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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Can a quantum field theory be completely simulated by a quantum computer? [closed]

I heard a talk on quantum computing and black hole. In this talk Leonard susskind raised a question: can QFT be completely simulated by using a quantum computer? But he said he was not going to answer ...
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Peskin & Schroeder QFT,eq. (2.56) derivation

I'm trying to derive the eq.2.56 of P&S's QFT textbook step by step: $$(\partial^2+m^2)D_R(x-y)=-i\delta^{(4)}(x-y). \tag{2.56}$$ I have no problem with the first step: $(\partial^2+m^2)D_R(x-y)=(\...
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What energy is produced in cable connecting the two terrestrial magnetic poles following this discovery of a variable magnetic field around the earth?

First thank you for trying to understand the content of the message not the form because I do not speak English. Principle of operation with scientific sources: Earth's interior is a far from quiet ...
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The relation between full Green's function and S-matrix

I'm learning Green's function in condensed matter. The full Green's function is defined as $$G(k_2,t_2;k_1,t_1) = <\Omega |T a_{k_1}(t_1)a_{k_2}^{\dagger}(t_2) |\Omega> $$ The $\Omega$ is the ...
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What is the physical significance of the running mass $m^2(\mu)$? [duplicate]

In QFT under the $\overline{\text{MS}}$ subtraction scheme the renormalized mass $m_R$ becomes a $\mu$-dependent quantity which "runs" via a differential equation $$\frac{1}{m_R^2}\frac{d ...
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What is the relationship between density respose function and spectral function?

In ultracold atomic experiments, Bragg spectroscopy and Radio-frequency spectroscopy both can measure the property of the energy specturm. But one says that Bragg spectroscopy measures the density ...
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From where can I study $SU(2)\times U(1)$ Symmetry Breaking [duplicate]

I have done till $U(1)$ Symmetry Breaking for my master's thesis and need to do $SU(2)\times U(1)$ Symmetry Breaking. My supervisor suggested the book 'Gauge theory of elementary particle physics' for ...
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Propagation of a wavefunction on a Riemannian sigma model

I have a question about Riemannian sigma model, in particular how wavefunctions propagate. Here the Riemannian sigma model refers to the one introduced in 10.4.1 and 10.4.2 of the book $\ulcorner$ K. ...
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Peskin & Schroeder Chapter 16.1 derivation

I am trying to derive the term shown in chapter 16.1 in Peskin & Schroeder. We have defined our polarisation vectors as $$ \epsilon^+_\mu(k)=\left(\frac{k^0}{\sqrt{2}|\vec{k}|},\frac{\vec{k}}{\...
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Polarization vector basis in Peskin & Schroeder

I am studying chapter 16.1 of Peskin & Schroeder and I am trying to understand how the chosen polarization vector basis works. It is given by the following: $$ \epsilon_i^T\cdot\epsilon_j^{*T}=-\...
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What are critical dimensions in statistical field theories (SFTs) and quantum field theories (QFTs) and how do they relate to divergences?

My question is the following. Statistical field theories (SFTs) and quantum field theories (QFTs) are usually associated with some upper critical dimension (UCD) and lower critical dimension (LCD). ...
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How to second-quantize an operator if the field operator is a spinor

In non-relativistic QM, one normally second-quantizes an operator using $$ \hat O=\int d^3r~\hat\psi^\dagger(r)O~\hat\psi(r),\qquad(1)$$ where the field operator $\hat\psi$ is given by $$\hat\psi(r)=\...
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Steps in Quantizing Electromagnetic Field for the Gauge Condition $A_0=0$

While reading section 9.3 of QFT An Integrated Approach by Fradkin, it is shown (see equations $(9.49)$ and $(9.54)$ of the book) $$B_{j}(\boldsymbol{x})^{2}=\boldsymbol{p}^{2} A_{j}^{T}(\boldsymbol{p}...
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Is CPT symmetry a direct consequence of Special Relativity?

