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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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 ...
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5answers
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Online QFT video lectures

I'm aware of Sidney Coleman's 1975/76 sequence of 54 lectures on Quantum Field Theory. Are there any other high-quality QFT lecture series available online?
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1answer
497 views

A reading list to build up to the spin statistics theorem

Wikipedia's article on the spin-statistics theorem sums it up thusly: In quantum mechanics, the spin-statistics theorem relates the spin of a particle to the particle statistics it obeys. The spin ...
8
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1answer
457 views

Identification of the state of particle types with representations of Poincare group

In the second chapter of the first volume of his books on QFT, Weinberg writes in the last paragraph of page 63: In general, it may be possible by using suitable linear combinations of the ...
13
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3answers
742 views

In what sense is a scalar field observable in QFT?

Consider a QFT consisting of a single, hermitian scalar field $\Phi$ on spacetime (say $\mathbb R^{3,1}$ for simplicity). At each point $x$ in spacetime, $\Phi(x)$ is an observable in the sense that ...
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4answers
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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 ...
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3answers
1k 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 ...
7
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2answers
268 views

What is the exact relationship between on-shell amplitudes and off-shell correlators in AdS/CFT?

In this answer to a question, it is mentioned that in the AdS/CFT correspondence, on-shell amplitudes on the AdS side are related to off-shell correlators on the CFT side. Can somebody explain this ...
7
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3answers
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Noether theorem, gauge symmetry and conservation of charge

I'm trying to understand Noether's theorem, and it's application to gauge symmetry. Below what I've done so far. First, the global gauge symmetry. I'm starting with the Lagragian ...
6
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3answers
712 views

If photons carry 1 spin unit, why does visible light seem to have no angular momentum?

Spin 1 silver atoms have a definite spin axis, e.g. up or down along an axis labeled X. This in turn means that they carry angular momentum in an overt, visible fashion. However, spin 1 photons do ...
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3answers
1k views

Decay of massless particles

We don't normally consider the possibility that massless particles could undergo radioactive decay. There are elementary arguments that make it sound implausible. (A bunch of the following is ...
10
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4answers
4k views

Why don’t photons interact with the Higgs field?

Why don’t photons interact with the Higgs field and hence remain massless?
9
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1answer
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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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3answers
736 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 ...
14
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6answers
442 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 ...
8
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2answers
910 views

EM wave function & photon wavefunction

According to this review Photon wave function. Iwo Bialynicki-Birula. Progress in Optics 36 V (1996), pp. 245-294. arXiv:quant-ph/0508202, a classical EM plane wavefunction is a wavefunction (in ...
10
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2answers
345 views

Born rule for photons: it works, but it shouldn't?

We can observe double-slit diffraction with photons, with light of such low intensity that only one photon is ever in flight at one time. On a sensitive CCD, each photon is observed at exactly one ...
10
votes
6answers
883 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 ...
4
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1answer
320 views

Time-ordering vs normal-ordering and the two-point function/propagator

I don't understand how to calculate this generalized two-point function or propagator, used in some advanced topics in quantum field theory, a normal ordered product (denoted between $::$) is ...
16
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3answers
720 views

“Slightly off-shell”?

I'm not new to QFT, yet there are some matters which are quite puzzling to me. I often come across the statement that real particles (the ones we actually measure in experiments, not virtual ones) are ...
10
votes
2answers
472 views

The derivation of the Belinfante-Rosenfeld tensor

It seems me that there is a "difference" (at least apparently) in how the Belinfante-Rosenfeld tensor is thought of in section 7.4 of Volume 1 of Weinberg's QFT book and in section 2.5.1 of the ...
10
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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 ...
5
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2answers
468 views

the causality and the anti-particles

How can I quantitatively and qualitatively understand the fact that there is a relevence between the existence of anti-particles and the causality?
4
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3answers
741 views

What are some approaches to discrete space-time used in modern physics?

This thought gave rise to some new questions in my mind. What are the consequences for: How would it affect duality i.e. particle, wave property of photons? How does this statement affect the ...
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4answers
783 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 ...
12
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2answers
361 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 ...
5
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2answers
650 views

What is the role of the vacuum expectation value in symmetry breaking and the generation of mass?

Consider a theory of one complex scalar field with the following Lagrangian. $$ \mathcal{L}=\partial _\mu \phi ^*\partial ^\mu \phi +\mu ^2\phi ^*\phi -\frac{\lambda}{2}(\phi ^*\phi )^2. $$ The ...
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2answers
1k views

Why do neutrino oscillations imply nonzero neutrino masses?

