is by reducing the distance the component fields must travel. Since the spacing between atoms and molecules, and hence the dimensions of an object, are determined by the nature and configuration of the force fields that bind them together, the dimensions of an object must therefore be affected by motion"

He also explains why time dilation occurs because the fields need finite time to travel in between atoms. And the reason c can't be exceeded is because the fields need finite speed. And mass increase because of more inertia the fields have to resist. Ok. Why don't I see these explanations given by the average physicists? And how many subscribe to this view?

About General Relativity. It says something like "What Schwinger is saying is that four dimensional geometry does not exist in the real world - it is "impossible", but matheticians "who think algebraically" are free to construct equations that would describe it if is did exist. By stretching our minds, some of us can even form a vague mental image of what four-dimensional curvature would be like if it did not exist. Nevertheless, saying that the gravitational field equations are equivalent to curvature is not the same as saying there is curvature. In QFT, the gravitational field is just another force fields, like the EM, strong and weak fields, albeit with a greater complexity that is reflected in its higher spin value of 2."

Read the rest in the book.

For others besides Bill. Can you share or comment what could possible be wrong with it?

Last edited by a moderator:
Edward Wij said:
Bill. Have you actually read the book you recommended days ago (the "Fields color theory escaped Einstein"? I finished reading it and it's a very unusual book with a different interpretation of QFT and even special relativity. For example. There is a passage inside that says:

There are a few areas of disagreement, but it's overall OK.

Please understand this is written at the populist level. For example why C can't be exceeded is the reason he states - but what he didn't point out is the laws of physics must be the same in all inertial frames, nor does he give an exact definition of inertial frames, which are in fact the most important things - the speed of light thing simply fixes a constant that follows from those. It must be said neither do other books at the lay level either - the full truth requires a reasonable grasp of calculus and linear algebra:
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

So you are left with analogies and picturesque language.

Its different - and it's intended to be because its presenting a very advanced topic, QFT, to a lay audience.

Also note Dr Brooks is no dummy - he studied QFT under an acknowledged master - Julian Schwinger.

Thanks
Bill

Last edited:
bhobba said:

There are a few areas of disagreement, but it's overall OK.

Please understand this is written at the populist level. For example why C can't be exceeded is the reason he states - but what he didn't point out is the laws of physics must be the same in all inertial frames, nor does he give an exact definition of inertial frames, which are in fact the most important things - the speed of light thing simply fixes a constant that follows from those. It must be said neither do other books at the lay level either - the full truth requires a reasonable grasp of calculus and linear algebra:
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

So you are left with analogies and picturesque language.

Its different - and it's intended to be because its presenting a very advanced topic, QFT, to a lay audience.

Thanks
Bill

QFT is about operators acting on the state vectors and these are not supposed to be physical.. but why did the author kept emphasizing the field is physical and in fact literally pass thru both slits and then the fields vanish when one part gets "detected" by the detector atom? Who are other physicists who hold this view?

Edward Wij said:
QFT is about operators acting on the state vectors and these are not supposed to be physical

Why do you think that? IMHO its about putting time and position on equal footing as required by relativity and making position a parameter rather than an observable. This leads to quantum fields which means operators are assigned to points in space - the state space becomes a lot trickier being a Fock space. There are deeper analysis possible as detailed in Wienberg's texts but challenging would be a very mild way of describing it.

Edward Wij said:
but why did the author kept emphasizing the field is physical and in fact literally pass thru both slits and then the fields vanish when one part gets "detected" by the detector atom? Who are other physicists who hold this view?

Because it is physical in exactly the same way as any other observable in QM is physical eg in ordinary QM momentum and position are physical.

He isn't talking about ordinary QM here - he is talking about its most fundamental and advanced incarnation - QFT.

Thanks
Bill

bhobba said:
Why do you think that? IMHO its about putting time and position on equal footing as required by relativity and making position a parameter rather than an observable. This leads to quantum fields which means operators are assigned to points in space - the state space becomes a lot trickier being a Fock space. There are deeper analysis possible as detailed in Wienberg's texts but challenging would be a very mild way of describing it.
Because it is physical in exactly the same way as any other observable in QM is physical eg in ordinary QM momentum and position are physical.

He isn't talking about ordinary QM here - he is talking about its most fundamental and advanced incarnation - QFT.

Thanks
Bill

I read in sci am that "A classical field is like a weather map that shows the temperature in various cities. The quantum version like a weather map that does not show you "40 degree," but "sqrt ()". To obtain an actual temperature value, you would need to go through an extra step of applying the operator to another mathematical entity, known as a state vector, which represents the configuration of the system in question"

How could these operator fields be physical like in qm position or momentum? And our instrument just detects particles.. we can't detect the raw field.. in the same manner we can't detect wave function because these are just mathematical devices to produce detections. Do you attribute the quantum fields as more real than wave function? But function fields are composed of configuration of wave functions too, and they collapse similarly to QM wave function so how can the quantum fields wave function be more real?

