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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 ...

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Dirac field local observables

This is actually a continuation of calculation I've been working on. It is well known that, in the case of Dirac fields $\psi(x)$, they satisfy anticommutatation relationships since they're fermionic ...
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58 views

Non-zero Hamiltonian matrix elements in a generic QFT

Consider a generic QFT. Let's assume that all the charge operators (momentum, electric charge, etc.) commute with both free and full Hamiltonians. For simplicity, let us also assume that all the ...
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Is there any threat to the results of our effective field theories from unknown higher energy theories?

We use renormalization arguments (and experiments) to change the couplings of a theory and suppress the higher energy physics (saying things like “whatever the fundamental theory, this will be true of ...
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44 views

Dirac propagator causality

I was studying the Dirac propagator and came across an excelent article which includes all the derivation, and interestingly we can conclude that the anticommutator is zero for space-like intervals. ...
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51 views

Can a unified physics theory have a smaller number of couplings than its effective field theory?

Suppose that we have a QFT that has $n$ number of physical coupling constants, or there are $n$ coupling constants required to perturbatively renormalize the given QFT. Suppose this QFT to be an ...
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Fluctuations in the value of a quantum field at a point?

Suppose there’s a scalar field that permeates the universe. Do quantum fluctuations really cause the field value ϕ to fluctuate, making the field value higher at some points in space and lower at ...
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Octet wavefunction for heavy Quarkonium

Charmonium/Bottomonium can exist in singlet or octet state. I'm looking for a way to determine the octet state wavefunction. I came across arXiv:hep-ph/9907489v2, which does give the octet ...
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Quantum mechanics inside our body [on hold]

How close are we to explain the biological phenomena such as protein synthesis, mutations, DNA & genes concepts using quantum mechanics?
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Nature of electron or our weakness? [duplicate]

We say that we cant know the position of an electron. Is this because of the nature of electron to behave like a probability wave or our weakess to identify the "equation" of its position ?
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RG approach for KT-transition

Recently I have studied renormalization group (RG) approach for Kosterlitz-Thouless-transition (KT-transition) with help of "Condensed Matter Field Theory" by Altland & Simons. There is one ...
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1answer
21 views

How can both horizon and outgoing modes be kept together in this state if evaporation eliminates the horizon?

In the original computation of Hawking radiation one starts with a gravitational collapse spacetime (like the Vaidya geometry with $M(v)=M_0\theta(v-v_0)$). Then one introduces three complete sets of ...
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82 views

Vacuum Energy Calculation using Path Integral

I am currently reading Zee's book on quantum field theory, and I am in the chapter where he is introducing Grassmann integrals. He re-introduces the path integral evaluated for the vacuum, i.e. no ...
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41 views

Chronology protection: current status

I am looking for some fresh references on the Chronology Protection Conjecture. I am aware of this question, but the answer there seems to resort to energy conditions. But, weren't they shown violated ...
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Recovering nonrelativistic quantum mechanics from quantum field theory

In quantum field theory -- specially when applied to high energy physics -- we see that the requirements of Lorentz invariance, gauge invariance, and renormalizability strongly limit the kinds of ...
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Why Alan Guth limit inflaton field mechanism into range $10^{-35}$ to $10^{-34}$ seconds to justify an isotropy and homogeneity?

The field, originally theorized by Alan Guth, provides a mechanism by which a period of rapid expansion from $10^{-35}$ to $10^{-34}$ seconds after the initial expansion can be generated, forming a ...
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Black hole evaporation and QFT scattering

In QFT we usually deal with scattering problems. On the asymptotic past we have free particles, they interact, and we compute the overlap with distinct free particle states on the asymptotic future to ...
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34 views

External radiation in quantum particle systems

In describing system of quantum particles external radiation is often assumed to be classical. Is there any text book that give a proof why can we assume that?
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Commutator of normal ordered squared scalar field

The teacher left us prove the following statement. Let $\phi(x)$ be a scalar field $$ \phi(x) = \int \frac{d^3p}{2\pi \sqrt{2\omega_{\boldsymbol{p}}}} \left[ a_{\boldsymbol p} e^{-ip \cdot x} + a^+_{...
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Particle Multiplicity (Differential Spectrum)

In annihilation / decay processes $a\to b\ y$, they usually define a physical quantity for the annihilation / decay product $x$ called particle multiplicity or differential spectrum $dN_y / dE_y$. C.f....
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Calculation of Matrix Element in “Old-Fashioned Perturbation Theory”