I'm wondering about the origin of $\mathcal{CPT}$ symmetry in the Standard Model. The Wikipedia entrance makes me understand it is a direct consequence of Special Relativity. Is it right?
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Currently self-studying QFT and The Standard Model by Schwartz and I'm stuck at equation 1.5 in Part 1 regarding black-body radiation

So basically the equation is basically a derivation of Planck's radiation law and I can't somehow find any resources as to how he derived it by adding a derivative inside. Planck says that each mode ...
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The Partition Function of $0$-Dimensional $\phi^{4}$ Theory

My question is related with this question. Several years ago, I posted an answer to the question, and the author of the reference removed the link permanently, now I have no clue what's going on. In ...
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EFT's $\hbar$ counting at loop level

In the Saclay Lectures on EFT, the author Falkowski claims under eq. (2.29) on p. 22: Note that $\hbar$ counting still works at the loop-level. To see this, one should take into account that, when $\...
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EFT matching: using tree-level to perform 1-loop-level

I'm reading the Saclay Lectures on EFT, and I don't understand how it uses the tree-level matching to compute the 1-loop-level matching. To simplify, in this post I'll put its $C_6,\lambda_1=0$ since ...
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Question about field configurations on the boundary of $\mathcal{I}^+$

I am reading Strominger's lecture notes "The infrared structure of gravity and gauge theory" (https://arxiv.org/abs/1703.05448). In chapter two, while trying to derive an expression about ...
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Antifields in BV formalism - do they also have gauge transformation laws?

I am studying Weinberg Vol 2 and the BV formalism of the gauge theory. There, the antifields are introduced somewhat out of thin air. I am a little bit confused about their properties. For example, ...
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Are the particles in the zero-energy Higgs field real or virtual?

We all know that in particle physics the vacuum state is the state with no real particles. Unless the vacuum has the least energy with particles, because the degenerate vacuum, lowest energy state ...
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Implicit renormalization of $\phi^4$ theory

In the lecture notes, I am following on Quantum Field Theory, we want to renormalize $\phi^4$ theory with the Lagrangian: $$\mathcal{L} = -\frac{1}{2}(\partial_\mu \phi^0)^2 - \frac{1}{2} m_0^2 (\phi^...
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Faddeev - Kulish paper questions

I have several questions regarding the paper Asymptotic conditions and infrared divergences in QED, written by Faddeev and Kulish in 1970. This is not a post about one question, but since all the ...
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Virtual soft photon exponentiation

I have a question regarding Weinberg's soft exponentiation result in his 1965 paper called 'Infrared Photons and Gravitons' (https://doi.org/10.1103/PhysRev.140.B516). When he tries to calculate the ...
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Subleading soft theorem and gauge invariance

I am reading a paper by Burnett-Norman and Kroll, called extension of the Low soft photon theorem (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.20.86). The authors claim that in order to ...
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What is the origin of these log terms in dimensional regularization?

The following limit is implied on page 250 of Peskin and Schroeder: $$\Gamma\left(2-\frac d2\right)\left(\frac 1 \Delta\right)^{2-\frac d2} \xrightarrow{d\rightarrow 4} \frac 2\epsilon - \log \Delta -\...
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Dimensional regularization vs. hard cutoff and their relation to the renormalization scale in 2d vs 4d to find $\beta$ functions

I would like to understand some shortcuts people are using to calculate $\beta$ functions using dim. reg. with mass scale $\mu$ and/or the hard cutoff $\Lambda$. My end goal is to use equation 12.53 ...
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Is there a relationship between the beta function and the dimensions on which a theory is built? [closed]

The beta function tells us the relationship between the coupling parameter and the energy scale on which we study a system. What happens to this function when a QFT is formalized in, say, 3 dimensions?...
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Path integral on many-body quantum mechanics

Suppose $\mathscr{H}$ is a Hilbert space describing a one-particle quantum system and $\mathcal{F}(\mathscr{H})$ is its associated Fock space, which is used to describe a many-body quantum system. Let ...
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Deriving non-relativistic potentials from QFT

Some systems, like atoms, are described well by quantum mechanics, where one just gives the Hamiltonian in the form $H=T+V$ and computes the eigenvalues and eigenvectors of this operator to figure out ...
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Why is $\mathcal{M}(k)$ given by this? (Ward Identity derivation in Peskin & Schroeder)

In page 160 of Peskin & Schroeder we are considering an amplitude $\mathcal{M}(k)$ with an external photon as given in equation (5.77) $$ \sum_{\epsilon}|\epsilon_\mu^*(k)\mathcal{M}^\mu(k)|^2=|\...
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Why does expressing the Faddeev-Popov determinant as this lead to such problems?

Background In the following, I am interested in the Schwinger function associated with the gluon propagator when one considers the Gribov no-pole condition in the partition function. Defining $\nabla^{...
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Does the neutrino interact with the photon?

I know that the straight answer is no, but in my EFT course, where we're interested in nonrenormalizable operators of the Lagrangian, things aren't so straightforward. The non-minimal QED Lagrangian ...
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In the electron vertex function, why is the square of the momentum of the incoming photon negative?

On page 191 of Peskin and Schroeder, they state: Since $q^2<0$ for a scattering process… where $q$ is the momentum of the incoming photon in the electron vertex function. Why is this so? Shouldn’...
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Did I understand RG correctly?

