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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Why does trying to remove a non-existing electron from a state give zero?

Setup Creating an electron that is already in a basis set is zero (Pauli's principle): \begin{equation} a_i^+ | \chi_i \cdots \chi_k \cdots \chi_l \rangle = | \chi_i \chi_i \cdots \chi_k \cdots ...
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Phenomena in the intersection of general relativity and quantum mechanics

I am looking for physical phenomena that have aspects involving both general relativity and quantum mechanics. The only example I know is Hawking radiation. While black holes are objects that cannot ...
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Situation after Saini & Stojkovic's paper on unitarity in gravitational collapse and non-formation of black holes?

In their paper, Anshul Saini and Dejan Stojkovic [1] claimed that by calculations it is possible to demonstrate that in a gravitational collapse of a disk, an event horizon is never made for a far ...
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How many quantum fields are there?

I'm just an aficionado, but my understanding is that in QFT, the photon is an excitation of the electromagnetic field, the electron is an excitation of the electron field, and so on. Is there a ...
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104 views

Vanishing of conjugate momentum $\Pi^0$ and non-existence of propagator

We know that if we try to quantize the free electromagnetic field without a gauge fixing term added to the Lagrangian, then one of the conjugate momentum density $\Pi^0$ vanishes. We also find that ...
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217 views

Question on derivation of Ward identity

I'm currently reading these notes about the Ward identity (pages 259 - 261). I will repeat some of the steps to make the question self-contained. Let us consider a local transformation on the field ...
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859 views

How to construct the charge conjugation matrix for any given dimension?

Generally, Gamma matrices could be constructed based on the Clifford algebra. \begin{equation} \gamma^{i}\gamma^{j}+\gamma^{j}\gamma^{i}=2h^{ij}, \end{equation} My question is how to generally ...
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291 views

Dimensional aspects of the imaginary unit $i$ in physics [duplicate]

From a real world perspective each dimension in the 3-D Cartesian System can be represented by an axis that is perpendicular to 2 other axes. I read somewhere else that the effect of ${i}$ is to ...
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172 views

Momentum Space Renormalization of $\phi ^6 $ Model

I'm trying to find the RG flow to lowest order in $\epsilon = 3 -d $ for the energy functional: $$ f=\frac{1}{2} \phi ^2 +u \phi ^6 +\frac{c}{2} (\nabla \phi ) ^2 $$ where $\ d$ is the dimension ...
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36 views

Temperature and Renormalization Scale in QFT

A particle physicist told me that everything in Peskin & Schroder is at zero temperature, and once you consider finite-$T$ QFT, things become more complicated. Meanwhile, I sometimes see people ...
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Why is Planck's constant the same for all particles?

This question came to me while reading Where does de Broglie wavelength $\lambda=h/p$ for massive particles come from? This question has a nice answer that explains that wave number has be ...
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Why is it correct to estimate divergences by the cutoff in QFT?

Let's say we have a linear divergence in a quantum field theory. The way to deal with this infinite quantum correction is to go through the whole process of renormalization. However, quite often, ...
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How do you prove that $L=I-V+1$ in $\lambda\phi^4$ theory?

It is known that the number of loops in $\lambda\phi^4$ theory is given by the formula $$L=I-V+1$$ where $L$ is the number of loops, $I$ the number of internal lines and $V$ the number of vertices. ...
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57 views

Order of Feynman diagrams for electroweak processes?

I want to compare two Feynman diagrams and be able to say which one describes a process that is more likely to happen. As far as I understand, this is done by considering the order of the diagram. ...
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50 views

Why is the strong CP term $ \theta \frac{g^2}{32 \pi^2} G_{\mu \nu}^a \tilde{G}^{a, \mu \nu}$ never considered for $SU(2)$ or $U(1)$ interactions?

The Lagrangian one would write down naivly for QCD is invariant under CP, which is in agreement with all experiments. Nevertheless, if we add the term \begin{equation} \theta \frac{g^2}{32 \pi^2} ...
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What's the phenomenon where it looks like more particles exist at relativistic speeds?

