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 particle physics. Don’t combine with the [quantum-mechanics] tag.

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In quantum tunnelling, what does actually propagate through the potential barrier: the wavefunction or the physical entity, which is described by it?

The wavefunction describes the quantum particle. The wavefunction exists on both sides of the tunnel barrier. It's the eventual detection on the other side that indicates the particle has tunnelled. ...
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If object (as tennis ball) can't be described by one wavefunction, how can we say there's non-zero probability for quantum tunnelling of such object?

A "macroscopic" object (e.g. a cup) cannot be described by one wavefunction (in the sense of a solution of ONE quantum mechanical equation). And even though the object can be described by ...
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Path integral and the Generator Functional [closed]

Does the path integral: $$\int D[\psi] e^{i(S[\psi]+\int J\psi d^4x)}\tag{1}$$ always equal: $$e^{iW(J)}\tag{2}$$ where $W(J)$ is the generator functional? Basically, is quantum field theory about ...
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Reference for anomalies

I'm reading the preface to the Dover edition of Itzykson and Zuber's "Quantum Field Theory". On page xix, Zuber says "... Perhaps the most dramatic obsolescence in the book is the ...
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How to verify the corectness of a renormalization scheme?

I am currently studying renormalization and have the above question about the renormalization scheme. So as far as I understand when we renormalize, we come from the realization that there are ...
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What do I need and where do I start to understand unitary (projective) representations in QFT? [closed]

Currently I'm studying QFT from Weinberg and also watching the lectures of Prof. Tobias Osborne through his YouTube channel. He started the first lecture by talking about unitary representations and ...
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Does Adler-Bell-Jackiw anomaly break also the $SU(2)_{\mathrm{vectorial}}$ symmetry?

I noticed that in the case of $U(1)_{\mathrm{axial}}[U(1)_{EM}]^2$ anomaly ($U(1)_{\mathrm{axial}}$ is a subset of $SU(2)_{\mathrm{axial}}$ symmetry), supposing the quarks have equal masses by a ...
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According to quantum mechanics, can a "macroscopic object" (e.g. tennis ball) spontaneously get in coherent state?

According to quantum mechanics, can a "macroscopic" object (e.g. tennis ball) spontaneously and without any manipulation/intervention get in coherent state?
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Why the mean field value of Lagrangian multiplier is real in slave boson method for Kondo problem and other

When dealing Kondo problem (or any other similar problems) with slave boson method, we write $$S_i=\frac{1}{2}\sum_{\alpha\beta}f_\alpha^\dagger\sigma^{i}_{\alpha\beta}f_\beta$$ with constraint $n_f=1$...
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How is the Feynman propagator (Green's function) connected with the field?

Let's take a look at the Feynman propagator for a massive scalar field: $$D_F(x-y)=\int\frac{dp^3}{(2\pi)^3}\int\frac{dp^0}{2\pi}\frac{ie^{-ip \cdot (x-y)}}{p^2-m^2}$$ We can use this as the Green's ...
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Anomalies in physics [closed]

My question is when to take anomalies seriously and when not to.(Neutron muon $g^-2$ anomaly just disappeared)
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Classical Mechanics Lagrangian from Underlying Quantum Field Theory

Does the K - T classical mechanics Lagrangian emerge from some structure of the Lagrangian of the underlying QFT?
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Understanding Gaussian ground state wave functional

Right now I'm looking into Gaussian state preparation for quantum simulation of field theories. These Gaussian states are important because they are the ground state of the free fields of interest. I'...
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How does QFT describe an electron in a magnetic field?

Is the electron represented by some kind of wavepackage (localized in space) or by a Fock state and not localized in space? Does then a collapse of the wavefunction occur when one sees the points of ...
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What are the beta functions for electroweak and strong constants of interactions?

