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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 is going on in “nonlinear gravity from entanglement in conformal field theories”?

I have been working through a paper by Faulkner et al. (1705.03026) titled "nonlinear gravity from entanglement in conformal field theories". I have been having serious trouble reproducing their ...
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OPE Kac-Moody Currents

We have the following operators: \begin{align} J^a(z) = \frac{1}{2}\psi_s^{\dagger}(z)\sigma^a_{s s'}\psi_{s'}(z), \hspace{10 mm} \bar{J}^a(z) = \frac{1}{2}\psi_s^{\dagger}(\bar{z})\sigma^a_{s s'}\...
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1answer
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Does the Compton wavelength put a limitation on how precise we can measure the position of a particle?

I have read on Wikipedia (https://en.wikipedia.org/wiki/Compton_wavelength) that we cannot measure the position of a particle more precise than half of its Compton wavelength, since the photon we ...
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Gauge theory in Condensed Matter physics

Always come across these two jargons, namely Matter Field and Gauge Field, please explain what is the difference between them and why it is important in condensed matter physics? There are many ...
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9 views

Simplest model of laser coupling

I am not familiar with classical/quantum optics. I have a possibly very basic question about physics of laser interaction. I think my question can be broken into two parts: (1) What is the simplest ...
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22 views

S-matrix branch cuts properties

I'm trying to formally understand some non-perturbative results in scattering theory but the material available on the topic are not too friendly, so there are some very simple and essential facts I ...
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1answer
56 views

QFT must vacuum states have non zero energy?

Vacuum states of different quantum fields corresponds to different energy levels. Some sources say they are mostly zero, some other says that it is a limit imposed by heisenberg uncertainty principle, ...
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304 views

Cutoff-Scheme Renormalization and Order of Integration in QFT

The following is the result of Fubini's Theorem, describing when you can replace a double integral with an iterated integral safely: For a set $X \times Y \subset \mathbb{R}^2$, if $\iint |f(x,y)| d(...
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1answer
53 views

Is positron creation operator times electron creation operator equal to the ground state?

This is part of a larger problem, but the important part is that at one point I have: $$ bb^\dagger+bd+d^\dagger b^\dagger + d^\dagger d + b^\dagger b +db + b^\dagger d^\dagger+d d^\dagger $$ where $...
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1answer
47 views

Microcausality for Dirac's current

I`m supposed to show as an exercises that for the Dirac field's associated current: $$j^\mu=\bar{\Psi}\gamma^\mu\Psi$$ The microcausality relation holds: $$ [j^\mu(x),j^\nu(y)]=0 \text{ for } (x-y)^...
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Hypercharge normalization for $SU(5)$ GUT

Reading about $SU(5)$ unification, texts says that they use the renormalization factor $\sqrt{3/5}$ for weak hypercharges in order to embed SM into a $SU(5)$ group. This implies a new $U(1)_Y$ ...
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47 views

Are theta vacua topologically protected?

In discussions of Yang-Mills instantons it is often stated that one should sum in the path integral over all contributions of fluctuations around all the topologically distinct vacua labelled by ...
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Second book on QFT before understanding Conformal Field Theory [duplicate]

I'm a newcomer to Quatum Field Theory, recently I started to work with the very basic book of Lancaster. My final destination is to learn Conformal Field Theory applied to Quantum Phase Transitions ...
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48 views

Conservation of $\int |\psi|^2$ for Dirac wave

When $\psi$ be Schrodinger wave $\int |\psi|^2$ is conserved even when this wave interact whit another wave say electromagnetic wave. and this is very necessary for one particle interpretation of this ...
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Casimir effect: where did the pressure come from?

From my understanding of Casimir effect, there exists a difference in energy between plates and that of the outside environment. How did this translate to a pressure difference and eventually where ...
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BKT transition: nature of topological transition

BKT-transition is one of the most well-known topological transition in $O(2)$ model.But I misunderstand the physical interpratation of this transition. I started from the low-temperature expansion of ...
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20 views

Muon capture cross-section

I would like to understand how the cross-section of muon capture depends on the nuclear charge. My attempts are based on the following thinking. Muon is captured to "high" orbital and then muon goes ...
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1answer
106 views

Expressing the Schrödinger equation in 2nd quantised language

For times sake, I will only write about the non-interacting part of the Hamiltonian, $$H_0=\sum_{j=1}\left(-\frac{\hbar^2}{2m}\frac{\partial}{\partial x_j^2}+U(x_j)\right)$$ where $U(x_j)$ is some ...
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Detemining whether a particle is stable with respect to the electromagnetic, EM or strong force

