Questions tagged [quantum-field-theory]

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 this tag for many-body quantum-mechanical problems and the theory of [tag:particle-physics]. Don’t combine with [tag:quantum-mechanics].

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What's the physical meaning of the statement that “photons don't have positions”?

It's been mentioned elsewhere on this site that one cannot define a position operator for the one-photon sector of the quantized electromagnetic field, if one requires the position operator have ...
2
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2answers
42 views

Do virtual mesons exchanged between nucleons in the nuclear force ever decay before reaching the recipient nucleon?

So my understanding of the nuclear force so far is this (please correct anything I have wrong): Being a residual of the strong force, the nuclear force is mediated (in part) by the emission of ...
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0answers
62 views

What is difference between $U(1)$ symmetry and $U(1)$ gauge invariance

According to Wen's description if two states $|a\rangle$ and $|b\rangle$ with $\langle a|b\rangle=0$ have same physical properties, they are symmetric. On the the other hand if we label same ...
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0answers
46 views

Why is the $\theta$-term sometimes proportional to $g_s$?

In some sources, the CP violating $\theta$-term is written as $$ \frac{g_s^2 \theta}{32\pi^2} F \tilde F \, ,$$ while others write it as $$ \frac{ \theta}{16\pi^2} F \tilde F $$ or $$ \frac{ \...
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0answers
31 views

Realtivistic interaction in graphene

Near the Dirac points, Graphene can be described by the Lagrangian equivalent to free massless Weyl spinors: $$ L_0 = \overline{\Psi}\gamma^\mu\partial_\mu\Psi \quad. $$ From the theoretical point of ...
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1answer
53 views

Diagrammatic Representation of non-Gaussian perturbation expansions

I have no experience in graph theory and am a little confused with how Hugh Osborn represents a perturbation expansion with diagrams on page 15 of these notes. We have a perturbation expansion My ...
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0answers
25 views

Commutation relations in QFT [duplicate]

So I have just started learning QFT. So you take a classical field and turn the degrees of freedom into operators. All fine, just like normal quantum. However I am confused about the commutation ...
0
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1answer
49 views

Show that time derivative of creation-annihilation operators of Klein-Gordon field are zero

For example, for the annihilation operator \begin{equation} a(\vec{k}) = C \int d^3x e^{i k\cdot x}\partial^ \leftrightarrow _t\phi(x), \end{equation} where C is a constant that I will ignore, the ...
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1answer
63 views

A Question About $4$-Spinor Contractions

Let $f_{abc}$ be a constant which is totally anti-symmetric with respect to indices $a$, $b$ and $c$. Let $\psi^{a}$, $\psi^{b}$, $\psi^{c}$ and $\epsilon$ be Grassmann-valued Majorana fermions. How ...
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0answers
17 views

BPS Wilson loop operators and supersymmetries

In recent papers the circular Wilson loop in $\mathcal{N}=4$ SYM is always called a 1/2 BPS operator. So, my initial idea was that a 1/2-BPS operator was an operator that preserves half of the ...
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1answer
51 views

Dipole moments in QFT

We say that an electron has a dipole moment (let's arbitrarily focus on magnetic dipole moment), which we can calculate classically and also add quantum corrections. Suppose we measure the electron's ...
3
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1answer
107 views

Large $c$ limit and connected correlation functions in $2d$ QFT

EDIT: This question has been edited thanks to a comment. One of my definitions was wrong, so I have rewritten the whole question. I was reading this paper about $T \bar{T}$ deformations of $2d$-QFTs ...
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0answers
48 views

Possible Feynman diagram for $\tau^+ \rightarrow p \mu^+ \mu^-$ and $\tau^+ \rightarrow \bar{p} \mu^+ \mu^+$?

I want to know the possible Feynman diagram for these two lepton family, lepton and baryon number violating tau decays. These decays are forbidden in the Standard Model. But the further extension of ...
1
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1answer
76 views

Perturbation expansion with path integrals

This is from Hugh Osborn's 'Advanced Quantum Field Theory' notes, Lent 2013, page 15. I want to evaluate the expression $$ Z = \exp\Big(\frac{1}{2} \frac{\partial}{\partial \underline{x}} . A^{-1} \...
2
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1answer
46 views

The “Hartree-Fock energy” in the Feynman formalism vs the Hartree-Fock method

This question has been previously asked, but I do not understand the answer. When calculating the ground state energy of an interacting system by a perturbative expansion in terms of Feynman diagrams,...
3
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1answer
100 views

Difference between QFT In curved spacetime, semiclassical, and quantum gravity?

