138 votes

What is more fundamental, fields or particles?

This is a tricky question because it asks about the meaning of words. People use the word "particle" to refer to various, not always well defined, notions in physics. In the end, I think the simplest ...
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104 votes

Why isn't the universe full of electrons?

I think this is a very creative question. You are thinking: There are so many atoms in the universe that all of their electron wavefunctions should overlap and lead to a detection everywhere. But ...
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  • 1,835
81 votes

What is a complete book for introductory quantum field theory?

Lecture notes. David Tong's lecture notes. These are very basic and intuitive, and may be a good starting point for someone who has never acquainted themselves with QFT. My suggestion is to skim over ...
76 votes

Do photons truly exist in a physical sense or are they just a useful concept like $i = \sqrt{-1}$?

There is lots of experimental evidence that the electromagnetic field exchanges energy with atoms in discrete chunks, and if we call these chunks photons then photons exist. Which is all very well, ...
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69 votes

Is gravity just electromagnetic attraction?

Short answer: No. Long answer: Nooooooooooooooooooooooooooooooooooooooooooooooooooooo. Moral of the story: Gravity and EM are two very different things that look similar to some people because they ...
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  • 24k
65 votes
Accepted

Resolving Conflicting Reports on Fermilab $g-2$ Results

This seems rather incredible that these two seemingly conflicting announcements come on the same day. The pre-print for the Nature paper by the BMW group was placed on arXiv in 2020 around the same ...
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  • 3,703
56 votes
Accepted

What does it mean to say that "the fundamental forces of nature were unified"?

When we say that the forces were unified, we mean that the interaction was described by a single gauge group. For example, in the original grand unified theory, this group was $SU(5)$, which ...
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  • 95.5k
50 votes

What does it mean that there is no mathematical proof for confinement?

The problem In case you were not aware of this, finding a proof for confinement is one of the Millenium Problems by the Clay Mathematics Institute. You can find the (detailed) answer to your question ...
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47 votes
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The concept of particle in QFT

Somewhat surprisingly, the "generic" particle of QFT is in fact totally delocalized. More precisely, particles are thought to come from the mode expansion of free fields. Since every free ...
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  • 108k
46 votes
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Why are particles thought of as irreducible representations, in plain English?

As you probably know, the Lie group of physical transformations of a quantum system acts on the Hilbert space of states of the system by means of a (strongly-continuous projective-) unitary ...
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46 votes

Can the photoelectric effect be explained without photons?

Yes, the photoelectric effect can be explained without photons! One can read it in L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, Cambridge University Press, 1995, a standard reference ...
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44 votes
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What's the physical meaning of the statement that "photons don't have positions"?

We could spend forever playing whac-a-mole with all of the confusing/confused statements that continue popping up on this subject, on PhysicsForums and elsewhere. Instead of doing that, I'll offer a ...
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43 votes
Accepted

Do virtual particles actually physically exist?

Ever since Newton and the use of mathematics in physics, physics can be defined as a discipline where nature is modeled by mathematics. One should have clear in mind what nature means and what ...
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  • 223k
40 votes

Mathematically rigorous QFT text

This question cannot be aswered as it is asked. There is no general mathematical rigorous definition of QFT in general, but rather different approaches with different goals and applications. First of ...
39 votes

What is the Wilsonian definition of renormalizability?

This is a very good question which, however, shows the extent of the reigning confusion about renormalization even four decades after Wilson's Nobel Prize winning theory on the matter. I essentially ...
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39 votes

What role does "spontaneous symmetry breaking" play in the "Higgs Mechanism"?

It is frequently stated the Higgs mechanism involves spontaneous breaking of the gauge symmetry. This is, however, entirely wrong. In fact, gauge symmetries cannot be spontaneously broken. A ...
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  • 3,026
39 votes

What physical evidence is there that subatomic particles pop in and out of existence?

$$\sin(x) = x-\frac{x^3}{3!} + \text{trigonometric fluctuations}$$ Above you can see why I don't like the language of "quantum fluctuations" -- what people mean by them is just "terms in ...
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  • 19.3k
39 votes

Is gravity just electromagnetic attraction?

The answer to the question is no. There are several logical mistakes and flawed arguments in the article; I will comment on a few: Sunlight does not point back to the sun’s true center of gravity,...
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37 votes
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Why we don't have macroscopic fields of Higgs bosons or gluons?

There are slightly different answers for each particle type. Macroscopic photon and graviton fields can exist because these forces are long-ranged, which is directly related to the force carriers ...
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  • 95.5k
37 votes
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Complex integration by shifting the contour

A simple reference problem Suppose we want to analyse the problem of a forced harmonic oscillator. Denote as $\phi(t)$ the time dependent position of the oscillator. The oscillator experiences two ...
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36 votes
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What is the issue with interactions in QFT?

There are many different problems with interactions; or, rather, many manifestations of the same problem. For example, interactions are always non-linear in the equations of motion, e.g., $$ (\...
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35 votes
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I'm missing the point of renormalization in QFT

Here's the thing: renormalization and divergences have nothing to do with each other. They are conceptually unrelated notions. Renormalization Simply put, renormalization is a consequence of non-...
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35 votes
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Why are relativistic quantum field theories so much more restrictive than non-relativistic ones?

One of the reasons relativistic theories are so restrictive is because of the rigidity of the the symmetry group. Indeed, the (homogeneous part) of the same is simple, as opposed to that of non-...
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35 votes
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Difference between regularization and renormalization?

Regularization and renormalization are conceptually distinct. As you essentially indicate, regularization is the process by which one renders divergent quantities finite by introducing a parameter $\...
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  • 54.8k
34 votes
Accepted

Why is quantum mechanics called 0+1 dimensional QFT?

In field theory, a field can be thought of as a map from the spacetime $M$, usually a Lorentzian manifold---a particularly popular choice is $\Bbb R^{1,n-1}$ (Minkowski space)---to some other space. ...
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  • 15.8k
34 votes

Why do many people say that virtual particles do not conserve energy?

The short answer to your question is that the statements that "virtual particles need not conserve energy" and "intermediate components of Feynman diagrams need not be on the mass shell" are ...
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  • 5,630
34 votes

What is more fundamental, fields or particles?

What follows is an answer from an experimental particle physicist, i.e. one who has more knowledge of theoretical physics than the average educated person, but not in a position to teach it :). I can ...
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  • 223k
33 votes
Accepted

What's the basic ontology of QFT?

I'm interpreting the question like this: What are the general principles of QFT, conceptually? Not sure if this is the kind of answer the OP is looking for, but I'll give it a try and see how it's ...
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33 votes

Are vacuum fluctuations really happening all the time?

I think it’s possible to give a beginners guide to what is meant by vacuum fluctuations, but it necessarily involves taking a few liberties so bear that in mind in what follows. Before we start let’s ...
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33 votes
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Are vacuum fluctuations really happening all the time?

Particles do not constantly appear out of nothing and disappear shortly after that. This is simply a picture that emerged from taking Feynman diagrams literally. Calculating the energy of the ground ...
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