Neutrinos can pass from one family to another (that is, change in flavor) in a process known as neutrino oscillation. The oscillation between the different families occurs randomly, and the likelihood ...
4
votes
2answers
379 views

Normalization of the path integral

When one defines the path integral propagator, there is the need to normalize the propagator (since it would give you a probability density). There are two formulas which are used. 1) Original ...
3
votes
1answer
355 views

Why helicity is proportional to the spin of particle and has two values?

How can it be shown without using the little group formalism? Let's have the Wigner's classification for the irreducible represetation of the Poincare group. For the massless case the eigenvalues of ...
6
votes
1answer
414 views

Why Zeta regularization is not valid for multiple-loops?

Why zeta regularization only valid at one-loop? I mean there are zeta regularizations for multiple zeta sums. Also we could use the zeta regularization iteratively on each variable to obtain finite ...
2
votes
1answer
324 views

Is it possible to take a QFT class knowing only basic quantum mechanics?

I'm in grad school and notice there are no prerequisites required for QFT in the physics department. In fact, the system allows me to sign up for the course just fine as a technical elective. But... ...
2
votes
3answers
288 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, ...
1
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0answers
89 views

Prerequisites for QFT? [duplicate]

Possible Duplicate: Book recommendations Is there a book that covers everything you need to know (and possibly more) before starting a course on QFT. Alternatively, I need a list of what ...
13
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1answer
460 views

Regulator-scheme-independence in QFT

Are there general conditions (preservation of symmetries for example) under which after regularization and renormalization in a given renormalizable QFT, results obtained for physical quantities are ...
15
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1answer
616 views

Zero modes ~ zero eigenvalue modes ~ zero energy modes?

There have been several Phys.SE questions on the topic of zero modes. Such as, e.g., zero-modes (What are zero modes?, Can massive fermions have zero modes?), majorana-zero-modes (Majorana zero ...
14
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4answers
466 views

Separability axiom really necessary?

I know other people asked the same question time before, but I read a few posts and I didn't find a satisfactory answer to the question, probably because it is a foundational problem of quantum ...
14
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4answers
855 views

What is anti-matter?

Matter-- I guess I know what it is ;) somehow, at least intuitively. So, I can feel it in terms of the weight when picking something up. It may be explained by gravity which is itself is defined by ...
12
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3answers
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Equivalence of canonical quantization and path integral quantization

Consider the real scalar field $\phi(x,t)$ on 1+1 dimensional space-time with some action, for instance $$ S[\phi] = \frac{1}{4\pi\nu} \int dx\,dt\, (v(\partial_x \phi)^2 - \partial_x\phi\partial_t ...
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2answers
1k views

Poincare group vs Galilean group

One can define the Poincare group as the group of isometries of the Minkowski space. Is its Lie algebra given either by the equations 2.4.12 to 2.4.14 (..as also given in this page - ...
7
votes
1answer
641 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 ...
12
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2answers
880 views

Time ordering and time derivative in path integral formalism and operator formalism

In operator formalism, for example a 2-point time-ordered Green's function is defined as ...
10
votes
1answer
286 views

What is the reason why anyons escape spin-statistic theorem?

I'm wondering about the exact reason why anyons escape the spin-statistic theorem (SST), see e.g. http://en.wikipedia.org/wiki/Spin–statistics_theorem. I've read somewhere (the wikipedia page is ...
10
votes
3answers
2k 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 ...
12
votes
1answer
403 views

What really are superselection sectors and what are they used for?

When reading the term superselection sector, I always wrongly thought this must have something to do with supersymmetry ... DON'T laugh at me ... ;-) But now I have read in this answer, that for ...
7
votes
5answers
531 views

What is the path integral exactly?

I asked a question here about path integrals and QFT. I just want to confirm something. Is the path integral in quantum field theory a mathematical tool only? I thought the path integral meant that ...
3
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2answers
250 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?
14
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3answers
674 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, ...
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4answers
517 views

On-shell symmetry from a path integral point of view

Normally supersymmetric quantum field theories have Lagrangians which are supersymmetric only on-shell, i.e. with the field equations imposed. In many cases this can be solved by introducing auxilary ...
8
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2answers
650 views

Why do some anomalies (only) lead to inconsistent quantum field theories

In connection with Classical and quantum anomalies, I'd like to ask for a simple explanation why some anomalies lead to valid quantum field theories while some others (happily absent in the standard ...