What is the relation between particle and field?

[zhangyang]

From electrodynamics we have a viewpoint about this question. From wave-particle nature in quantum mechanics,we also have a viewpoint (de Broglie' opinion).And in particle physics,we have a much higher understanding.

Who can summerize the general relation between particle and field in opinion of modern physics?

 

[lpetrich]

All our physical theories are based on something called quantum field theory. It pictures elementary particles as wavelike entities whose total amount of wave is quantized.

For free particles, it is relatively simple, especially in the scalar / spin-0 / spinless case. If you can do the quantum-mechanical harmonic oscillator, you should be able to do the quantum field theory of spinless particles without much trouble. Each momentum value corresponds to a harmonic-oscillator mode of the field.

Nonzero spins present complications. Spins are associated with field geometry, and this adds particle modes. However, the field equations impose various constraints, and that subtracts modes from some of them. Half-odd spin produces the complication that the operator commutators must be replaced by anti-commutators, and this, in turn, yields the Pauli Exclusion Principle. But the harmonic-oscillator approach is still at least partially valid.

Interacting particles are much more difficult.

 

[zhangyang]

All our physical theories are based on something called quantum field theory.

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I'm afraid not. Because I don't understand the thermodynamics in quantum field theory.

 

[Lapidus]

For free particles, it is relatively simple, especially in the scalar / spin-0 / spinless case. If you can do the quantum-mechanical harmonic oscillator, you should be able to do the quantum field theory of spinless particles without much trouble. Each momentum value corresponds to a harmonic-oscillator mode of the field.

Does that apply for any spacetime point of the field? Does a quantum field create at any x a superposition of infinite many momentum states, where each momentum state corresponds to one mode of the field?

How do we interpret <k|psi(x,t)|0> = exp(ikx)? Does the quantum field psi(x,t) create a particle at any point x, while it at the same time annihaltes a particle at any x (each time with a superpostion of infinite many modes), and by that it fabricating the propagation of a particle through space??

thanks for any help

 

[Lapidus]

I like to reiterate my question: what does <k|psi(x)|0> = exp(ikx) mean?

On the right we have the amplitude for finding in space a free quantum particle of a given k. Or, the amplitude for finding at a given x a particle of some momentum k.

How does the left hand side of the equation "achieve" the same thing? Assuming that psi(x) is the sum of an annihalting and creation operator. Does psi(x) hammer out of the vacuum state |0> a superpostion of infinite number of momentum states at any point x?

thanks

 

[A. Neumaier]

I'm afraid not. Because I don't understand the thermodynamics in quantum field theory.

Even though it is difficult to understand, there is thermal quantum field theory.

On the lowest level where we have detailed understanding are only quantum fields. Oarticles are the elementary excitations of these fields, in a similar way as sine waves are (in some approximation) the elementary excitations of a guitar string.

 

[A. Neumaier]

I like to reiterate my question: what does <k|psi(x)|0> = exp(ikx) mean?

Why should this be a correct statement?? To me it seems meaningless.

 

[Lapidus]

Why should this be a correct statement?? To me it seems meaningless.

Uuups, I meant of course <0|phi(x)|k> = exp(ikx)

boldface means as usual that they are three-vectors

I got that from P&S page 24 and Ryder page 134

Again my question

On the right we have the amplitude for finding in space a free quantum particle of a given k. Or, the amplitude for finding at a given x a particle of some momentum k.

How does the left hand side of the equation "achieve" the same thing? Assuming that psi(x) is the sum of an annihalting and creation operator. Does psi(x) hammer out of the vacuum state |0> a superpostion of infinite number of momentum states at any point x?

thanks!

 

[nonequilibrium]

On the lowest level where we have detailed understanding are only quantum fields. Oarticles are the elementary excitations of these fields, in a similar way as sine waves are (in some approximation) the elementary excitations of a guitar string.