Also what is the theoretical reason why we can't apply QFT to a piece of wood such that the atoms can be annihilated or be created making the wood indeterminate.. I read something like QFT can be applied to free fields (?) only and not to bound states like atoms. Why?

Edward Wij said:
How could these operator fields be physical like in qm position or momentum?

A field is just as real as momentum etc - you can measure it - eg you can measure EM fields.

Edward Wij said:
Also what is the theoretical reason why we can't apply QFT to a piece of wood

Why don't you think we cant? It's just mathematically much more difficult than QM which is so difficult we can't even apply that to atoms more complex than hydrogen and have to use computer approximations. For wood - that's way beyond our present ability in any kind of exact sense - but qualitatively we know what's going on as biology texts explain - from dim memories of biology at school.

QFT can be applied to free fields.

Thanks
Bill

bhobba said:
A field is just as real as momentum etc - you can measure it - eg you can measure EM fields.

But how do you detect electron fields? We detect electron particle instead of the electron field.

Why don't you think we cant? It's just mathematically much more difficult than QM which is so difficult we can't even apply that to atoms more complex than hydrogen and have to use computer approximations. For wood - that's way beyond our present ability in any kind of exact sense - but qualitatively we know what's going on as biology texts explain - from dim memories of biology at school.

QFT can be applied to free fields.

Thanks
Bill

But QFT deals with annihilation and creation operators.. if you apply this to wood.. won't this just destroy it since you are annihilating the wood atoms making it vanish?

The problem is that there is no apple tree fields interacting with EM field. If so we could easily get fruits from a laser.

vanhees71
Edward Wij said:
But how do you detect electron fields? We detect electron particle instead of the electron field.

What makes you say that?

It's not true - but I am curios why you would think that.

The reason fields exist is its required to ensure conservation laws are respected as required by Noethers theorem. If you have access to it the following book explains it:
https://www.amazon.com/dp/1107012945/?tag=pfamazon01-20

Specifically it has to do with certain no-go theorems worked out by Wigner.

Thanks
Bill

Last edited by a moderator:
Edward Wij said:
But QFT deals with annihilation and creation operators.. if you apply this to wood.. won't this just destroy it since you are annihilating the wood atoms making it vanish?

You reasoning for such a statement escapes me. What QFT shows is that a quantum field is mathematically equivalent to creation and annihilation operators but the QM of everyday objects is the dilute limit of that where you deal with one or no particles. If you want to delve into that see the following reference:
https://www.amazon.com/dp/9812381767/?tag=pfamazon01-20

Be aware however you are delving into mathematically advanced waters.

The book I recommended takes you about as far into QFT without delving into such detail.

Thanks
Bill

Last edited by a moderator:
bhobba said:
You reasoning for such a statement escapes me. What QFT shows is that a quantum field is mathematically equivalent to creation and annihilation operators but the QM of everyday objects is the dilute limit of that where you deal with one or no particles. If you want to delve into that see the following reference:
https://www.amazon.com/dp/9812381767/?tag=pfamazon01-20

Be aware however you are delving into mathematically advanced waters.

The book I recommended takes you about as far into QFT without delving into such detail.

Thanks
Bill

In QM, time is a parameter in that all system have similar time. But Einstein says time varies in different locations, so in QFT, we have time as coordinate.. but a fixed coordinate. .

General Relativity teaches us that spacetime is curved in the presence of matter.. so QFT can be further improved to have fields that can interact with the geometry. I'd like to know if general relativitisic QFT would be simply about Planck scale physics (or quantum gravity) or it would also predict or model other above Planck scale effects like information dynamics (for example from the holographic principle) akin to how QFT can give us interactions and particles that can annihilate or create (larger than Planck scale) versus that of plain QM?

Last edited by a moderator:
bhobba said:
Advanced texts do not discuss if electrons are particles or waves - that's the domain of popularisations and beginning texts. It well known to be neither and that was decided ages ago when Dirac came up with his transformation theory at the end of 1926.
Due to mathematical difficulty you do not use QFT to solve the usual problems of QM. QM is in fact a limit of QFT so while its correct to say electrons are excitations of an electron field a hammer is not usually chosen to crack a nut and for ordinary QM its a bit more vague - but mathematically easier.

Indeed the Effective Field Theory approach to renormaliation thinks of QFT as basically just effective.

I think you might find the following book interesting:
https://www.amazon.com/dp/0473179768/?tag=pfamazon01-20

Thanks
Bill

Can you recommend any other books that are as suited for the non-physicist as is the book "Fields of Color" you mention here? I have read and thoroughly enjoyed this book. I am not adverse to math in such a book (I am a retired electrical engineer and have had many couses on the level used for QFT books) but I have never found such math-focused books to be really clear about the links to physical realities of the equations presented. Perhaps (don't laugh) it is just that I have a hard time relating/visualizing solutions of partial differential equations to the empirical physical phenomena of the real world, so I like to read books that are on the "pop-sci" level for my own enlightenment.

