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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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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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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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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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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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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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26 views

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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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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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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2answers
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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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Combinatorics geometric series two-point function

In this answer Proof of geometric series two-point function it is said: Now what about the coefficients in front of each Feynman diagram? Due to the combinatorics/factorization involved it ...
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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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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
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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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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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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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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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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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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
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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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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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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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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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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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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
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Is the electron a bound state of two Weyl fermions?

The massive Dirac fermion is strange in that it transforms under the Poincare group as a direct sum of two spin-1/2 representations of the group $(\frac{1}{2},0)\oplus (0,\frac{1}{2})$. This suggests ...
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Deriving effective interactions, e.g. phonon-mediated electron-electron interaction

Upshot of the question: how can I derive the effective electron-electron interaction brought about by the electron-phonon interaction? I've read derivations of the electron-phonon interaction and ...
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1answer
70 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
38 views

Interacting term in Jellium model

I have a question about the deduction of interacting term in Jellium model. In the text book Condensed Matter Field Theory ed.2 Alexander Altland, Ben Simons, pg.52. Author gives the expression of e-e ...
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1answer
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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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How to calculate $n$-point functions of interacting fields in curved spacetime (Schwarzschild metric)?

How to renormalize quantum field theory in curved spacetime? (or in Schwarzschild spacetime?)  I want to calculate n-point functions $$<0|Tφ(x_1)...φ(x_n)|0>$$ in massless $φ^4$ theory in ...
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1answer
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Non-Abelian Gauge Field and Fermions Under Parity?

Under a discrete parity transformation, how does a non-abelian gauge field $A^a_{\mu}(x)$ transform? Is it possible to get mixing between the colors? How about the fermion $\psi_n(x)$ which is coupled ...
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1answer
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Field operator commutation: If two operators commute, then their fourier transforms also commute?

Im doing this in the context of field operators $$\psi(x)=\sum_k a_k e^{ikx},$$ $$\psi^T(y)=\sum_k a_k^T e^{-iky},$$ and their being defined as the fourier transform of the creation/annihilation ...
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quantum fluctuations at the horizon

So suppose we have a black hole with hair, that is a background solution in our field theory that describes a black hole spacetime and in which a field coupled to gravity has a non zero configuration. ...
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Asymptotic LSZ reduction formula (Peskin & Schroeder)

Peskin & Schroeder, An Introduction to Quantum Field Theory, write at page 224 $$\int d^{4} x e^{i p \cdot x}\left\langle\Omega\left|T\left\{\phi(x) \phi\left(z_{1}\right) \cdots\right\}\right| ...
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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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Masssive mediator boson, a game changer, so is the weak force fundamentally different from the other forces?

I have read this question: How it is possible to mediate a weak interactions by very heavy particle such as Boson? How can a pion have a mass, given it's a "field mediator" and ...
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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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Is the Black Hole a very slow motion star explosion?

Inside the black hole, in the event horizon, the time dilates, thats it : it stops! If the viewer is outside the event horizon, he/she will seeg something fall in the black hole and freeze(inside the ...
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Correlation diagram for related branching ratios. How to interpret?

I wonder how to interpret the following diagram and how one can see where to place the diagonal lines? Source:https://arxiv.org/pdf/0809.0608.pdf So my thoughts on this: The two axis are two ...
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Applying Schwinger-Dyson equations within the LSZ formula

My problem will be formulated in terms of $\phi^3$ theory, and I would appreciate answers within the framework of $\phi^3$ or another scalar field theory. This question is to help me understand what ...
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3answers
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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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How do we make sense of the number of particles in the universe in quantum field theory?

This might be a relatively straight forward answer but given the number of particles in the universe is in the region of 10 to the 80, how does this play out in a field-theoretic setting? Can we ...
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Photo pair production: differential cross section

In a scientific paper, I need for my Bachelor thesis, the differential cross section for photo pair production $\gamma\gamma\to e^{+}e^{-}$ is given as follow: $\mathrm{d}\sigma = \frac{r_{0}^{2}\...
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1answer
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Are Instantons Massless?

That is, are the only field configurations which give a non-zero winding number ones in which the Fourier transform includes a factor like $\theta(k^0)\hat{D}\delta(k^2)$, where $\hat{D}$ is some ...
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What this quantum field operator represents $ b_{in}(t) = \frac{1}{\sqrt{2 \pi}} \int e^{-i \omega t} b(\omega)$

In Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation Physics Department, Uniuersity of Waikato, Hamilton, ¹tuZealand (Received 29 ...
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Again on Spin Operator in Dirac Field Theory (Peskin & Schroeder)

Good morning, I've already seen that this topic has been discussed so long, but my doubts remain unchanged. At page 61 of Peskin & Schroeder, An Introduction to QFT, there is the demonstration ...
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Failing to show $\xi$-gauge-independence in an abelian Spontaneously Broken Gauge Theories (SBGT)

I am studying the following paper: Appelquist, Carazzone, Goldman & Quinn, Renormalization and Gauge Independence in Spontaneously Broken Gauge Theories, https://doi.org/10.1103/PhysRevD.8.1747 ...