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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How do non-commutative fields arise in the low-energy description of the lowest Landau level?
We use quantum field theory in condensed matter physics regularly. Let us focus on bosons. Usually, the field theory picture is motivated using a trotterization of the Hamiltonian using the coherent ...
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Is the only consistent massless spin-2 QFT really exactly General Relativity in the classical limit or only linearized limit?
I'm trying to understand to what extent it is a "miracle" that a massless spin-2 field "postdicts" general relativity. I think there is some early theorem of Weinberg that shows ...
- 7,228
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Parton distribution functions and virtual particles
Parton distribution functions are distributions of quarks and gluons inside the nucleon, but besides the three valence quarks, they are virtual particles right? So if virtual particles are just a ...
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45
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Miraculous cancellations in a-priori non-renormalizable theories
Einstein's gravity is non-renormalizable since its coupling constant in 4D (I would like to limit the discussion to 4D) has negative mass dimension of -2.
Nevertheles it has been hoped that -- may be ...
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Introduce Ghost Field to eliminate unphysical degrees of freedom in case of Photon Field
In wikipedia's article about ghost fields is stated the following which requires a bit more clarification:
An example of the need of ghost fields is the photon, which is usually described by a four ...
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36
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feynman scalar integral with on-shell condition
There are many integration written down in the standard QFT textbooks for scalar integrals in the computation of matrix elements. For example, in Peskin and Schroeder, we see
$$\int \frac{d^d \ell_E}{(...
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Landau Ginzburg path integral (PI) for the Ising model at gaussian order
I am stick with a problem in computing explicitely the gaussian PI in the Landau-Ginzburg theory for the Ising model.
If we do a procedure of coarse graining, we can define $m(x)$ as a continuous ...
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1
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57
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Are creation and annihilation operators functions of momentum?
In QFT, we usually write creation and annihilation operators in the following way: ${a^s_{\textbf{p}}}^\dagger$, $a^r_{\textbf{q}}$, where $r,s$ denote the spins and $p,q$ the three-momenta of ...
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Explicit Form of Feynman Propagator for a Scalar Field in Position-space: Derivation Details
This is Problem (6.1) from Schwartz's QFT and the Standard Model. I am trying to directly calculate, by performing the integral over momenta, the explicit position-space expression of the Feynman ...
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About Second-Order Poles of Matsubara Sum
I would like to ask about the calculation regarding Matsubara sum of the form
\begin{equation}
\frac{1}{\beta}\sum_{i\omega_n} \frac{1}{(i\omega_n-\xi)^2}
\end{equation}
which is a second order pole ...
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Why the massive spin-1 photon gets more degrees of freedom than massless case; while the massive spin-1/2 electron stays the same as massless case?
Spin 1 field without mass term like photon has 2 real degrees of freedom. The polarization with two states. I think I can denote it as quantum state $|s,s_z> = |1,1>$ and $|1,-1>$.
Spin 1 ...
- 131
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Renormalization group trigonometric integral
I am going through Wen's QFT of many-body systems, namely the section on the renormalization of non-compact clock model. He has a calculation there of a particular integral over the fast fields that I ...
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Fourier transformation of $\log(\mathbf{q}^2)/\mathbf{q}^4$ in $d=3$
(Note: I posted the exact same question in the math StackExchange, but I am trying to get more people to view it (I posted it here: same question on math StackExchange). The Fourier transformation has ...
- 491
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Application of Cauchy residue theorem to Matsubara sums
For reference, this derivation is closely related to the discussion on pp. 169-173 of Altland and Simons. In quantum field theory (specifically when calculating free fermionic propagators via coherent ...
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Why do the members of $SU(2)$ doublets gain different masses after spontaneous symmetry breaking?
Before spontaneous symmetry breaking (SSB) elementary particles belonging to the same $SU(2)$ doublets are indistinguishable, which clearly is not the case after SSB.
I am comfortable with the idea of ...
- 536
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External leg correction to 3-point QED Green's function
I am trying to calculate the following diagram to solve the Callan-Symanzik equation for the three-point Green's function (two massless fermions and a photon).
The counterterm to the photon ...
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Conservation of angular momentum in LSZ reduction formula
I recently solved a problem involving calculating an LSZ reduction formula for the decay of a polarized photon into two pions. Specifically, I wrote an expression for the matrix element $\langle p_+,...
