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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499 views

What is a “free” non-Abelian Yang-Mill's theory?

I hope this question will not be closed down as something completely trivial! I did not think about this question till in recent past I came across papers which seemed to write down pretty much ...
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0answers
130 views

Decay Amplitudes Notation

This question is mostly about how to interpret notation used in Particle Physics. I am given that at lowest order the rate of $b\rightarrow s\gamma$ is proportional to $\langle B_p|b^\dagger ...
9
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2answers
371 views

In what sense are loop diagrams quantum corrections?

What's so not-quantum about tree-level diagrams?
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3answers
326 views

Dimensional Regularization Integral Formula

In the formula $$\int \frac {d^{4-2\epsilon} \ell} {(2\pi)^{4-2\epsilon}} \frac 1 {(\ell^2-\Delta)^2} = \frac i {(4\pi)^{2-\epsilon}} \Gamma(\epsilon) \left(\frac 1 \Delta\right)^\epsilon,$$ how ...
9
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1answer
1k views

Why is there extra minus sign in Feynman's rules for every closed fermionic loop?

I know this is connected to the fact that fermions are represented by anticommuting operators, but I still cannot find the way to get this minus in Feynman rules.
19
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1answer
317 views

Asymptoticity of Pertubative Expansion of QFT

It seems to be lore that the perturbative expansion of quantum field theories is generally asymptotic. I have seen two arguments. i)There is the Dyson instability argument as in QED, that is showing ...
3
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1answer
379 views

Higgs Field compared to EM field

So, I've been reading about the Higgs because of all of this excitement lately with the LHC. I'm just a layman in physics but one thing I understood was that the Higgs field permeates all of space ...
2
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0answers
79 views

Why are interacting noncommutative quantum field theories with space-time noncommutativity unitary?

Can anyone explain in a simple manner why interacting noncommutative quantum field theories with space-time noncommutativity of the Moyal bracket sort are unitary? Thanks.
9
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4answers
978 views

The Schwinger model

The Schwinger model is the 2d QED with massless fermions. An important result about it (which I would like to understand) is that this is a gauge invariant theory which contains a free massive vector ...
4
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2answers
750 views

Zeta-function regularization in QFT for heat kernels

When one is doing zeta-function regularization of the heat-kernel for QFT then one is doing these following steps, the integral over the imaginary time taking the trace of the heat-kernel or the ...
5
votes
1answer
491 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 ...
4
votes
1answer
216 views

Convergence of quantum effective action to finite loop order

Consider the quantum effective action of a fixed QFT. If we compute it perturbatively to finite loop order $\ell$, we get a sum over an infinite number of Feynman diagrams. For example, the 1-loop ...
5
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0answers
101 views

Can the Lamb shift be expressed in more-or-less closed form in terms of the renormalized 2-, 3-,…,n-point VEVs of QED?

I see here that there are three contributions to the Lamb shift, from vacuum polarization (-27 MHz), from electron mass renormalization(+1017 MHz), and from the anomalous magnetic moment (+68 MHz). ...
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3answers
8k views

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 ...
4
votes
1answer
128 views

Derivatives of fluctuations about a condensate

Firstly I am not sure as to whether I am using the word "condensate" in the right context. In QFT contexts I think I see it getting used to mean the space-time independent solution which would solve ...
5
votes
1answer
44 views

A question from Ticcati's red QFT textbook.

From Ticcati's textbook, he asks to show that from the axioms of position operator we get that: $$ \text{e}^{-ia\cdot P} |x\rangle = |x+a\rangle $$ where the axioms are: $$ X=X^{\dagger} $$ If ...
5
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2answers
1k views

Why are anticommutators needed in quantization of Dirac fields?