As the title says I want to find beta function for electroweak and strong constants ($g$ for W-boson, $g'$ for B-boson and $g_s$ for gluons) Beta function is the function that describes change in ...
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Determine vector of spin in Proca equation

We have Proca field $A_\mu$ that has 4 components and obeys the following equation (with Lorentz gauge) $\square A^\mu+m^2A^\mu=0$ This equation has plane wave solution $A_\mu=a_\mu e^{ik^\nu r_\nu}$ ...
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Feynman rules after a Hubbard-Stratanovich transformation, i.e. for a field with no kinetic term

I am trying to calculate the beta function of the 2D Gross-Neveu model after performing a Hubbard-Stratanovich transformation. Of course, you can calculate it without this transformation, but I am ...
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Characterization of quark & gluon fields inside a nucleon [closed]

I was just reading a recent Quanta transcript of Steven Strogatz talking with David Tong about QFT. In the discussion, Tong talks about describing the constituents of a nucleon as "the [quark and ...
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Rigorously building a Fock space, creation/annihilation operators and inner products in a QFT

I would like to understand how one can install a set of states, starting with a vacuum, define creation/annihilation operators for the vacuum, solve for mode functions and define inner products in a ...
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Vacuum Energy in QFT

I am studying from Zee's 'QFT in a Nutshell' and very elegantly he reduces all of QFT into one single equation (Pages 43, 88). Where the phi and m are for the free field, phi-4 is the anharmonicity ...
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Does String Theory predict things like Unruh effect and Hawking radiation?

I've seen the other post about this, but the answer only discusses Unruh effect rather than String theory. Hawking radiation and Unruh effect solidify fields as the universe's fundamental objects. ...
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In what sense is string theory not expected to be a QFT?

This question came to mind while reading about Weinberg's folk theorem that any quantum theory that is Poincare covariant and satisfies cluster decomposition will look like a quantum field theory at ...
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Feynman Two Loop Integrals

Is there any reference suitable for a beginner that you recommend for learning two loop integrals evaluation by hand ( and/or some package) that you know of?
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The distinction between real and virtual particles

I will take the simple case of a spin-0 field: $$W(J)=-\iint d^4xd^4y J(x)D(x-y)J(y)$$ which in the Fourier transform becomes: $$W(J) = -\int d^4 p J(p)^* \frac{1}{p^2-m^2+i\epsilon} J(p)$$ what I ...
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How to calculate two-particle spectrum/density of states

In quantum many body theory, there is a convenient process for calculating the single particle density of states using the imaginary-time Green's function $$\mathcal{G}(k,i\omega)= \langle \psi(k,i\...
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Where do large logarithms come from? Weinberg, Chapter 18, QFT Volume 2

I am having trouble understanding a statement from Weinberg's book. Let me give you a bit of background before I ask about the statement. Weinberg considers the following: Let's take a physical ...
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How do quantum probabilities transform under Lorentz transformations?

I think I get how scattering probabilities transform under Lorentz transforms. Once the interaction phase is over, the final probabilities become time independent. Hence, every observer could describe ...
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$\delta$-function integral when calculating the differential cross section

I am reading an article and trying to do step-by-step calculations for some other similar work I am working on. The article is about scattering of a photon on a positronium. In the initial state there ...
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$\varphi^4$ propagator of the complete theory with cut-off in position: can I define things like that?

I am interested in a theory that reduces to a Euclidean $\varphi^4$ one in a specific limit. I want to calculate the full propagator of the theory, which means not using the perturbative expansion. I ...
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Why Electron Quantum Field Wants Little Energy But Photon Field Doesn't

In this Quora post: https://qr.ae/pv5tac, it states that the electron quantum field "wants" to reduce the energy it has, so when a particle and an anti-particle interact and the charges ...
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Problems encountered in simplification with Wick's theorem [closed]

$$U_k=\cosh \lambda_{k}$$ $$V_k=\sinh \lambda_{k}$$ $$ \langle0| \sum_{k,p,q} U_{k+q} V_{k+p} U_{p} V_{q} b_{-k-p} b_{k+q}^{\dagger} b_p b_{-q}^{\dagger} |0\rangle$$ By using wick' theorem we can ...
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Hadrons as partons? e.g. hadron distribution function inside another hadron

Parton distribution functions (PDFs) are typically seen as describing the probability that a parton, e.g. a quark or gluon, can be found in a hadron with particular momentum fraction $x$. They can be ...
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In double-slit experiment with single atoms/molecules, how does the "gun" actually work?