- 21
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Clarification Needed for The Klein-Gordon Field Acting on the Vacuum State (Peskin and Schroeder)
In Peskin and Schroesder's Introduction to Quantum Field Theory, section 2.3, the Klein Gordon Field has the expression
$$
\phi(x,t) := \int \frac{d^{3}p}{(2\pi)^{3}} \frac{1}{\sqrt{2\omega_{p}}} [a_{...
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What is the difference between wavefunction renormalization and field strength renormalization?
A while ago I asked a question asking what is field strength renormalization (What exactly is field strength renormalization?). I now have a better way of thinking about this, which is that it relates ...
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Is quantum field theory conceptually equivalent to the Schrodinger equation, as claimed in Franck Laloe's 2019 book? [closed]
The book is `Do we really understand quantum mechanics?' (Cambridge, 2nd edition, 2019)
Here is the full quote (from section 1.1.3):
A generalization of the ideas of gauge invariance of ...
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66
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QFT Fourier expansion of the fields
This is probably a silly question, but I'm studying QFT and our professor did not give us a good explanation about this, why we can always expand the fields operator in terms of Fourier decomposition, ...
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Gauge invariance of simplified weak interaction
I am having difficulties with a homework set. We are given the following lagrangian for a simplified weak interaction between an electron $\psi$, neutrino $\chi$, and a massive (complex) vector-boson $...
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Renormalizability of QFTs having a finite spatial extent of particles
Suppose we model elementary particles by fields but with the internal degrees of freedom being the Hilbert space of a quantum rotor. The spin measurements correspond to the internal angular momentum ...
- 6,308
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1
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Boundary conditions and field quantization in AdS
While studying the AdS/CFT correspondence, one encounters very early the example of a scalar field in AdS. The general solution to the Klein-Gordon equation in the limit $z\rightarrow 0$ may be ...
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System interacting with Fermi Gas [closed]
My question denoted by a reduced dynamic for a system interacting with a reservoir.
Before asking the question, for completeness I will write in detail the statement of the problem and notation.
...
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1
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Renormalization in $\lambda\phi^4$-theory: Why renormalize at one-loop instead of renormalizing at order of the coupling constant $\lambda$?
I am reading about one-loop renormalization in the $\lambda\phi^4$-theory. Instead of doing renormalization at order $\lambda$, why are we interested in renormalization at one-loop which contains both ...
- 11.1k
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+50
Angular momentum and the $S$-matrix
I have been curious about the status of angular momentum in the context of the $S$-matrix and scattering amplitudes. In particular, if we pass to a classical scattering problem and imagine scattering ...
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Space and Time on equal footings for QFT "Equations of Motion"? [closed]
How can we write the equations of motion for the free field (Spin 0) in QFT, which put space and time on an equal footing? (Canonical Quantization)
In this setting, is said that space and time are on ...
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1
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Proper definition of spontaneously broken symmetry
I am currently working on generalized symmetries and i was reading https://arxiv.org/abs/2301.05261. In footnote 23 the authors state:
To
be precise, by spontaneous symmetry breaking, we mean
a phase ...
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1
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What happens when a photon interacts with a free electron?
When an electromagnetic wave interacts with a free electron the electron starts to oscillate in the direction perpendicular to the propagation of the wave meanwhile when a photon interacts with a free ...
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Proving that Retarded K-G Propagator is Green function (Peskin & Schroeder 2.56) [closed]
I am trying to derive Peskin & Schroeders expression $2.56$:
$$(\partial^2 +m^2)D_R(x-y)=-i\delta^{(4)}(x-y)\tag{2.56}$$
with $$D_R(x-y)=\theta(x^0-y^0)\langle 0|[\phi(x),\phi(y)]|0\rangle.\tag{2....
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How does the expansion around the free theory relate to the idea of Gaussian fixed point in RG?
I have been wondering about the relationship between the Wilsonian picture of renormalisation, and the perturbative picture for quite some time now (in the context of QFT).
What I am puzzled about ...
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About On-shell subtraction and renormalization
I really want your help, i have tried to solve it for two days but I couldn’t, therefore if you could help me by giving guidance and hint, i really appreciate it.
My question is that how to perform ...
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Feynman diagrams in statistical physics
Feynman diagrams were, to my understanding, first developed in QED to calculate things such as scattering amplitudes and the running of the coupling constants.
They have later been adopted to ...