Could someone describe the difference, qualitatively, between QFT in curved spacetime, semiclassical gravity, and quantum gravity? I know that each is an approximation to the next and the end goal is ...
-4
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2answers
169 views

Did Dirac derive the correct equation for the wrong reasons? [closed]

Did Dirac derive the correct equation for the wrong reasons? This is a question about the historical discovery of the Dirac equation and how it was deduced. Looking back at that discovery with our ...
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0answers
37 views

Evaluation of Wilson loop in QED

I'am trying to figure out the evaluation of the expectation value of the Wilson loop for QED. (Its actually the problem 15.3 in Peskin and Shroeder) Lets say the Wilson loop is $W(x) = exp(-ie\oint_P ...
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0answers
45 views

Can we remove IR divergences in continuous QFT?

During a QFT class, my professor briefly explored the fact that infrared (IR) divergences can be removed from QED by considering "soft" photons that have an energy inferior to the detector sensitivity,...
3
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2answers
202 views

Quantizing Klein Gordon Field: Sign Problem

I'm trying to re-derive the Quantization of the Klein Gordon Field but I'm running into sign problems. My starting point is: $$ \phi(x,t) = \frac{1}{(\sqrt{2 \pi})^3} \int \tilde{\phi}(k,t) e^{i kx}...
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0answers
43 views

Hamiltonians and Hilbert spaces in QFT

Suppose we start from a theory with a given $\mathcal{L}$ and correspondigly a Hamiltonian $\mathcal{H}$. Now a state of this $\mathcal{H}$ is (say) $|p,q,r>$. Now suppose that we do a set of ...
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0answers
47 views

Quantum integrable models with no classical integrable counterpart

I am looking for examples for quantum integrable systems that have no classical integrable limit.
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1answer
75 views

Quantum field theory self-study [closed]

Some background: I recently finished by Bachelors in Physics from a quite intensive program. We did all the theory to the core (Things that you would expect in grad level courses in the states were ...
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1answer
36 views

Contribution of a second-order Feynman diagram for the one-particle Green function

I am studyng how to construct Feynman diagams for the perturbative expansion of the one-particle Green function (or propagator) using the book "A Guide to Feynman Diagrams in the Many-Body Problem". ...
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0answers
22 views

Difference between coherent and incoherent energy transfer (e.g. in photosynthesis)?

Several authors distinguish between incoherent and coherent when describing the energy transfer mechanism that forms the basis for photosynthesis. (e.g. Clegg & Sener 2010 and Keren & Paltiel ...
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1answer
51 views

Is total mass conserved for free Dirac fermions?

I am studying quantum field theory and stumbled across the following problem: Is the total mass conserved for free Dirac fermions? I.e., does the total mass operator commute with the Dirac ...
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1answer
85 views

(Coleman's lecture note) scattering in QFT

I am currently reading Coleman's lecture note on QFT.(https://arxiv.org/abs/1110.5013) I have several questions regarding the scattering theory. Let $\phi$ be a real scalar field, and consider the ...
0
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1answer
35 views

Evaluation of transition amplitude between two field configurations

Consider a field theory of a scalar field $\phi$ described by an action $\mathcal{S[\phi]}$. Is there a way to determine the transition amplitude $\langle \phi(x,t)'|\phi(x,0)\rangle$? Any relevant ...
4
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1answer
102 views

What's the ground state wave-functional of a fermion?

The vacuum state, free field wave-functional of a scalar field $\hat\phi(x)$ in the Schrödinger representation of quantum field theory is $$\begin{array}{cl} \Psi_0[\phi] &= C\prod_k e^{-\omega(k)...
5
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0answers
65 views

Physicist path integral and cylinder set measures

Path integral via discretization So let me start with what seems to be the point of view of physicists (corrections are highly appreciated since this is what I understood!). Let a quantum system with ...
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2answers
51 views

Are decay Feynman diagrams really Feynman diagrams too? Or just vertices?

So I was wondering, the vertex diagrams for the standard Model, can they also be feynman diagrams with on shell particles? For instance here is the W - boson vertex which decays into electron and ...
1
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1answer
76 views

I really wonder about the time derivative of creation and annihilation operators in the derivation of LSZ

In Schwartz book, they assume that $$\lim_{t \to \pm\infty}\partial_0 a_p(t)=0.\tag{1}$$ But I thought that is just assumption. so we have to construct the mathematical description. I found the Gell-...
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0answers
43 views

Off-shell vs half off-shell vs fully off-shell $T$-matrix

I know what are on-shell particles, but I want to know what are off-shell, and half off-shell, and fully off-shell states? and how we decide to consider one of these states in evaluating $T$-Matrix?
2
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2answers
71 views

Why field redefinitions that leave Lagrangians unchanged are allowed?

