QFT, excitation of quantum field, physical or mathematical?

[ajv]

In, QFT, an elementary particles is an excitation of its quantum field. Quantum fields are just mathematical. For example an electron is excitation of the electron field. But is the excitation of the field physically real or just mathematical? What i mean is, is there something physically existing where the excitation is?

 

[A. Neumaier]

Properties of the quantum fields (its mass density, charge density, response to external fields, etc.) can be measured and predicted in the same way as all quantum observables. There is therefore nothing unreal about a quantum field. They are at least as real as their excitations, the elementary particles.

In fact, quantum fields are far more physical than mathematical. In particular, interacting quantum fields in 4 dimensions do not yet make mathematical sense, while physicists use them all the time.

The field is what really exists, i.e., the medium, and the excitations are its oscillations. Just like water waves are excitations (local, extended oscillations) of water, which is the medium carrying the waves. The main difference is that water waves are not quantized, so that there are no 'elementary' excitations.

 

[fresh_42]

In particular, interacting quantum fields in 4 dimensions do not yet make mathematical sense, while physicists use them all the time.

Do you have an example at hand?

 

[A. Neumaier]

The most accurate physical theory currently known, namely QED, is not known to exist as a mathematically well-defined conceptual framework. The reason is that there is so far no logically consistent definition of a quantum field for which the physicist's (renormalized) QED interaction has been proved to exist. QCD, weak interactions, or the standard model are other examples.

On the other hand, the quantum fields considered in solid state theory, have a solid mathematical existence. They describe the deformation of crystals, currents in metals, and the like.

 

[ajv]

The most accurate physical theory currently known, namely QED, is not known to exist as a mathematically well-defined conceptual framework. The reason is that there is so far no logically consistent definition of a quantum field for which the physicist's (renormalized) QED interaction has been proved to exist. QCD, weak interactions, or the standard model are other examples.

On the other hands, the quantum fields considered in solid state theory, have a solid mathematical existence. They describe the deformation of crystals, currents in metals, and the like.

What college do you teach physics at? I am just curious that's all

 

[A. Neumaier]

I teach mathematics. Type my name into Google to find out.

 

[ajv]

I teach mathematics. Type my name into Google to find out.

Then how do you know stuff about QM? Did you get your PhD in physics?

 

[A. Neumaier]

Through reading, thinking, and discussing it. QM is no different form other subjects - they can be learned given interest, dedication, and not too little intelligence.

See Chapter C4: How to learn theoretical physics of my theoretical Physics FAQ.

 

[fresh_42]

The most accurate physical theory currently known, namely QED, is not known to exist as a mathematically well-defined conceptual framework. The reason is that there is so far no logically consistent definition of a quantum field for which the physicist's (renormalized) QED interaction has been proved to exist. QCD, weak interactions, or the standard model are other examples.

On the other hands, the quantum fields considered in solid state theory, have a solid mathematical existence. They describe the deformation of crystals, currents in metals, and the like.

Thank you.