So what we call the "particles" are actually absolutely delocalized? (just like the sine waves on a string)

 

[A. Neumaier]

Uuups, I meant of course <0|phi(x)|k> = exp(ikx)

I got that from P&S page 24 and Ryder page 134

|k> =a^*(k)|0> denotes the single-particle state with momentum k, |0> the vacuum state (not the single particle state with momentum 0). Thus phi(x)=a(x)+a^*(x) implies
<0|phi(x)|k> = <0|a(x)a^*(k)|0>+<0|a^*(x)a^*(k)|0>. The second term vanishes since it is the inner product between the vacuum and a 2-particle state. The first term is the inner product of the two 1-particle states a^*(x)|0> and a^*(k)|0>. Expand a^*(x) into its Fourier components and use <k'|k>=\delta(k'-k) to get the formula <0|phi(x)|k> = exp(ikx) you quoted.

 

[A. Neumaier]

So what we call the "particles" are actually absolutely delocalized? (just like the sine waves on a string)

Suitable superpositions of plane waves (comparable to the sine waves on a string) can give wave packets that are significant only in a small region of space. Under suitable experimental conditions (e.g., a single electron released by ionization with a a photon) the excitations have the form of such wave packets. Indeed, electron waves can be localized within one Compton wavelength (but, due to relativistic effects, not better), which makes them nice particles when looked at not too closely.

Thus the particle picture makes approximately sense at not too small distances and not too short times.

For photons, the corresponding approximation is called the ''geometric optics'' approximation; it breaks down precisely when interference effects start to be come relevant.

 

[bohm2]

There was a recent paper published sort of discussing this question. The author's conclusions:

The majority of physicists do certainly agree that quantum “particles” are not really particles, as they fail to possesses all the required corpuscular attributes. However, can we affirm that so-called quantum “fields” are fields, as Hobson suggests? In fact, as we shall briefly explain in the present comment, quantum “fields” are no more fields than quantum “particles” are particles, so that the replacement of a particle ontology (or particle and field ontology) by an all-field ontology, will not solve the typical quantum interpretational problems.

Quantum “fields” are not fields. Comment on “There are no particles, there are only fields,” by Art Hobson
http://lanl.arxiv.org/pdf/1204.6384.pdf

 

[A. Neumaier]

There was a recent paper published sort of discussing this question. The author's conclusions:

Quantum “fields” are not fields. Comment on “There are no particles, there are only fields,” by Art Hobson
http://lanl.arxiv.org/pdf/1204.6384.pdf

The analysis assumes that in quantum field theory, the wave function is considered to be a field. But this is not the case, so the analysis is irrelevant.

In quantum field theory, the observables are fields, more precisely, distribution-valued, so that only averages over open reagions in spacetime make sense, which is fully consistent with what we actually can measure. This makes for a good field ontology immune to the objections of the author.

 

[bohm2]

The analysis assumes that in quantum field theory, the wave function is considered to be a field. But this is not the case, so the analysis is irrelevant...

Massimiliano Sassoli de Bianchi in that paper is criticising Art Hobson's concept of "field" in the following paper:

Thus the Schroedinger field is not a probability amplitude for "finding, upon measurement, a particle" but rather a real space-filling field; the field for an electron is the electron; each electron comes through both slits in the 2-slit experiment and spreads over the entire pattern; and quantum physics is about interactions of microscopic systems with the macroscopic world rather than just about measurements.

There are no particles, there are only fields
http://lanl.arxiv.org/ftp/arxiv/papers/1204/1204.4616.pdf

 

[zhangyang]

Perhaps the real problem is how to understand particle and field as the common matter,they are the different form of identicle material, they can transform into each other.

In dialectics of Hegel,we can have clear concept of them.

Bohr had built The Complementary Principle,which is relative to this problem. I think it is the guideline in the quantum field theory.Field is not a mathematical concept but a physical concept.

We know that in thermodynamics and statistical physics,we use the way of probability to treat the macro physical quantity of a material system,calculate the mean value of micro physical quantity as the real value;in the same time ,we also use the way of probability to treat the physical quantity of a material system with amplitude of probability (wave function ),confessing the reason-result regulation of statistics.What is the relation between these two statistics?Completely the same? Or one can include the other?