I am retired and have a very large collection of such books on all sorts of science-related topics. I have searched for more books of this "pop-sci" type on QFT but find hardly any that do more than give a cursory treatment of QFT when presenting quantum physics to the lay reader. Is there really nothing out there at my level on this fascinating topic?

Thanks
Pete B

peteb said:
Can you recommend any other books that are as suited for the non-physicist as is the book "Fields of Color" you mention here? I have read and thoroughly enjoyed this book.

Feynman - QED - The Strange Theory Of Light And Matter:
https://www.amazon.com/dp/0691024170/?tag=pfamazon01-20

Thanks
Bill

bhobba said:
Feynman - QED - The Strange Theory Of Light And Matter:
https://www.amazon.com/dp/0691024170/?tag=pfamazon01-20

Thanks
Bill
Thanks, already have that one. I was hoping for something a bit more current and comprehensive. But I will go back and read that one again!

Pete B

Edward Wij said:
But it says qft didn't solve the mystery of the double slit too. Quoting in the book:

"Field collapse: Field collapse is not an easy concept to accept- perhaps more difficult than the concept of a field. Here I have been working hard, trying to convince you that fields are a real property of space - indeed, the only reality - and now I am asking you to believe that this field quantum, spread out as it may be, suddenly disappears into a tiny absorbing atom. Yet it is the process that can be visualized without inconsistency. In fact, if a photon is an entity that lives and dies as a unit, field collapse must occur. A quantum cannot split and put half its energy in one place and half in another, or live here and die there. That would violate the basic quantum principle. While QFT does not provide an explanation for when or why collapse occurs, some day we may have a theory that does. In any case, field collapse is necessary and has been demonstrated experimentally."

This is nonsense, due to severe oversimplification. A disappearing photon just makes the state of the quantum electromagnetic field change its photon occupation number. Not the field disappears, only the photon. The quantum field never collapses; it is eternal (within the domain of traditional quantum field theory; quantum gravity might change the eternal aspect.)

bhobba
Did you read "QFT ln a nutshell" written by Anthony Zee?
Great book!

peteb said:
I am not adverse to math in such a book (I am a retired electrical engineer and have had many couses on the level used for QFT books) but I have never found such math-focused books to be really clear about the links to physical realities of the equations presented.
Then you might enjoy large parts of my online book Classical and Quantum Mechanics via Lie algebras. The first half of the book features almost nowhere partial differential equations.

A book worth looking at if you don't mind advanced math but want to understand its relations to quantum field theory is Volume 1 of Zeidler's book http://www.mis.mpg.de/de/eberhard-zeidler/quantum-field-theory.html. Very thorough.

peteb said:
Thanks, already have that one. I was hoping for something a bit more current and comprehensive. But I will go back and read that one again!

Others have suggested some more advanced tomes.

If that's how you would like to proceed my favourite at that lrevel is:
https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20

I would suggest it before Zee, who I would suggest before what Professor Neumaier mentioned.

I generally prefer, even if you have the background to handle it, starting from less difficult tomes then going to the more difficult. In my experience it generally works out better.

Thanks
Bill

## 1. What is quantum field theory?

Quantum field theory (QFT) is a theoretical framework in physics that combines the principles of quantum mechanics and special relativity to explain the behavior of particles at the subatomic level. It describes particles as excitations of underlying fields, and interactions between particles are mediated by the exchange of virtual particles.

## 2. What are the applications of quantum field theory?

Quantum field theory is used in many areas of physics, including particle physics, condensed matter physics, and cosmology. It has also found applications in other fields such as chemistry and biology.

## 3. How does quantum field theory differ from classical field theory?

In classical field theory, particles are described as continuous objects moving through space and time. In quantum field theory, particles are described as discrete excitations of fields, and their behavior is governed by probabilities rather than definite trajectories.

## 4. What are Feynman diagrams and how are they used in quantum field theory?

Feynman diagrams are graphical representations used in quantum field theory to calculate the probabilities of particle interactions. Each diagram represents a possible interaction between particles, and their calculation involves summing over all possible diagrams to determine the overall probability of an event.

## 5. What are some current challenges in quantum field theory?

One of the biggest challenges in quantum field theory is reconciling it with general relativity and developing a theory of quantum gravity. Other challenges include understanding the nature of dark matter and dark energy, and resolving the hierarchy problem in particle physics.

• Quantum Physics
Replies
1
Views
787
• Quantum Physics
Replies
18
Views
584
• Quantum Physics
Replies
2
Views
1K
• Quantum Physics
Replies
6
Views
403
• Quantum Physics
Replies
3
Views
769
• Quantum Physics
Replies
36
Views
1K
• Quantum Physics
Replies
6
Views
499
• Quantum Physics
Replies
31
Views
2K
• Quantum Physics
Replies
2
Views
867
• Quantum Physics
Replies
4
Views
1K