If we have some beautiful hadron , how can we decide based on the quantum numbers and masses of the other beautiful hadrons whether it is stable under the electromagnetic, weak or strong interaction . ...
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Using Isospin symmetry to find the decay width of an interaction

Say we have two decays $\Delta^+\rightarrow \pi^+n$, and $\Delta^+\rightarrow \pi^0p$. I want to show, using isospin symmetry that the probabilities for these decays is in the ratio $\tfrac{Γ(\Delta^+\...
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1answer
393 views

Wick Theorem: Performing contractions in the right order

The first line is one of four terms that one gets after applying Wick theorem to the time-ordered product of these field operators and as far as i understand it is just a short-hand notation for which ...
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465 views

Symmetries in Wilsonian RG

I wanted to know if there is a theorem that in writing a Lagrangian if one missed out a term which preserves the (Lie?) symmetry of the other terms and is also marginal then that will necessarily be ...
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1answer
91 views

Politzer, Gross & Wilczek running formula

I've been told that for any group of SM, the running of the corresponding coupling constant, $g$, is given by: $$ \frac{dg}{d(\ln{Q})} = b·g^3/(16\pi^2) $$ Where $$ b = -\frac{11}{3}C_2(A) + \sum\...
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1answer
366 views

Question on Wick's theorem for fermions

I have a guilty suspicion this should be obvious. What is the difference between these two expectations taken over the same measure ($\int \mathrm{d}\mu(\bar\psi,\psi)\exp{\sum \bar\psi A\psi}$ for ...
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1answer
37 views

Are there viable alternatives to the no boundary proposal?

As I understand it, quantum field theory can be described as the evolution of a wave function $\psi_t[\phi]$ depending on some fields, $\phi$. But when we include gravity and we admit that time is ...
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2answers
123 views

Initial values of creation/annihilation operators

I have a question about creation/annihilation operators. For example, if I have an evolution equation for annihilation operator of photon $$ \frac{da_k}{dt} = -i \omega_k a_k$$ I obviously obtain $$...
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Diagrammatic expansion of an operator insertion in path integral for Trace Anomaly calculation

Starting with a scale invariant classical field theory, we can prove that the energy-momentum tensor will be traceless. \begin{equation} \Theta^\mu_{\ \mu }=0 \end{equation} In the context of the ...
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What is the source of the difficulty (within the variational approach framework) in the attempt to unify quantum mechanics with general relativity? [duplicate]

It seems to me that quantum mechanics can be formulated within the general mathematical framework of variational  principles. Derivation of the equations of nonrelativistic quantum mechanics based on ...
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39 views

Can we create a random variable using QED effects?

Quantum Electrodynamics (QED) has some observable effects such as the lamb shift, which is mainly caused by the vacuum polarization and the electron self-energy. These effects contribute to the "...
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1answer
52 views

Quantum statistical mechanics formalism

How do we solve a Hamiltonian written in second quantization by using quantum statistical formalism? For example, the following Hamiltonian $$H = \sum_{i=1}^L c_{i+1}^\dagger c_i + h.c.$$ I have ...
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61 views

Is it possible that gravitons don't exist, but are actually something like phonons? [on hold]

Why or why not? String theory says that gravity arises due to spin 2 closed strings. If gravitons were actually phonons, is it against the possibility that gravitons are actually closed strings? How ...
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130 views

OPE double-contractions between $T$ and $e^{ikX}$

I am reading David Tong's lecture notes chapter 4 http://www.damtp.cam.ac.uk/user/tong/string.html On the top of page 82 in the eq. before eq. (4.27), we are computing the OPE between $T$ and $e^{ikX}...
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1answer
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Sum over real photon polarizations. The minus sign

Ok for real photons there is the formula when summing over the polarizations: $$ \sum_{\lambda=\pm}\epsilon^{*\mu}_\lambda\epsilon^\nu_\lambda = -\eta^{\mu\nu}$$ But if I have a matrix element of ...
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32 views

Density matrix expression by path integral

I came across an expression which I don't understand for the density matrix $\rho$ given by the path integral method (Fradkin, p.760) - $$ \left< \phi(x) \left| \rho\right| \phi\left(x'\right) \...
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2answers
477 views

Annihilation and Creation Operators in QFT

I have following question about creation and annihilation operators in QFT: The Klein-Gordon field is introduced as continuous interference of plane waves $\mathrm{e}^{i(\omega_kt-\vec{k}\cdot\vec{x})...
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Electron-positron annihilation into proton-antiproton

How can I obtain the differential cross-section of the process $e^{+}e^{-}\rightarrow \bar{p}p$ from the cross section of $ep$-scattering? I have calculated the amplitude of $ep$-scattering and see $...
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1answer
49 views

Is the two-point correlaction function equivalent to a sum of two-point correlaction function?