Why is the anticommutator actually needed in the canonical quantization of free Dirac field?
6
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1answer
478 views

Defining the ground state energy of a QFT

I would like to hear of some general discussion on how is the ground state and its energy defined in QFT and how does one go about finding it. (..at least in some simple cases I have seen the use of ...
12
votes
1answer
1k views

How to interpret vacuum instability of Higgs potential

If the Higgs mass is in a certain range, the quartic self-coupling of the Higgs field becomes negative after renormalization group flow to a high energy scale, signalling an instability of the vacuum ...
4
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0answers
99 views

Seeking chiral anomaly EFT example

If an effective field theory has a chiral anomaly it means that chiral symmetry isn't a symmetry of the underlying theory which has been cut off to make the EFT. My question is whether there's a good ...
2
votes
1answer
114 views

Spinors in more dimensions and new degeneracies?

As you more than probably know spinors dimensions go as $2^{\frac{D}2}$ in D spacetime dimensions. If we look at the peculiar case of D=2*4, spinors have 4 components and we usually say that's related ...
3
votes
1answer
261 views

If LHC searches of a Higgs boson won't be a success, what consequences for the theory of electroweak interaction it can bear?

Whether it is necessary to search still for variants of an explanation of spontaneously breaking gauge symmetry, giving masses for a W, Z-bosons? Goldstone bosons are bosons that appear necessarily ...
9
votes
1answer
122 views

Conformal QFTs for D > 2

Which conformal QFTs do we know for spacetime dimension d > 2? I know that for D = 4 we have N = 4 SYM and some N = 2 supersymmetric Yang-Mills + matter models. What is the complete list of such ...
4
votes
1answer
241 views

Massive excitations in Conformal Quantum Field Theory

Single particle states in quantum field theory appear as discrete components in the spectrum of the Poincare group's action on the state space (i.e. in the decomposition of the Hilbert space of ...
23
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4answers
1k views

Why do or don't neutrinos have antiparticles?

This was inspired by this question. According to Wikipedia, a Majorana neutrino must be its own antiparticle, while a Dirac neutrino cannot be its own antiparticle. Why is this true?
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7answers
820 views

Why regularization?

In quantum field theory when dealing with divergent integrals, particularly in calculating corrections to scattering amplitudes, what is often done to render the integrals convergent is to add a ...
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1answer
193 views

What type of symmetry specifies in presence of what each not-charged particle (for example, neutrino) should have an antiparticle?

I think that charging symmetry assumes antiparticle presence, which has an opposite charge sign . And what symmetry assumes existence of an antiparticle at a neutral particle
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0answers
624 views

Find equations of motion from given Lagrangian density [closed]

Could someone help me solve this probably not very hard problem? Given Lagrangian Density: $\mathcal ...
14
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1answer
1k views

Difference between 1PI effective action and Wilsonian effective action?

What is the simplest ay to describe the difference between these two concepts, that often go by the same name?
7
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3answers
3k views

Electron Positron annihilation Feynman Diagram

I am having some trouble understanding this fenyman diagram, it seems to indicate that the electron produces the positron, as the arrow of the positron is pointing from the electron. Additionally ...
2
votes
2answers
885 views

Who first realized the uncertainty principle allows for virtual particle pair production?

For all I've read about Quantum Field Theory I've never seen the concept of the living vacuum accredited to someone in particular. Given the importance of this very application of the uncertainty ...
15
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4answers
2k views

Tree level QFT and classical fields/particles

It is well known that scattering cross-sections computed at tree level correspond to cross-sections in the classical theory. For example the tree level cross-section for electron-electron scaterring ...
3
votes
1answer
179 views

Pauli-Villars (PV) regularisation breaks supersymmetry. How to see that?

