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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Conserved current from the three SU(2) transformations

We are asked to show that the following Lagrangian is invariant under the three SU(2) transformations $\Phi \rightarrow exp{({\frac{i}{2}{\alpha_j\sigma^j}}) \Phi}$, where $\Phi$ is a doublet complex ...
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Do loop-level three-point scattering amplitudes have branch cuts?

I know that higher point scattering amplitudes at a sufficiently high loop level have branch cuts and discontinuities. I wonder whether the number of scattering particles plays a role in this? Is ...
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Can I use dimensional regularization with this integral?

I would like to extract the divergence of this integral in 4d Euclidean space: $$\int d^4z \frac{1}{(x-z)^4}\tag{1}$$ This divergence is expected to cancel with other divergences, which I got using ...
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Appearence of higher spin algebra

I start from massles & free scalar field theory in $d$-dimenisonal space. It is clear that this theory has conformal symmetry. My question is devoted to derivation of conserved current $$J_{\mu_1\...
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How to calculate the correlation length from the (connected or disconnected) correaltion function?

Here, "How to determine correlation length when the correlation function decays as a power law?" has a similar question, and Adam gave a good answer. However, I don't know how to derive the ...
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Calculating CFT on 2D curved manifolds

In 2D we can always choose coordinates in a coordinate patch so that the metric is conformally flat $$g_{\mu\nu}(x)=\kappa(x)\delta_{\mu\nu}$$ A simple example is the sphere $S^2$ in stereographic ...
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The Gell-Mann and Low theorem and the expansion of the Green function

If we have a system with Hamiltonian $H = H_{0} + V$, with $| \Phi_{0} \rangle$ being the ground state of the system without the interaction, the Gell-Mann and Low theorem say that the quantite $$ |\...
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Deriving transition amplitude with $S$-matrix

Here is the part that is bothering me: Yeah, already here? So, my question: In the first line we have int picture states at time zero and in the second line we have limit of time evolv operator with ...
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Proving that $$ [\phi(\vec{x}, 0), \phi(\vec{x}, t)] \sim e^{-i m t}-e^{+i m t} $$ in QFT

So far, I get the following (for the left term in the integral, $d$=3): \begin{equation} \begin{aligned} \Delta_{+}(x) &= \int \frac{\mathrm{d} \vec{p}^{d}}{(2 \pi)^{d} 2 e(\vec{p})} \exp (-i t e(...
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How is a T-violation inherited in a QFT?

CP violation In quantum field theory (QFT), ${\rm CP}$ symmetry or ${\rm CP}$ violation is a property of the Lagrangian. For a ${\rm CP}$ violating QFT, in general, the absolute square of the Feynman ...
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Exact solution of SU($N$) model in large $N$ limit

There is the statement about U($N$) model: It is not possible to solve U($N$) model even in large $N$ limit I do not understand this statement. If I go to large $N$ limit I know that only planar ...
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Why D-brane can be attached to NS5 branes?

What is NS5 brane? Is it possible (in analogy with D-brane) understand appearance of NS5 brane in perturbative string spectrum? Why D-brane can be attached to NS5 branes?
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Calculating an amplitude with Feynman diagrams [duplicate]

Note, I’m sure there are countless questions like this but I’m trying to find a specific, step-by-step solution for this specific problem. I’m trying to compute the probability amplitude of an ...
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Do “delayed choice” experiments send information back in time?

Consider the wave function collapse of a pair of entangled photons: wave function is collapsed, let's call this state '0' normal wave function, let's call this state '1' In a "delayed choice" ...
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Are photons locked in time, and does this explain the “delayed choice quantum eraser” experiment?

I'm trying to wrap my head around the "Delayed Choice Quantum Eraser" experiment and how events in the future affect light in the past. I'm sure I'm wrong but to me this seems to indicate that ...
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Why do we need the coupling small when doing perturbative QFT calculation?