From the perspective of an observer moving close to the speed of light, the surrounding environment has very high energy which leads to pair production. What is the name of this phenomenon? I can't ...
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37 views

Pion decay exercise in Griffiths books

I have questions about pion decay problem. In Griffith "Introduction to Elementary Particles" 1st edition, 1987, question number 10.10 : Analyze $\pi^-$ decay as a scattering process, using the ...
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78 views

Anderson-Higgs mechanism for the (non-relativistic) $U(1)$ gauge theory under the unitarity gauge

On Page 138, Quantum Field Theory of Many-body Systems: From the Origin of Sound to an Origin of Light and Electrons by Xiaogang Wen, when he demonstrates the Anderson-Higgs mechanism for the $U(1)$ ...
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Non-relativistic QFT Lagrangian for fermions

Take the ordinary Hamiltonian from non-relativistic quantum mechanics expressed in terms of the fermi fields $\psi(\mathbf{x})$ and $\psi^\dagger(\mathbf{x})$ (as derived, for example, by A. L. Fetter ...
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27 views

Are there any in depth superfluid mechanic analyses of spacetime?

Has there been much work done that treats particles as vortexes in a fluid, or dark matter as bubbles in this fluid (bending space in the same way massive particles (vortexes) are observed to do, but ...
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42 views

Topological term under electron-electron interaction

By integrating out fermions in gapped Dirac Hamiltonian, one can obtain a topological term for topological insulator. Why there is no further correction to this term when electron-electron interaction ...
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745 views

What is the physical meaning of anti-commutator in quantum mechanics?

I gained a lot of physical intuition about commutators by reading this topic. What is the physical meaning of commutators in quantum mechanics? I have similar questions about the anti-commutators. ...
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Why do electrons in a superconductor lack energy to produce “massive” photons

My two questions are based around looking for a good, simple (if possible) explanation of the Cooper pair effect in superconductors. I follow the idea that, in intuitive terms, "a Cooper Pair" ...
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Hamiltonian linearly proportional to momentum

In this question, it is discussed why, in Lagrangians we usually stick to first derivatives and quadratic terms we never see higher derivatives. The selected answer shows that, if a Lagrangian $L(q, ...
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What is the physical interpretation of the automorphism on bounded operators induced by an S matrix?

In a QFT, the S-matrix $S$ is a unitary operator, that fixes the vacuum and commutes with the unitary operators implementing the action of the Poincare group on an appropriate Hilbert space $H$. ...
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Why possibility for X-ray to excite inner electrons higher than outer electrons?

It seems X-ray absorption spectroscopy is usually ascribed to the interation between photons and inner electrons. Does it mean inner electrons are much preferred by X-ray photons to outer electrons? ...
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What is the difference between Fermi golden rule and Wigner-Weisskopf theory?

What is the difference between Fermi golden rule and Wigner-Weisskopf theory? They both deal with the spontaneous emission process. So what is the difference? As far as I know, the fermi golden rule ...
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Does Peskin & Schroeder Eq. (4.26), $U(t_1,t_2)U(t_2,t_3) = U(t_1,t_3)$ imply $[H_0,H_{int}] = 0$?

Peskin & Schroeder equation (4.17) define the operator, \begin{equation} U(t,t_{0})~=~e^{i(t-t_{0})H_{0}}e^{-i(t-t_{0})H} \tag{4.17} \end{equation} where $$H~=~H_0+H_{\text{int}}\tag{4.12}$$ is ...
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2answers
59 views

Why do the $u$ and $d$ quark not have an associated quantum number?

All the other quarks ($c$,$s$,$b$ and $t$) have quantum numbers of charmness, strangeness, bottomness and topness that are conserved in strong interactions. This allows, among other things, flavour ...
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35 views

Dirac Current Spectral Representation

I'm reading Strocchi's book on The Non-Perturbative Foundations of Quantum Field Theory. In the chapter concerning point-splitting regularization, where the free Dirac current is defined as follows ...
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180 views

Origin of quark masses

Does all the mass of the quarks in the standard model come from the Higgs sector or is there also a contribution to quark masses due to QCD chiral symmetry breaking?
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How to tell the order of a Feynman diagram?

