All Questions
Tagged with anomaly or quantum-anomalies
393 questions
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Standard model extension
this Semester I have my first QFT class and we have a homework where I got stuck at the beginning.
I have some ideas but I am not sure if they are correct, so I don't want a solution, I only want to ...
- 11
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103
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Higher point anomalies cancellation from trace
I had asked this question within this one before, but having also made other 2 independent enough questions there, decided to ask this one by itself here.
So, it is a well known fact that the ...
- 1,782
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212
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Diagrammatic expansion of an operator insertion in path integral for Trace Anomaly calculation
Starting with a scale invariant classical field theory, we can prove that the energy-momentum tensor will be traceless.
\begin{equation}
\Theta^\mu_{\ \mu }=0
\end{equation}
In the context of the ...
- 4,737
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201
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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, ...
- 2,646
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Trouble Understanding Computation in Weinberg Quantum Theory of Fields Vol. 2 Chapter 22
In Chapter 22 (Anomalies) of Weinberg Vol. 2, the author is evaluating the anomaly function
$\mathcal{A}(x) = -2[Tr(\gamma_5 t f(-(\not{D}/M)^2))\delta(x-y)]_{y\rightarrow x}$,
following Fujikawa'...
- 739
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Showing that $U(1)_R$ charge is non-anomalous in SUSY QCD when $r=\frac{F-N}{F}$
I'm trying to show that the value of the R-charge $r$ for which the R-symmetry is non-anomalous is given by $r=\frac{F-N}{F}$.
To do this we must calculate the triangle diagrams for the quarks $\...
- 4,820
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180
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$Z_1=Z_2$ without Ward-Takahashi identity?
In the renormalization of QED, the way that $Z_1=Z_2$ is treated e.g. in Schwartz is by first giving a simple "heuristic argument" based on gauge invariance (in the beginning of section 19.5) before ...
- 121
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173
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Calculation of Hall Conductance from Feynman Diagram
I'm trying to understand the calculation of the Hall conductance for a Chern insulator from a field theory standpoint. Specifically, I want to understand how, when integrating out the fermions from ...
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346
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The locality of Wess-Zumino terms
Suppose the simple theory with chiral fermions possessing non-trivial gauge anomalies cancellation:
$$
S = \int d^4 x \big(\bar{\psi}i\gamma_{\mu}D^{\mu}_{\psi}\psi + \bar{\kappa}i\gamma_{\mu}D^{\mu}_{...
- 8,971
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223
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The anomalous Hall effect in Weyl semimetals
Suppose the semimetal - the solid material, in which the conducting and valence zones are intersected at isolated points - the so-called Weyl nodes. Near this points, the Hamiltonian of electrons is ...
- 8,971
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99
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How to visualize a sphere bundle?
In the paper ``Gravitational Anomaly Cancellation for M Theory Fivebranes", the authors consider removing a tubular region of radius $\epsilon$ around the M5 brane (in order to make sense of the three ...
- 2,105
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260
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Why is it that the conformal anomaly has to be scale invariant?
When reading about conformal anomalies, such as in this paper it is often stated that the anomaly (ie. $ \delta W[g]/ \delta \sigma$ where $ W[g]$ is the quantum effective action for gravity) must be ...
- 86
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86
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QCD condensate and lepton mass
I read that the QCD U(1) anomaly is caused by the QCD condensate giving rise to quark masses. Does the QCD condensate also give masses to leptons (electron, mu, tau, neutrinos), or are these masses ...
- 1,803
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409
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Specific Reference for 't Hooft Anomaly Matching Condition
Does anyone know, in exactly which paper did G.'t Hooft "propose" anomaly matching condition?
I scrambled across his list of publications, but I am unable to make out.
- 415
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102
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How to solve the following set of equations (magnetohydrodynamics with anomaly term)?
Let's have system of equations:
$$
\tag 1 [\nabla \times \mathbf E^{(1)}(\mathbf r , t) ] = -\frac{\partial \mathbf B^{(1)}(\mathbf r , t)}{\partial t} ,
$$
$$
\tag 2 [\nabla \times \mathbf B^{(1)}(\...
user8817
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147
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Peskin and Schroeder Chapter 19 anomalies 19.63 Lagrangian
I am (self) studying chapter 19 of Peskin and Schroeder's Introduction to Quantum Field Theory. Around equation (19.63) they state the Lagrangian is invariant if $\alpha$ is a constant, and if $\...
- 57
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188
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Fujikawa Jacobian for Baryon number anomaly
Reviewing the anomalies of the standard model, one knows that the Baryon number is not conserved because of an anomaly associated to the global $U(1)$ symmetry that quarks have. That is the current
$$...
- 4,478
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1
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87
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Nuclei violating B number
Within SM, it is know that baryon number is not preserved and changes as
$$
\Delta B = 3·\Delta n_{CS}, \quad n_{CS} \in \mathbb{Z}\ ({\rm Chern-Simons\ index\ for\ vacuum})
\tag1$$
Then, its ...
- 1,607
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91
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Why is $Tr_R(T_a\{T_bT_c\})=-Tr_\overline{R}(T_a\{T_bT_c\})$ for $SU(N)$ representations?
I'm looking at the chiral anomaly in QFT and the term
$$d_{abc}=Tr_R(T_a\{T_b,T_c\})$$
shows up where $Tr_R$ means the trace in the representation $R$, $\overline{R}$ is the conjugate representation ...
- 248
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427
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Chiral symmetry of the Euclidean action for fermions
In the literature, such as QFT Volume-II by Weinberg, p.368, the chiral anomaly is derived using Euclidean path integral. To formulate the question, let's start with the Minkowski space with signature ...