This may be a stupid question but I will ask it because I am not fully happy. In any quantum field theory, we start with a couple of fields $\phi_1,\phi_2,...$, and a Lagrangian involving various ...
2
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1answer
70 views

What's the exact relationship between the scale $Q$ at which parameters are probed and the “fake parameter” $\mu$?

It is well known that couplings change depending on the scale $Q$ at they are measured. This effect is experimentally well documented: From a theoretical point of view, the running $\alpha_S(\mu)$ ...
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0answers
16 views

Charge conjugate of lepton triplet

I am reading a paper on type-III seesaw model, where the authors have defined the charge conjugate of the lepton triplet as: $\Sigma_L^c=C\bar{\Sigma_L}^T$, where $\Sigma_{L}=\left(\begin{array}{cc}{\...
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0answers
43 views

Feynman rules for space-dependent coupling

Let's say I have an effective action which looks like (I got this action from large $N$ method for $\varphi^4$ theory): $$\int \frac{d^4x}{2g}\phi^2(x)+\int d^4x \ \log(-\nabla^2+\mu^2+i\phi(x)). $$ ...
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0answers
44 views

Rigorous derivation of the ground state projector using euclidean time evolution

Usually one argues that the euclidean path integral is able to recover the ground state of a system along the following lines: Take the time evolution operator $U(t,t_0)=e^{-iH(t-t_0)}$. Transform to ...
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0answers
32 views

Approximate solution to the resolvent of an open quantum system

I have an open system which evolves according to some master equation: $$ \partial_t\rho(t) = \mathcal{L}\rho(t) $$ where $\mathcal{L}$ is the Liouvillian of the system which generates completely ...
2
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1answer
56 views

What's the difference be Wilsonian and continuum EFT?

In his review on Effective Field Theory, Georgi emphasizes Within the general framework of the effective field theory idea, there are two rather different approaches, which I will call the Wilson ...
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1answer
64 views

Regularization is mandatory. What about renormalization?

We need to regularize in order to declare with confidence that infinities drop out from measurable quantities, e.g. in the form of a cutoff scale. In general, the amplitudes in QFT depend on the ...
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0answers
42 views

How do we end up with the renormalization group equations in the Wilsonian perspective?

We start with a Lagrangian $L$, which is valid up to some scale $\Lambda$ and includes couplings $g,m$. In the Wilsonian perspective, we note that the contributions from fluctuations at scales ...
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0answers
23 views

Quantizing Complex Klein gordon Field, how do they get rid of Crossed terms?

I was working through the exercises on Peskin and Schroeder specifically 2.2, I get the Following equation: $ Q=\frac{1}{2}\int \frac{d^{3}p}{(2\pi)^{3}}(a_{p}^{\dagger}a_{p}-b_{p}^{\dagger}b_{p}+a_{p}...
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0answers
41 views

Why sharp cutoff RG introduces long range interaction and smooth cutoff doesn't

In momentum shell RG we introduce a sharp momentum cutoff, and integrate out those high momentum modes to get an effective action. I heard that this kind of RG will introduce long range interaction, ...
4
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0answers
63 views

Has the conjecture of Guillemin-Sternberg been proven for relevant physics cases?

From a working physicist's perspective, the conjecture of Guillemin-Sternberg (and its generalisations) seems to state in a highly technical manner that quantization commutes with gauge-fixing. In ...
5
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1answer
61 views

Why the randomness in glass/water/air does not destroy coherence of light over fairly macroscopic scales?

When light passes through glass/water/air, photons are absorbed and re-emitted by the chemical bonds, so that the speed of light in medium is reduced. However, in these media, it would appear that the ...
3
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0answers
77 views

Why can a renormalizable quantum field theory only include spin 0, 1/2 and 1 fields?

Hitoshi Murayama writes in his 221A Lecture Notes on Spin How do we choose spin when you introduce a field, then? A consistent ( i.e. , renormalizable) quantum field theory can include only spin 0, ...
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67 views

Relation between functional measures and states in AQFT

Let $(M,g)$ be a globally hyperbolic spacetime and $\phi$ a KG field. In AQFT we consider the algebra of observables $\mathfrak{A}$ generated by $\phi(f)$ where $f\in C^\infty_0(M)$ is a test function....
4
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0answers
56 views

Quantum corrections to metric on non-linear sigma model target space

I am trying to make sense of what physicists mean when they talk of quantum corrections to the metric on the target spaces of nonlinear sigma models, for example [GHL99]. First some quick notation. ...
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0answers
64 views

Gluon-gluon scattering: Problem 8.28 in Griffiths' “Intro. to Elementary Particles” (2nd edition)

The "Introduction to Elementary Particles Instructor's Solution Manual" (available online) does not give the solution to this particular problem, which asks: (a) Draw the lowest order diagrams (there ...