Does the PV regulator breaks SUSY? Take for instance the 1-loop (top/stop loops) correction to the Higgs squared-mass parameter in the MSSM, and you'll get something like, $$\delta m^2_{h_u} = - ...
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vote
0answers
375 views

Non-minimal coupling of electromagnetic field

For a massless scalar field the equation of motion in a general curved Space time is $\frac{1}{\sqrt{g}}\partial_\mu(\sqrt{g}g^{\mu\nu}\partial_\nu\phi)=0$. Though, in the action, we can by hand ...
4
votes
3answers
587 views

Special conformal transformations and locality

In the conformal symmetry, used in some QFT theories, the infinitesimal generators, applying to space-time, are all linear (translations, rotations, boosts, dilatation), except the special conformal ...
3
votes
2answers
203 views

An integral related to QFT

How to show $$\displaystyle\int\int\int f(p,p')e^{ip\cdot x-ip'\cdot x}d^3pd^3p'd^3x=(2\pi)^3\int f(p,p)d^3p$$ ? I have $p\cdot x=Et-\bf p\cdot x$
10
votes
2answers
81 views

Examples of heterotic CFTs

I'm trying to get a global idea of the world of conformal field theories. Many authors restrict attention to CFTs where the algebras of left and right movers agree. I'd like to increase my intuition ...
3
votes
1answer
507 views

Why the pion does not get mass under Spontaneus breaking of chiral symmetry, but the quarks do?

Some sources state that when the mass of a quark goes to zero, it allows for Spontaneous Breaking of Chiral Symmetry and gets a constituent mass of about $200\, \mathrm{MeV}$. Other sources state ...
7
votes
2answers
142 views

Expectation values of interacting fields

I was motivated to ask this question by the equality claimed in equation 10.3.3 of Weinberg's volume 1 of QFT books. My interpretation of that, If $O_s$ is a quantum field of spin $s$, $\psi_s$ is ...
3
votes
1answer
158 views

Unconstrained action in Yang-Mills theory

Is there any gauge in which Yang-Mills theory (4d, non-SUSY) can be written as a local action containing only the propagating modes?
9
votes
1answer
367 views

“finite” QFTs and short-distance singularities and vanishing beta functions

I am not sure that I can frame this question coherently enough - it springs from various things in QFT that I have recently been thinking and reading about. May be these thoughts are mis-directed but ...
7
votes
1answer
666 views

Explanation of Cardy's “a theorem”

There seems to have been some discussion of Cardy's "a-theorem" recently: “It is shown that, for d even, the one-point function of the trace of the stress tensor on the sphere, Sd, when suitably ...
1
vote
1answer
303 views

Why *should* the mass of elementary particles theoretically be of the magnitude of the Planck mass?

Why should the mass of elementary particles be theoretically of the magnitude of the Planck mass? I've read that already a few times but I don't understand why it should be that way. For example: ...
25
votes
4answers
1k 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 ...
13
votes
2answers
383 views

Possible research implications of proof of John Cardy's a-theorem in QFT

According to this recent article in Nature magazine, John Cardy's a-theorem may have found a proof. Question: What would the possible implications be in relation to further research in QFT? ...
7
votes
3answers
76 views

Operator norm directly from phase space representation of photonic quantum operator

I'm interested in calculating the operator norm of a Hermitian operator, say $B$, acting on the Hilbert space of square integrable functions. The context is I have an optical system in all its ...
5
votes
0answers
198 views

What happens to a Luttinger liquid under time reversal?

Suppose you a have an ordinary Luttinger liquid with $$ H = \int dx \sum _{\eta= \pm 1 , \sigma =\uparrow,\downarrow } \psi^\dagger_{\eta, \sigma} (x) (-i v \eta \partial _x) \psi _{\eta,\sigma} (x). ...
4
votes
1answer
800 views

Help with Cutkosky cutting rules for fermions

I know that a cut boson propagator is replaced with the mass shell delta function. But what happens when you cut a fermion propagator? Do you just replace the denominator with a mass shell delta ...
3
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1answer
413 views

Proca theory and renormalization

What is the simplest physical argument to claim that Proca theory (involving a massive spin-1 boson) is not renormalizable?
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0answers
99 views

Convergence and well-definedness of Lorentzian path integrals

Wick rotation of quantum field theories to Euclidean path integrals with a nonnegative measure everywhere is a wonderful tool. Not so with Lorentzian path integrals. Events far separated in ...