I would like to better under the manipulations/formalism applied in order to evaluate the following matrix element from Schwartz "Quantum Field Theory and the Standard Model" (Eq. 4.16) $$\quad V _ {...
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28 views

UV divergence in QFT and trouble with 4-dimensional volume integral

This might seem like a very stupid question but I'm currently struggling to see how this type of integral diverges at high energies when considering $d^4p$ as Fourier transform of $d^4x$ $$ \int{d^4p}...
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when and where are we eligible to drop the Feynman prescription during the calculation? [closed]

It seems unclear to me why the $i\epsilon$ in Feynman integral disappear during the calculation. Some textbook said it's due to Wick Rotation but I couldn't get the reason.
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37 views

Lorentz invariance of volume element

In Srednicki's QFT book, in chapter 3 (eqn. 3.16 onwards) he talks about the lorentz invariance of the volume element. For this he writes $d^3k/f(k)$ should be invariant under lorentz transformations. ...
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54 views

Sign confusions in solution to Klein Gordon's equation

I have two basic questions on the solution of the Klein Gordon equation. The Lagrangian of the Klein Gordon field is $$\mathcal{L}=\frac12\partial_\mu\phi\partial^{\mu}\phi-\frac12m^2\phi^2 $$ ...
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Orientation of eigenspaces after transformations

I'm sorry but I will have to go a bit into detail of my system, to make my question clear. I have finitely many modes (n) of two different bosons (i=1,2). Without a coupling between the different ...
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1answer
38 views

How does the global $G^2G'$ anomaly make all the $\theta$-vacua associated to the gauge group $G$ physically equivalent?

Consider a gauge group $G$ and suppose that there is a $\theta$-term associated to it. According to this answer, the existence of a global anomalous symmetry $G'$ which rotates the $\theta$-term, ...
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What is the meaning of propagator in the context of lattice theory?

Say in $1+1D$ free fermion theory, it is easy to calculate the propagator in the (effective) field theory to be $$\langle \psi^\dagger(z)\psi(z')\rangle = \frac{1}{2\pi}\frac{1}{z-z'}$$ (in the ...
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98 views

Perturbative vs Wilsonian renormalization in 2D

In 2D a scalar field is dimensionless so terms in the Lagrangian $\phi^n$ of arbitrary power are renormalizable (indeed we can even have two derivatives). This has two consequences that seem to be in ...
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55 views

What does $B+L$ anomaly have to do with a phase redefinition of the left-handed quark field?

According to this answer, the reason why $SU(2)_L$ weak theory does not have a theta vacuum is because any theta term can be reabsorbed with a phase redefinition of the left-handed quark field. ...
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1answer
71 views

Mistake in Peskin & Schroeder, Renormalization of Linear Sigma Model?

In section 11.4 of Peskin & Schroeder's "Introduction to Quantum Field Theory", the authors calculate the effective potential of the linear sigma model to one-loop order: $$\begin{align*} V_{\...
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Spin spin correlation function in topological phase transition?

during my vacation i have decided to study Kosterlitz and thouless phase transition (i have already posted 2-3 questions about that). I don't know quantum field so I did not expect to understand ...
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Process $3\to n$ in QFT

How to calculate the probability of the process where 3 particle in the initial state interact. In such it is impossible to use cross section. It is necessary to use some another quantity.
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Determinant of d'Alembert Operator $\mathop\Box-m^{2}$

In quantum field theory, the partition function of a free scalar is $$\mathcal{Z}=\int\mathcal{D}\phi\exp i\int d^{n}x\frac{1}{2}\left[(\partial_{\mu}\phi)(\partial^{\mu}\phi)-m^{2}\phi^{2}\right]$$ $...
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The meaning of gauge-fixing in covariant quantization of the electromagnetic field

I am having trouble wrapping my head around the idea behind the covariant quantization for the electromagnetic field that is usually done in textbooks (I'm currently following Mandl & Shaw and ...
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Using a time-like boundary as a computer?

Question and Summary Using classical calculations and the Robin boundary condition I show that one calculate the anti-derivative of a function within time $2X$ (I can compute an integral below) $$\...
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1answer
105 views

How many connected components are there in the vacuum manifold of $\phi^4$ theory?