I don't really understand why, when we calculate say the 2-point Greens function in a scalar QFT with interaction $\lambda \phi^4$, we need the coupling constant $\lambda$ to be small? Everywhere I ...
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Reference for Quantum field theory in $S^1 \times R$

I am looking for a reference where it is considered QFT on a space given in a circle, plus a time coordinate, namely QFT in $S^1\times R$.
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Proof that representation of proper orthochronous Poincaré group is unitary

We have defined the action of the representation of the Lorentz group on the Fock space by $U(\Lambda)a^*(k_1)\dots a^*(k_N)\Omega = a^*(\Lambda k_1)\dots a^*(\Lambda k_N)\Omega$. I am now to proof ...
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Weinberg Volume II: Abelian Anomaly Function

The following is from page 363 of Weinberg volume II. We wish to evaluate the RHS of \begin{align}\label{EQbbvbv} [d \psi][d \bar{\psi}] \rightarrow(\operatorname{Det} \mathscr{U} \operatorname{Det}...
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Renormalization and fluid dynamics

Both Quantum Field Theory and fluid dynamics rest upon discarding finer details of the system and/or small-scale degrees of freedom. I understand that both frameworks require such removal ...
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How do quantum field values combine?

I am interested in how quantum field values combine under superpositions of states in the case of free real scalar fields. I believe I understand the following: A fock basis of a free real scalar ...
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Asymptotic quantization and scattering theory

There is one idea presented on some papers by Ashtekar called "asymptotic quantization". This is reviewed in the case of gravity on this paper. Moreover, this seems to be the basis of the recent work ...
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Quantization of field with other complete orthogonal system

I've learned the quantization of Klein-Gordon field using Fourier expansion. I understand that this process is kind of exchanging complex fourier coefficients to operator and makes it satisfying the ...
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Simple question on computing commutation relation

In bosonization, one faces with the following commutator: $$[\phi(x_1), \theta(x_2)]=\sum_{q\neq 0} \frac{\pi}{Lq} e^{iq(x_2-x_1)-\alpha |q|}\tag{1}$$ where $q$ is an non-zero integer multiple of $2\...
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Finding and diagonalizing the mass matrix

I'm trying to find the mass matrix from the actions in $(2.10)$ and $(2.11)$ in this paper. The action is expanded around a classical background field $B^{i}$ and the action for fluctuations is given ...
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When can I set $d=4$ in dimensional regularization?

I am using dimensional regularization to extract the divergence of some complicated integral. I work in $d=2\omega$ dimensions, with $\omega\approx 2$. After I extract the divergence, I have an ...
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Peskin and Schroeder: Ward's identity in exercise 6.3 [closed]

On part a) of this exercise they ask to do a very similar procedure as to the one done with the photon propagator. In this case I am unable to have a vanishing $q^\mu$ term after integrating over the ...
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Doubt in Weinberg's book on QFT

In chapter 3 of his book on QFT (volume 1), while discussing the symmetries of the S-matrix, Weinberg makes the following statement For any proper orthochronous Lorentz transformation $x\rightarrow ...
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Hartree-Fock factorization

I am studying c-field methods applied to Bose-Einstein condensates to understand how one gets to e.g. the dissipative GPE. To do so, one splits the field operator for the Bose gas into a low- and a ...
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How to find ladder operators that diagonalize a Hamiltonian in QFT

I have some trouble understanding how one can, in the context of QFT, diagonalize a Hamiltonian $H$ by the introduction of ladder operators $a$ and $a^\dagger$ (I have trouble understanding how one is ...
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Can Hartree-Fock-Bogoliubov be used for dynamics?

I am aware of Hartree-Fock as both a tool to find interacting ground states for fermionic systems (eg the Roothan self-consistent field procedure). One way of deriving the ground state method is to ...
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Time dependence of Drude-like correlation function obtained from Matsubara formalism

I'm trying to calculate the real time dependence of the correlation function that I've obtained in my effective model (it is closely related to the electron density correlation function), given in ...
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Resolution between off-shell and on-shell views of particle interactions in popular writing

This question is based on this blog post 'Is Dark Matter Lurking in Neutron Decays?' and a following comment I re-read recently. It has something I have seen often in popular writing, which I believe ...
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How to solve integrals with $3$ Feynman parameters? [migrated]

I would like to evaluate integrals of the following type (in position space): $$\int \frac{d^{2\omega}z}{\left[(x_1-z)^2 (x_2-z)^2 (x_3-z)^2 \right]^A} \tag{1}$$ I can introduce three Feynman ...
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How did we know that the Dirac equation describes the electron but not the proton?