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129
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Minus sign on the chiral anomaly
I've been going through various derivations of the chiral anomaly for using the Fujikawa method, particularly that in Srednicki's QFT textbook (see chpt. 77 in particular).
A lot of literature ...
- 594
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2
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242
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How can we show the Lorentz symmetry is not anomalous in $\phi^{4}$ theory?
how can I show in a lagrangian with scalar fields and $\phi^{4}$ interaction, the energy-momentum tensor isn't anomalous?
- 1
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2
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386
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Why color anomaly is in the axion photon coupling?
The axion photon coupling is given by the expression
$ g_{a\gamma\gamma}= \frac{\alpha}{2\pi f_a}(\frac{E}{N}-\frac{2}{3}\frac{4m_d+m_u}{m_d+m_u}) $, where $f_a$ PQ symmetry breaking scale, $E$ and $...
- 13
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191
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Equality of positron and proton charge problem statement
When I hear that the equality of positron and proton charge is an unsolved problem I assume that we are putting the electric charge by hand in the electroweak section of the SM Lagrangian.
Is this ...
user56963
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1
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117
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Proposal of the Virasoro modes and algebra
Hi I am wondering what the first published paper on Virasoro modes was? And what about Virasoro algebra?
- 93
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82
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Simplified Explanation of Coleman-Weinberg Potential in QFT
I have been reading a research paper where the interaction potential between two scalar fields is given by $$=g\, \phi H^\dagger H .$$ The Coleman-Weinberg correction to the potential is: $$ \frac{n}{...
- 117
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59
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How many dimensions are in string theory? [duplicate]
How many dimensions are in string theroy? I heard that there are 11 but to my understanding, there is an infinite, also can strings be on a 2D plane?
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32
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What is the correct type of the Berry curvature?
I am studying Berry curvature for a specific material and faced different types of the Berry curvature formula. Some papers use only valence eigenstates (u1) like this $$i*(<(∂U1/∂kx)| (∂U1/∂ky)>...
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88
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Point-splitting regularization for anomaly in curved spacetime
In flat spacetime, the point-splitting regularization for (chiral) anomaly is discussed in great details in Peskin and Schroeder's QFT.
Does anyone know any good references for calculating anomaly ...
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33
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Why M-theory has eleven dimensions? [duplicate]
Why M-theory has exactly 10+1 dimensions?
Some combinatorics with tensor indices will do.
- 11
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90
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Chiral anomaly of Weyl fermion is half of Dirac
How can one mathematically see that the anomaly for a Weyl fermion is half of Dirac in the Fujikawa path integral method?
Edit
I do understand that a Dirac fermion is two Weyl fermions. What I wish to ...
- 53
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90
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Local scale invariance without conformal anomaly
I need to know if conformal symmetry can be localized in the same manner that global symmetries like $SU(2)$ is localized and gauge bosons pop up?(I assume the trace anomaly doesn't violate the scale ...
- 1,280
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139
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$U(1)^{3} $ anomaly, trace of a hypercharge?
I have recently found the definition of the $U(1)^{3}$ anomaly as:
$$\mathcal{A} = Tr[Y^{3}]_{L} -Tr[Y^{3}]_{R} $$
Where $Y$ is the hypercharge of the left, $L$ or right, $R$ components. What I don't ...
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67
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Critical dimension from the symmetries of the string action
(Related: This post and this post.)
In this thesis it is said (on page 13) that just by assuming that we have some general action with the same symmetries as the Polyakov action (Poincare invariance, ...
- 817
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60
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B violation and electric charge
Within SM you can prove that despite we have baryon number conservation respect to Noether theorem, at quantum level baryon (and lepton) number is violated as
$$
\Delta B = 3·\Delta n_{CS}, \quad n_{...
- 1,607
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234
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Peskin equation on the treatment of chiral anomaly
In page 666 (it couldn't be other way - bad joke), chapter 19, the Eq. (19.73) claims (see properties of the $\phi_n(x)$ functions in this post: Change of variables in path integral measure):
$$
\...
- 1,607
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424
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QCD Trace Anomaly and Mass
In the paper in equations 4 and 5, some of the mass of the nucleons comes from the "trace anomaly" of the QCD energy-momentum tensor (as described in the paragraph following these equations). Is there ...
- 1
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118
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A Universe with only a single fermion
Is a Universe with only a single fermion anomalous instead of free from anomalies?
(e.g. electron, defined through fermi statistics with exchange statistics with a gained $-1$ sign, or rotating 360 ...
user32229
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298
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From gauge anomaly to chiral anomaly
Suppose the theory of chiral Weyl fermion (say, left) $\psi_{L}$, which interacts with abelian gauge field. This theory contains gauge anomaly, which I write in the form
$$
\frac{dQ_{L}}{dt} = \text{A}...
- 8,971
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320
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Anomalous commutators and gauge anomaly
Suppose we know, that the dynamics of theory with chiral fermions (say, left) and gauge field (for simplicity, abelian) leads us to presence of anomalous commutator of canonical momentum $\mathbf E(\...
- 8,971
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309
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The scale anomaly and dependence on scale
The scale anomaly states that if we have renormalizable theory without dimensionful function, which is scale invariant, then corresponding quantum theory may lost this symmetry because of ...
- 8,971
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192
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Chiral anomaly and fermion number conservation
Chiral anomalies in QED and QCD violate fermion number conservation, since a U(1) vector symmetry corresponds to fermion number conservation. However, only the LH and RH fermion numbers are not ...
- 1,803
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353
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Why does the violation of Ward identity not require cancellation of global anomalies?
This question is a continuation of the answer posted for this question about anomalies.
Is there a violation of the Ward identity associated with an anomalous global symmetry? If yes, why is the ...
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