Quantum Field Theory (QFT) is the theoretical framework describing the quantisation of classical fields which allows a Lorentz-invariant formulation of quantum mechanics. QFT is used both in high energy physics as well as condensed matter physics and closely related to statistical field theory. Use ...
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Interaction potential in standard $\phi^4$ theory
In this paper, the authors consider a real scalar field theory in $d$-dimensional flat Minkowski space-time, with the action given by
$$S=\int d^d\! x ...
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4answers
3k views
Gauge symmetry is not a symmetry?
I have read before in one of Seiberg's articles something like, that gauge symmetry is not a symmetry but a redundancy in our description, by introducing fake degrees of freedom to facilitate ...
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2answers
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How does the Higgs mechanism work?
I'm not a particle physicist, but I did manage to get through the Feynman lectures without getting too lost.
Is there a way to explain how the Higgs field works, in a way that people like me might ...
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5answers
2k views
Are W & Z bosons virtual or not?
W and Z bosons are observed/discovered. But as force carrying bosons they should be virtual particles, unobservable? And also they require to have mass, but if they are virtual they may be off-shell, ...
11
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3answers
1k views
9
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1answer
725 views
Diff(M) as a gauge group and local observables in theories with gravity
In a gauge theory like QED a gauge transformation transforms one mathematical representation of a physical system to another mathematical representation of the same system, where the two mathematical ...
22
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6answers
2k views
Formalizing Quantum Field Theory
I'm wondering about current efforts to provide mathematical foundations and more solid definition for quantum field theories. I am aware of such efforts in the context of the simpler topological or ...
22
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3answers
1k views
Scattering of light by light: experimental status
Scattering of light by light does not occur in the solutions of Maxwell's equations (since they are linear and EM waves obey superposition), but it is a prediction of QED (the most significant Feynman ...
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1answer
587 views
What is the relationship between string net theory and string / M-theory?
I've just learned from this one of Prof. Wen's answers that there exists a theory called string net theory. Since I've never heard about this before it picks my curiosity, so I`d like to ask some ...
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3answers
840 views
How general is the Lagrangian quantization approach to field theory?
It is an usual practice that any quantum field theory starts with a suitable Lagrangian density. It has been proved enormously successful. I understand, it automatically ensures valuable symmetries of ...
11
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4answers
675 views
Is the world $C^\infty$?
While it is quite common to use piecewise constant functions to describe reality, e.g. the optical properties of a layered system, or the Fermi–Dirac statistics at (the impossible to reach exactly) ...
8
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3answers
699 views
Hypercharge for U(1) in SU(2)xU(1) model
I understand that the fundamental representation of U(1) amounts to a multiplication by a phase factor, e.g. EM. I thought that when it is extended to higher dimensional representations, it would just ...
10
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8answers
2k views
Is it possible to separate the poles of a magnet?
It might seem common sense that when we split a magnet we get 2 magnets with their own N-S poles. But somehow, I find it hard to accept this fact.(Which I now know is stated by Gauss's Law)
I have ...
36
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1answer
3k views
Why do we not have spin greater than 2?
It is commonly asserted that no consistent, interacting quantum field theory can be constructed with fields that have spin greater than 2 (possibly with some allusion to renormalization). I've also ...
21
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9answers
2k views
Rigor in quantum field theory
Quantum field theory is a broad subject and has the reputation of using methods which are mathematically desiring. For example working with and subtracting infinities or the use of path integrals, ...
11
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5answers
508 views
Reading list in topological QFT
I'm interested in learning about topological QFT including Chern Simons theory, Jones polynomial, Donaldson theory and Floer homology - basically the kind of things Witten worked on in the 80s. I'm ...
3
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1answer
717 views
How do I construct the $SU(2)$ representation of the Lorentz Group using $SU(2)\times SU(2)\sim SO(3,1)$ ?
This question is based on problem II.3.1 in Anthony Zee's book Quantum Field Theory in a Nutshell (I'm reading this for fun- it isn't a homework problem.)