How can we know the order of a Feynman diagram just from the pictorial representation? Is it the number of vertices divided by 2? For example, I know that electnro-positron annihilaiton is first ...
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135 views

Perturbation theory : quadratic external field

I'm trying to derive the explicit form of S-matrix of an interaction Hamiltonian $$H' = \frac{1}{2} \lambda \left[ \int d^3 x \rho({\vec x}) \phi({\vec x}, t)\right]^2\tag{1}$$ Even though the ...
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Is Parity really violated? (Even though neutrinos are massive)

The weak force couples only to left-chiral fields, which is expressed mathematically by a chiral projection operator $P_L = \frac{1-\gamma_5}{2}$ in the corresponding coupling terms in the Lagrangian. ...
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Do cosmic strings or global monopoles interact with magnetic field?

Does anyone know any phenomenon that shows the interaction between cosmic strings or global monopoles with magnetic field? I looked for that in Vilenkin and Shellard's book but, as I'm not a ...
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61 views

Independent Phases in Gauge Theory

Excuse my naivety. When we postulate a local gauge invariance we say that we allow the overall phase of the field variables $\psi(x)$ can be changed and that this overall phase can vary from point to ...
3
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115 views

Spin operator: tricky proof using gamma matrices

I have not dealt with the gamma matrices extensively so I am having a bit of trouble here. Basically I want to show that the spin operator defined by $$ \mathbf{\hat{S}} = \frac{1}{2}\gamma^5 ...
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Argument of E. Fradkin on the mean-field theory of spin liquids

I have read the chapter 8 of Field Theory of Condensed Matter Physics (2ed.) by E. Fradkin a couple of times, but I still confused by his argument at some points. I hope you can help me with that. ...
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46 views

Why is the photoelectric absorption coefficient finite at the threshold frequency?

I mean the photoelectric effect of the hydrogen atom. It is weird. By the Fermi golden rule, the transition or absorption rate is proportional to the density of the final states. At threshold, the ...
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27 views

dagger operator in spinor representation

I just have trouble understanding how hermitian conjugation is acting like this in the following example (dot represents right-handed Weyl field, undot represents left-handed Weyl field). For ...
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299 views

Seiberg-Witten theory and Superconductivity

There seems to have some (deep) relation between Seiberg-Witten theory and superconductivity. e.g. this Witten paper. Q: Could someone introduce the relations between the twos both physically in ...
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71 views

Can one apply the Hubbard-Stratonovich transformation to the exponential of the Laplacian?

Is there a generalization of the Hubbard-Stratonovich transformation that transforms the exponential of the Laplacian into a Gaussian integral? Or can anyone suggest me how I can find the ...
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1answer
56 views

Hermitian Adjoint of Spinor

Say we have a four component spinor $\psi$: $$ \psi=\begin{pmatrix}\psi_L\\\psi_R\end{pmatrix} $$ Is the Hermitian adjoint of this: $$ \psi^\dagger =\begin{pmatrix}\psi_L^\dagger ...
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What does the “UV” in “UV completion” stand for? [closed]

What does the "UV" in "UV completion" stand for? Also, I'm not sure which tags I should tag this question with.
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Dependence of finite part of loop integral on regularization

Recently I've calculated some process in which arise triangle loop with running two $W$ bosons and one massless fermion. The expression for integral is following: $$ I_{\alpha \beta}(r, q) = \int ...
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Strangeness of QFT [closed]

In quantum field theory, the particle-wave duality is resolved by assuming that a field can collapse to some quantum value. Suppose you are observing a distant star through a small aperture that ...
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Could one argue that h (Planck constant) and $\hbar$/2 (Dirac constant) are in fact independant constants?

My question is very naive and could sound strange but it seems to me natural in so far as the Planck constant is related to the first quantization (of newtonian particle mechanics/galilean relativity) ...
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2answers
551 views

What is Timelike Quantum Entanglement?

I came across a New Study at : http://arxiv.org/pdf/1101.2565 . Which talks about Time like quantum entanglement. What does that mean? Comment added by L.Motl: The same preprint has been discussed ...
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Why is the electric field operator normalized by a volume?

I came across the following definition of the electric field operator: But I am not sure what this $V$, the "volume of a box", is about. It seems to enter the discussion in order to have standing ...