Consider the following theory in $1+1$ dimensions $$\mathcal L = \frac12(\partial\phi)^2 - \frac\lambda4 (\phi^2 - v^2)^2 \,,$$ which exhibits a $\mathbb Z_2 = \{0,1\}$ symmetry, $\phi \to -\phi$, ...
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Scattering amplitude ($s$-, $t$-, $u$-channels)

Given the Lagrangian $$\mathscr{L}=\bar{\psi}\left(i\partial\!\!\!/-m\right)\psi+\frac{1}{2}\left(\partial\phi\right)^2-\frac{1}{2}M^2\phi^2-g\bar\psi\psi\phi^2-g'\bar\psi\gamma_\mu\psi\partial^\mu\...
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“The operators with nontrivial vacuum expectation values have to soak up the zero modes associated to the anomaly.”

I was reading ref.1, where one can read (emphasis mine) ... the vacuum expectation value $\langle \mathcal O_{\phi_1}\cdots \mathcal O_{\phi_\ell}\rangle$ vanishes unless $$ \sum_{k=1}^\ell\...
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What is the link between statistical and QFT correlation functions?

I'm studying statistical mechanics in particular correlation function: https://en.wikipedia.org/wiki/Correlation_function_(statistical_mechanics) and I have understood it. Now searching on internet ...
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Resonance propagator properties

(This is part of a problem from Schwarz book on QFT). 1. Show that a propagator only has an imaginary part if it goes on-shell. Explicitly, show that $$Im(M)=-\pi\delta(p^2-m^2)$$ when $$iM=\frac{i}{p^...
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Is $U(2)_{2, 1}$ Chern Simons Theory Completely Trivial?

I am using the method outlined in appendix C4 of a paper by Seiberg and Witten [1] to calculate the statistics of lines in $U(2)_{2, 1}$. However, this method shows that all lines are trivial. ...
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45 views

Correction to the fermion propagator

Given the Lagrangian $$\mathscr{L}=\bar{\psi}\left(i\partial\!\!\!/-m\right)\psi +\frac{1}{2}\left(\partial\phi\right)^2- \frac{1}{2}M^2\phi^2 - g\bar{\psi}\psi\phi^2,$$ calculate the propagator ...
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1answer
95 views

Why do we have freedom to choose a renormalization scale in massless QFT theories?

I thought that the freedom to choose renormalization conditions arises from the freedom to choose the arbitrary renormalization parameters. Let me exemplify this in a Massive $\phi^4$ scalar theory ...
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86 views

How do you write the Wightman function $\langle\phi(t_1)\phi(t_2)\rangle$ for a massive scalar field in position space?

For a free real scalar field $\phi(t,\mathbf{x})$, we define the Wightman function as: $$ W(t_1,t_2) \equiv \langle 0 | \phi(t_1,\mathbf{x}_1) \phi(t_2,\mathbf{x}_2) | 0 \rangle $$ I'm suppressing the ...
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How do the renormalization factors disappear from the computation recipe of the S-matrix in Peskin & Schroeder (p. 229 (7.45) & p.324)?

In the following I limit my considerations to 4-point diagrams. After the introduction of renormalized field operator (in renormalized perturbation theory) $\phi_r= (\sqrt{Z})^{-1} \phi$ in eq. (...
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Value of regularization scale

After regularising a transition amplitude, we end up with an expression which depends on regularisation scale. This means that our physical observables like cross section will be a function of ...
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Limitations of RPA (random phase approximation)

I'm interested in the possible limitations of the Random Phase Approximation (RPA). When is it expected to fail? As I understand it, RPA can be derived from the GW approximation, as can be seen here, ...
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What about objects' properties in physics?

Some scholars talk about propensities or dispositions when they refer to some non-manifest properties of entities. I.e. The property of being soluble is a non-manifest one because only if sugar is put ...
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Does Coleman-de Luccia instanton approach a Hawking-Moss instanton?

Suppose a Coleman-de Luccia instanton terminates in the basin with the true vacuum between the top of the potential barrier and the field value with potential energy equal to the potential energy of ...
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Fourier transform of free spin 1 field propagator

The aim of the question is the show that $\tilde{A}_a (k) k^a k^b \tilde{A}_b (k) - \tilde{A}_a (k) k^2 g^{ab} \tilde{A}b(k)$ in position space (i.e. Fourier transformed) is $A_a (x) \partial^2 A^b(x)...