Show, by explicit calculation, that ...
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7answers
2k views
What equation describes the wavefunction of a single photon?
The Schrödinger equation describes the quantum mechanics of a single massive non-relativistic particle. The Dirac equation governs a single massive relativistic spin-½ particle. The photon is a ...
3
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1answer
474 views
Schrodinger equation from Klein-Gordon?
One can view QM as a 1+0 dimensional QFT, fields are only depending on time and so are only called operators, and I know a way to derive Schrodinger's equation from Klein-Gordon's one.
Assuming a ...
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1answer
251 views
Why on-shell vs. off-shell matters?
The definitions between on- and off-shell are given in Wikipedia.
Why is it so important in QFT to distinguish these two notions ?
21
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13answers
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Suggested reading for renormalization (not only in QFT)
What papers/books/reviews can you suggest to learn what renormalization "really" is? Standard QFT textbooks are usually computation-heavy and provide little physical insight in this respect - after my ...
22
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3answers
1k views
A No-Nonsense Introduction to Quantum Field Theory
I found Sean Carroll's "A No Nonsense Introduction to General Relativity" (about page here. pdf here), a 24-page overview of the topic, very helpful for beginning study. It all got me over the hump ...
13
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1answer
601 views
Classical and quantum anomalies
I have read about anomalies in different contexts and ways. I would like to read an explanation that unified all these statements or point-views:
Anomalies are due to the fact that quantum field ...
7
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3answers
547 views
Covariant Quantisation and the Time Operator in String Theory
Covariant quantisation in string theory is accomplished by giving the commutator relations
$[X^\mu(\sigma,\tau),P^\nu(\sigma',\tau)] =
i \eta^{\mu\nu} \delta(\sigma - \sigma')$.
Although ...
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1answer
346 views
Is microcausality *necessary* for no-signaling?
There are proofs in the literature that QFT including microcausality is sufficient for it not to be possible to send signals by making quantum mechanical measurements associated with regions of ...
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7answers
944 views
Can energy be taken out of the QFT vacuum?
There have been recent questions about the vacuum. In my simplified knowledge the vacuum is like a ground state energy level, and also that there might even exist other lower energy levels than the ...
13
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6answers
253 views
Is there a theorem that says that QFT reduces to QM in a suitable limit? A theorem similar to Ehrenfest's theorem?
Is there a theorem that says that QFT reduces to QM in a suitable limit?
Of course, it should be, as QFT is relativisitc quantum mechanics.
But, is there a more manifest one? such as Ehrenfest's ...
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2answers
2k views
Shape of the Higgs branching ratio to ZZ
I've been looking at the, now very popular, graph of the SM Higgs decay branching ratios:
You see that the ZZ branching ratio has a funny dip around the $170\, GeV$, very different from the WW ...
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5answers
1k views
Why not using Lagrangian, instead of Hamiltonian, in non relativistic QM?
When we studied classical mechanics on the undergraduate level, on the level of Taylor, we covered Hamiltonian as well as Lagrangian mechanics.
Now when we studied QM, on the level of Griffiths, we ...
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2answers
2k views
What are zero modes?
What are zero modes in quantum field theory, and what are they used for? Or, where can I read about them? I was never able to find a good introduction on the subject.
I am particularly interested in ...
12
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2answers
182 views
Renormalization in string theory
I'm taking a course in string theory and have encountered renormalization for the first time (and I suspect it isn't the last).
Specifically, while quantizing the bosonic and spinning strings, an ...
2
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3answers
274 views
Could all strings be one single string which weaves the fabric of the universe?
This question popped out of another discussion, about if the photon needs a receiver to exist. Can a photon get emitted without a receiver? A universe containing only one electron was hypothetically ...
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3answers
181 views
Theory that gets rid of dark matter/energy
Is there any physics theory that either groups together gravity and dark energy/dark matter or eliminates dark energy/dark matter by modifying standard understanding of gravity or any force? If so, ...