I am currently self-studying Renormalization Group (RG) in Condensed matter physics (in preparation for graduate school while I'm in Alternative Military Service). While I'm writing bunch of ...
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Show that the energy of the electromagnetic field is given by half the norm of the Fourier transform of the electric field

Following Peskin and Schroeder on page 179-180, I am trying to show that $$\frac 12\int d^3x \left(|\mathbf E(x)|^2+|\mathbf B(x)|^2\right) = \int \frac{d^3 k}{(2\pi)^3}|\mathbf k|^2\sum_{\lambda = 1,...
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Defining normal-ordering in an OPE calculation

Suppose $\phi_1, \phi_2, \psi$ and $\bar{\psi}$ are free fields of a two-dimensional CFT with propagators on the plane given by $$\phi_1(y)\phi_1(z) \sim -\log(y-z),\quad\phi_2(y)\phi_2(z) \sim -\log(...
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Definition of a determinant Peskin&Schroeder

In page 514 of Peskin&Schroeder we are given the definition of a determinant as $$ \det\left(\frac{1}{g}\partial_\mu D^\mu\right)=\int{\cal{D}cD\bar{c}\exp\left[i\int {d^4x\bar{c}(-\partial^\mu D_\...
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Most general 4-fermion EFT

In order to understand EFTs, I'm trying to work with an example: namely, the UV Yukawa theory that reduces to 4-fermion theory in the IR: $$\mathcal{L}^\text{UV}=\frac{1}{2}(\partial\phi)^2-\frac{1}{2}...
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Approximating high-energy Compton scattering cross section

I’m trying to obtain the approximation (5.94) on page 164 of Peskin and Schroeder’s “Introduction to QFT”. Let an electron with momentum $p = (E,-\omega\hat z)$ scatter off a photon with momentum $k = ...
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Does the vacuum really have infinite energy density?

I said: As far as I understand it quantum field theory says that the vacuum has an infinite energy density. r/AskPhysics RedditorAbstractAlgebruh said: But wouldn't that be due to the way we do the ...
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Explicit check of Ward identity (Peskin & Schroeder p. 160)

I am trying to check explicitly that the (Compton) amplitude $$i\mathcal{M} = -ie^2\epsilon^*_\mu(k’)\epsilon_\nu(k)\bar u(p’)\left[\frac{\gamma^\mu \not k\gamma^\nu + 2\gamma^\mu p^\nu}{2p\cdot k}+\...
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Dirac propagator in Non-Abelian Theory

I am trying to derive equation (16.4) from chapter 16.1 page 506 of Peskin&Schroeder. Here is my derivation My Attempt We start here by considering the dirac spinor part of the Non-Abelian ...
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6 votes
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Gell-Mann Low formula vs time independent perturbation

Consider a nonperturbed Hamiltonain $H_0$ and an eigenstate $|\Psi\rangle$ satisfying $$H_0|\Psi\rangle=E_0|\Psi\rangle.$$ Now consider the perturbed Hamiltonian $H=H_0+\lambda H_1$ and let $H_\...
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Propagators in Quantum Field Theory at Finite Temperature

While reading section 5.8.2 of Quantum Field Theory An Integrated Approach by Fradkin, I had a few questions, not able to think them though myself. The thermal propagator is given as $$G_{T}^{(0)}(\...
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Wick's theorem: From operators to fields

I understand Wick's Theorem when operators are involved to be, $$\mathcal{N}(f(a,a^\dagger) = :\!\sum\textbf{All contractions}\!:$$ But I'm getting slightly confused when this is expanded to fields, I'...
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Wick's Theorem and Functional Derivative

In the Quantum Field Theory An Integrated Approach, Fradkin, the author derived the partition functional for a free scalar field (after analytic continuation to imaginary time ) as $$Z_{E}[J]=Z_{E}[0] ...
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What is the role of Hermitian Hamiltonians in relativistic QFT?

In single-particle quantum mechanics, the probability of finding the particle in all space is conserved due to the hermiticity of the Hamiltonians (and remains equal to unity for all times, if ...
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Polar decomposition of a complex scalar field theory

In the text I am referring to, the field was substituted in terms of a number density and phase: $$\psi(x) = \sqrt(ρ(x))e^{iθ(x)}.$$ While quantizing the field, a commutation relation was imposed: $$[\...
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References to superpositions of vacua states, for SSB

I would like to read more about this subject, about having an unbroken symmetric superposition of the vaccua (minimum energy state), instead of directly chosing one, for computing SSB as my teachers ...
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