I'm suddenly getting confused on what should be a very simple point. Recall that the $g$-factor of a particle is defined as $$\mu = \frac{ge}{2m} L$$ where $L$ is the spin angular momentum. For any ...
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Cross-sections at zero temperature and high temperature for a process and its reverse

If the Feynman amplitude for a $2-2$ forward scattering $ab\to cd$ is denoted by $\mathcal{M}_{ab\to cd}$ and that of the reverse scattering process, $cd\to ab$, is denoted by $\mathcal{M}_{cd\to ab}$...
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Interpretation of annihilation and creation operators

If we write some quantum field in a form using creation and annihilation operators we are, in a way, doing a Fourier series with annihilation and creation operators being coefficients. So, if they are ...
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Feynman diagrams in quantum transport theory

I'm looking to find references that describe the role that Feynman diagrams play in quantum transport theory. I have heard discussions where it is possible to just insert a self-energy loop into an ...
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Computing correlation function $\langle e^{i\beta \phi(x)}e^{-i\beta\phi(0)}\rangle$ for massless scalar field $\phi$

I am currently reading Shankar's "Bosonization: How to make it work for you in condensed matter" (http://inspirehep.net/record/408901/). In page 9, I am stuck with computing the correlation function ...
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Yang-Mills Feynman rules

Good morning/evening. In Peskin & Schroeder chapter 16 on gauge invariance, the gauge boson self interaction vertex rules are given. For three gauge bosons, the relevant interaction term in the ...
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What is the energy density of the zero Higgs field in SI units?

Higgs boson has a mass, and a vacuum expectation value, both are in electronvolts. An uncommon feature of the Higgs field is that to its zero energy density belongs a non-zero field value. Is it ...
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Lorentz transformation of hamiltonian

I'm really rusty on LT and hope to get soem clarification. How would the loretnz transformation of the following quantity turn out? $$\Lambda_\mu^\nu \int d^3ka^\dagger(k)a(k)$$
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How does specifying a vacuum-state fix the field-momentum-operator for given CCRs?

This is kind of a follow-up question to my last question about the uniqueness of the field-momentum-operator. The answer stated that the commutation-relation alone does not fix the field-momentum ...
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Renormalization when there is spontaneous symmetry breaking

Standard quantum field theory textbooks discuss spontaneous symmetry breaking with the following Lagrangian: $$L=\frac{1}{2}\partial_{\mu}\vec{\phi} \cdot \partial^\mu \vec{\phi}+m^2\vec{\phi}\cdot \...
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Why does calculating $\langle J^{\alpha 5}(x) J^{\mu}(y) J^{\nu}(z)\rangle$ involve certain triangle diagrams?

In deriving the chiral anomaly, one wishes to compute the correlation of the axial-vector-vector currents. One writes this explicitly as $$\int d^4xd^4yd^4z \, e^{-ipx} e^{iq_1y}e^{iq_2z} \langle [ \...
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What's the field strength and energy density of a spinor field?

The field strength and energy density of a vector field $A_\mu$ can be described using the field strength tensor $F_{\mu \nu}$. What is the field strength and energy density associated with a (Dirac) ...
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Can I add a classical potential to S-matrix

I'm a junior learner of QFT, and I wonder if I can add a classical approximated potential (like Coulomb potential) to a total interaction \begin{equation}V=V_{\mathrm{Coulomb}}+V_{\mathrm{internal}} \...
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What's the physical reason that a massive vector field has only three linearly-independent physical polarizations?

While a four-vector field $A_\mu$ has four components, for a massive field there are only three linearly independent combinations of these components that correspond to physical situations. This ...
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What's the meaning of a “temporal polarization”?

For a massive vector four-field there are only three physical linearly-independent polarizations. For a field excitation at rest, these can be described by \begin{align} \epsilon^1_\mu \equiv \begin{...
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Is the scalar propagator an even function?

The scalar propagator for the Klein-Gordon Lagrangian is given by: $$D(x-y)=\int \frac{d^{4} k}{(2 \pi)^{4}} \frac{e^{i k(x-y)}}{k^{2}-m^{2}+i \varepsilon}$$ I need to know if it is an even ...