13
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3answers
1k views
Good reading on the Keldysh formalism
I'd like some suggestions for good reading materials on the Keldysh formalism in a condmat context. I'm familiar with the imaginary time, coherent state, path integral formalism, but lately I've been ...
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18answers
2k views
Quantum Field Theory from a mathematical point of view
I'm a student of mathematics with not much background in physics. I'm interested in learning Quantum field theory from a mathematical point of view.
Are there any good books or other reference ...
12
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4answers
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Haag's theorem and practical QFT computations
There exists this famous Haag's theorem which basically states that the interaction picture in QFT cannot exist. Yet, everyone uses it to calculate almost everything in QFT and it works beautifully.
...
10
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2answers
1k views
Beginners questions concerning Conformal Field Theory
I started reading about Conformal Field Theory a few weeks ago.
I'm from a more mathematical background. I do know Quantum Mechanics/Classical Mechanics,
but I'm not really an expert when it comes ...
9
votes
1answer
788 views
Lagrangian of Schrodinger field
Usual Schrodinger lagrangian is $ i(\psi^{*}\partial_{t}\psi ) + \frac{1}{2m} \psi^{*}(\nabla^2)\psi $. It gives correct equation of motion, with conjugate momentum for $\psi^{*}$ vanishing. This ...
7
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1answer
375 views
Correlation function which has branch cut in momentum space
When correlation function has branch cut in momentum space,
how to find correlation in coordinate space?
For example
$$ \tilde {G}(\omega) = \frac{2i}{\omega+(\omega^2-\nu^2)^{1/2}}$$
How to get the ...
5
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4answers
2k views
Chemical potential
This is something probably very basic but I was led back to this issue while listening to a recent seminar by Allan Adams on holographic superconductors. He seemed very worried to have a theory at ...
14
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3answers
796 views
Why does dilation invariance often imply proper conformal invariance?
Why does a quantum field theory invariant under dilations almost always also have to be invariant under proper conformal transformations? To show your favorite dilatation invariant theory is also ...
13
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3answers
535 views
Quantum Field Theory Variants
I am a math guy, so sorry for the naivety. When I peruse the wikipedia I see many "variants" of quantum field theory...conformal quantum field theory, topological quantum field theory, ...
12
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1answer
735 views
dynamic casimir effect
A few years ago, when i studied the casimir effect interpretation as the filtering out of vacuum modes with appropiate boundary conditions, i had the following dilemma; supposedly the derivation of ...
4
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2answers
847 views
What does a Field Theory mean?
What exactly is a field theory?
How do we classify theories as field theories and non field theories?
EDIT:
After reading the answers I am under the impression that almost every theory is a ...
3
votes
2answers
167 views
Why is fractional statistics and non-Abelian common for fractional charges?
Why non integer spins obey Fermi statistics?
Why is fractional statistics and non-Abelian common for fractional charges?
10
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2answers
1k views
Virtual photon description of B and E fields
I continue to find it amazing that something as “bulky” and macroscopic as a static magnetic or electric field is actually a manifestation of virtual photons.
So putting on your QFT spectacles, look ...
9
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6answers
779 views
Is there any thing other than time that “triggers” a radioactive atom to decay?
Say you have a vial of tritium and monitor their atomic decay with a geiger counter. How does an atom "know" when it's time to decay? It seems odd that all the tritium atoms are identical except with ...
8
votes
2answers
459 views
Superconformal theories
Can anyone tell me where can I read about the notion of "short" and "long" representations? Like what they are etc.
From where can I learn the arguments which show that the bosonic subalgebra of ...
7
votes
4answers
209 views
Different kinds of S-matrices?
It seems to me that the notion of an "S-matrix" refers to several different objects
One construction you can find in the literature is allowing the coupling constant to adiabatically approach 0 in ...
7
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3answers
451 views
What was missing in Dirac's argument to come up with the modern interpretation of the positron?
When Dirac found his equation for the electron $(-i\gamma^\mu\partial_\mu+m)\psi=0$ he famously discovered that it had negative energy solutions. In order to solve the problem of the stability of the ...