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Question about proof of Weinberg-Witten theorem
In proving the Weinberg-Witten theorem, there is a step where one needs to show
\begin{align*}
\lim_{k' \to k}\langle k, \sigma | J^{\mu} |k', \sigma \rangle &= \frac{q k^{\mu}}{k^0}\frac{1}{(...
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2-point correlation function between two different fields
Suppose we have a lagrangian $\mathcal{L}$ made by different fields, i.e.
\begin{equation}
\mathcal{L}= \mathcal{L_0} + g\phi\partial_\mu\phi A^\mu,
\end{equation}
where $\mathcal{L_0}$ is the free ...
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How to choose contour of integration prescription Klein- Gordon Propagator? [duplicate]
I am going through the complex integral in peskin & Schroeder's intro to QFT (equation 2.54, deriving the Free Klein-Gordon Propagator):
$$\langle0|[\phi(x),\phi(y)]|0\rangle=\int \frac{d^3p}{(2\...
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Are there universality classes not found through a Ginzburg-Landau like free energy expansion
Usually the real free energy of a system is too complex to be exactly computed, thus one either expands it in power/gradient series or simply builds it from symmetry considerations. For example:
$$F[\...
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Using Compton scattering to derive the deep inelastic cross-section for the parton model
In the second volume of The Quantum theory of Fields, Weinberg provides the inelastic cross-section for the scattering of an electron from a nucleon with four momentum $p$ based on the parton model:
$$...
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Correlation function of three gauge fields with a derivative
I am trying to calculate the following correlation function
\begin{equation}
gt^at^bf^{bed}\langle \partial_\mu A^a_\nu(x)A^e_\alpha(y) A^d_\beta(y) \rangle
\end{equation}
where $A_\mu=t^aA^a_\mu$ are ...
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Particle Anti-Particle annihilation in Quantum Field Theory
What special distinction does the interaction of a particle with its anti particle have compared to an interaction with some other particle?
People often say when a particle and an anti-particle ...
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Derivation of the Conformal Ward Identity in Di Francesco et al
I am reading section 5.2.2. (titled The Conformal Ward Identity) from Conformal Field Theory by Di Francesco et al. The authors write
\begin{align}
\partial_\mu(\epsilon_\nu T^{\mu\nu}) &= \...
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Critical exponent from powercounting of the action through the renormalization group
This will be a very basic question. For example, when we write down a $\phi^4$ action in condensed matter, let's say for an Ising magnet:
$$F[\phi] = \int d^Dx \dfrac{1}{2}(\nabla \phi)^2 + \dfrac{1}{...
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What Do We Envision the Fabric of Space to Be? Physical or Immaterial? [closed]
Sorry if this question is a bit lackluster or based on mistaken proof, I’m a high school student who’s highly interested in the fields of Quantum Theory and particle physics, and I’m trying to get a ...
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Is the space between plates, in Casimir effect, empty of momentum?
Please correct me if I am wrong. In Casimir effect, when two plates are brought very close to each other, there is a Force felt. This force is due to quantum fluctuations.
The space between plates is ...
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0
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What does it mean to multiply two spinors?
In Peskin and Schroeder they introduce an initial (incorrect, but that's irrelevant) mode expansion of the Dirac field:
$$ \psi(x) = \int \frac{d^3p}{(2\pi)^3} \frac{1}{\sqrt{2 E_p}} e^{-ix \cdot p} \...
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Why do the subatomic particles like electron exhibits Dual-nature? And how does the particle knows when to change their state? [duplicate]
As we all know, Subatomic particles show dual-nature when observed but why? why does this happen? also I am genuinely confused as to how does the particle know when to change its nature, I mean i know ...
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Why Fock representation holds only in a free quantum field theory?
With a quantum system with $N$ degrees of freedom, all the representations are unitarily equivalent to Fock representation. However, if the number of degrees of freedom goes to infinity, there are ...
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1
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Does the probability wave of a photon determine its color?
The wavelength or frequency of light determines its color. Photons seen as particles are said to have a frequency, determined by its energy, so I assume that 'is' the same color.
But being quantum ...
- 579
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1
answer
80
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Expectation value of the exponential of a quadratic term in fields
I have the following relation in this paper (J.B. Kogut: Introduction to Lattice Gauge Theory and Spin Systems, equation 8.39, page 709) (RG), where the author while doing an RG calculation writes
$$\...
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