In double-slit experiment with single atoms/molecules, how does the "gun" actually work? How are the atoms/molecules "launched" to the slits?
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Primary fields in di Francesco's CFT

In the CFT book by Di Francesco et al. they use conventions such that part of the conformal algebra (see eq. 4.19) is $$ [D,P_\mu]=iP_\mu, \\ [D,K_\mu]=-iK_\mu, \tag{1} $$ where $P_\mu$, $D$ and $K_\...
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About QFT and wave packets as particles

I read Ryder's book on QFT but I couldn't understand what in facts are localized particles which are really observed and do they have any place at all in QFT. So I watched a Zee lecture in YT https://...
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Does the Unruh effect assume its conclusion?

Unruh effect says that accelerating observers see the single particle states of inertial frames as thermal baths. But it proves it by defining the particle states in the accelerating observer's frame ...
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Gauge transformation in Background Field Gauge, Weinberg Section 17.4, QFT 2

Whole idea of using background field method is to keep explicit gauge invariance, which is useful during renormalization. In section 17.4, background field gauge, Weinberg defines a ...
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Scalar QED - pair annihilation into photon cross section

I just spent the last three days trying to compute the cross section of a process of pair annihilation of complex scalars to a pair of photon in scalar QED. For some reason I don't seem to be able to ...
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Can a quantum Field State be mathematically treated as a Superposition of "classical Setups" with Particles evolving according to path integrals?

In quantum Mechanics, a State of the System (a Wavefunction) can be understood as a "Superposition" of a continuum of different "classical States" (Positionings of the Particles) ...
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Whats is a large fields problem in RG?

I was advised on MO to link this question and reproduce it here, so here it goes. I was reading Constructive Renormalization Group by V. Rivasseau and I got some points which I would like to clarify. ...
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Setting of renormalization scale in field theory calculations when more than 1 physical scales are involved

In beyond the Standar Model of particle physics, it is very common to have new particles in the game with respect to the Standard Model spectrum. When computing self energies for the light particles ...
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What are the adequate Hilbert spaces for Schrödinger, Schrödinger–Pauli, Dirac equations, and QFT?

In quantum mechanics (both non-relativistic and relativistic), it is possible to study physical systems by looking for solutions of PDEs, whose solutions belong to suitable Hilbert spaces: ...
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Path integral of Quantum Gravity while keeping Einstein's relation satisfied

Suppose we have a field $\phi(x)$ and the metric field is $g_{\mu \nu}(x)$. The action is the functional $S[\phi (x) , g_{\mu \nu } (x)] $. We want to do the path integral: $$\int d[\phi (x)] d[g_{\mu ...
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QFT-style vs. (NR)QM-style [closed]

This question refers to the differences between usual formalism of ordinary quantum mechanics (QM) and usual formulation of QFT. Speciffically, there are three questions I would like to know: The ...
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Inertial mass associated to a system of gauge bosons?

Both gluons and photons are massless bosons. The former ones produce a confining field, which explains that about 99% of the apparent mass of a proton or neutron is due to gluon interaction energy $...
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Greens Functions in Birrell and Davies "QFT in Curved Space" book

I am studying QFT in curved spacetimes from Birrell's and Davies' book. I am trying to derive the expressions for the Green's functions for a scalar field in flat space. My attempt, according to the ...
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Momentum dependence in 1-loop $\beta$ functions and renormalization conditions

Just for some practice, while calculating $\beta$-functions for a $\phi^4$ theory with graviton($D=4$), the functions I get are dependent on the incoming momentum, and are also algebraically very big (...
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Decomposition of the Photon Propagator into $K$ and $G$ propagators

I am reading a paper by B. Sahoo and A. Sen, called "Classical and Quantum Results on Logarithmic Terms in the Soft Theorem in Four Dimensions". To determine the logarithmically divergent ...
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Are the sources in QFT just particles?

I'm reading A. Zee's Quantum Field Theory in a Nutshell, where he introduces QFT using path integral formulation. One thing that I'm not sure I got correctly is this: Zee adds a source term to the ...
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Tong QFT Problem set 2, question 6: Normal ordering of angular momentum operator

I've been studying Tong's QFT notes and am trying to do problem sheet 2, question 6. here. We are asked to take the classical angular momentum of the field, $\begin{align} Q_i &= \epsilon_{ijk}\...
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