I'm doing a research and I came across an expression that to move forward, since $<\varphi(x)^2> = \left.\frac{\delta^2 W(j)}{\delta j(x)^2}\right|_{j=0}$, I have to assume that $<\varphi(x)...
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51 views

Where does the inconsistency between QM and general relativity stem from? [duplicate]

I understand special relativity works with QM (as seen by QFT) and I know that there is some discrepancy between GR and QM. Could someone elaborate on that? Where does the inconsistency stem from? ...
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1answer
71 views

Dimensional analysis of electron-positron spectrum

The theoretical formula for the numbers of particles per energy $\varepsilon$ with colliding photons with energies $\omega_{1}$ and $\omega_{2}$ is given by following expression (reaction $\gamma\...
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1answer
151 views

Why do not renormalization group equations explicitly depend on cutoff?

Suppose $g$ is the parameter set and $\Lambda\equiv\Lambda_0e^{-t}$ the momentum cutoff, then usually one finds the renormalization group equations to take the form $$\frac{dg(t)}{dt}=\beta(g).$$ My ...
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1answer
77 views

Electron Splitting in Peskin and Schroeder

I am confused by formula (17.88) and (17.89) on page 578 in P&S. They are computing the matrix element for electron splitting ($e^-\rightarrow e^-+\gamma$) in the massless limit. They call $z$ ...
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Eigen value of a unknown system [closed]

Why we are using operator for finding the eigen value of a unknown system
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1answer
345 views

How many bits of information does an elementary particle have?

I've been studying information theory, and I'm curious about how many bits of information an elementary particle, like an electron, could have. If we take only the spin, of course it has 1 qubit (2 ...
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3answers
89 views

Why do we demand that the counterterms in $\varphi^3$ theory be $O(g^2)$?

In Srednicki's QFT book, section 9, he introduces the $\varphi^3$ lagrangian: $$\mathcal{L}= -\frac{1}{2}Z_\varphi(\partial_\mu\varphi)(\partial^\mu\varphi) -\frac{1}{2}Z_mm^2\varphi^2 +\frac{1}{6}...
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20 views

Charge conjugation opearation in odd dimension

In my problem, I use the following set of $\gamma$-matrices (in (2+1) spacetime): $$\gamma^0=\sigma^1;\quad \gamma^{1}=i\sigma^2;\quad \gamma^{2}=i\sigma^{3},$$ where $\sigma^{(i)}$ are usual Pauli ...
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1answer
160 views

Feynman $i\varepsilon$-prescription in path integral by adding an imaginary part to time

It is known that the well-definiteness of the path integral leads to the Feynman's $i\varepsilon$-prescription for the field propagator. I've found many ways of showing this in the literature, but it ...
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25 views

Hawking radiation of massive scalar field

There are some calculations about Hawking radiation (expectation value of particle number operator, 2-point function, stress-energy tensor, and so on.), which are often done under the condition that ...
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Do condensed-matter field theories with multiple fields generically have multiple speeds of sound?

It is well known that the low-energy physics of many non-relativistic condensed matter systems can be described by field theories that display emergent Lorentz symmetry. The heuristic way to figure ...
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1answer
53 views

Scalar product of free field and conjugate momentum

Given $[\Phi (x), \Pi(y)] = \delta^{3}(x-y)$,$ $ $\Phi|\phi\rangle = \phi(x)|\phi\rangle$ and $\Pi|\pi\rangle = \pi(x)|\pi\rangle$, I am trying to prove $\langle\phi|\pi\rangle \sim e^{i\int d^{3x}\...
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1answer
292 views

Decay of a scalar Particle-Symmetry factors

Consider the Lagrangian $$\mathcal{L} = \dfrac{1}{2} (\partial_{\mu}\phi_{1})^2 + \dfrac{1}{2}(\partial_{\mu}\chi)^2 - \dfrac{M_1^2}{2}\phi_{1}^2 -\dfrac{M^2_\chi}{2} \chi^2 - \dfrac{\mu_\chi}{2} \...