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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Relation among anomaly, unitarity bound and renormalizability
There is something I'm not sure about that has come up in a comment to other question:
Why do we not have spin greater than 2?
It's a good question--- the violation of renormalizability is linked
...
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Experimental tests of Cluster Decmposition
How tight are experimental and astrophysical tests on whether Cluster Decomposition is satisfied at various space-like separations?
Is there a review paper or a standard reference on the question?
I ...
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What is the rate of B violation expected in the standard model during high energy collisions?
In a recent question Can colliders detect B violation? I asked about detecting B violation in collisions. Here I am interested in the theory aspect. (I asked both questions originally in the same ...
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Why can i replace a gauge field by the current it couples to in the calculation of a greens function?
i am reading about Anomalies in QFT at the moment and there is a question that appeared on the way.
Often i find it that people are calculating the time ordered expectation value of some fields (in ...
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Semiclassical QED and long-range interaction
I'm interested in the (very) low energy limit of quantum electrodynamics. I've seen that taking this limit does not yield Maxwell equations, but a quantum corrected non-linear version of them.
If ...
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From vertex function to anomalous dimension
In a $d$ dimensional space-time, how does one argue that the mass dimension of the $n-$point vertex function is $D = d + n(1-\frac{d}{2})$?
Why is the following equality assumed or does one prove ...
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Does it make sense to speak of amplitudes of finite closed boundaries in QFT?
A example of amplitude in Relativistic Quantum Mechanics or specifically in QFT is the amplitude of a field configuration on a space-like hyper-surface of space-time to "lead" to another field ...
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functional representations of free quantum fields
The free real quantum field, satisfying $[\hat\phi(x),\hat\phi(y)]=\mathrm{i}\!\Delta(x-y)$, $\hat\phi(x)^\dagger=\hat\phi(x)$, with the conventional vacuum state, which has a moment generating ...
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Is there precision experimental evidence for Furry's theorem — that only even degree VEVs are non-zero?
Is there precision experimental evidence for or contradicting Furry's theorem -- that only even degree VEVs are non-zero, specifically for the EM field?
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Gauge redundancies and global symmetries
It is often said that local (gauge) transformation is only redundancy of description of spin one massless particles, to make the number degrees of freedom from three to two. It is often said that ...
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Can the Lamb shift be expressed in more-or-less closed form in terms of the renormalized 2-, 3-,…,n-point VEVs of QED?
I see here that there are three contributions to the Lamb shift, from vacuum polarization (-27 MHz), from electron mass renormalization(+1017 MHz), and from the anomalous magnetic moment (+68 MHz).
...
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What happens to a Luttinger liquid under time reversal?
Suppose you a have an ordinary Luttinger liquid with
$$ H = \int dx \sum _{\eta= \pm 1 , \sigma =\uparrow,\downarrow } \psi^\dagger_{\eta, \sigma} (x) (-i v \eta \partial _x) \psi _{\eta,\sigma} (x). ...
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What is the 2-point correlation function of the electron field in QED?
The Feynman propagator for the free electron field is the Fourier transform w.r.t. $y$ of the time-ordered 2-point VEV $\left<0\right|\mathcal{T}[\hat\psi(x)\hat\psi(x+y)]\left|0\right>$, taking ...
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190 views
When can the source term of a partition function be put in?
More specifically, in quantum field theory books, we usually have this:
\begin{equation}
Z = \int D(\bar{\psi}, \psi) e^{-S + \int_0^\beta d\tau \sum_l [\bar{\eta}_l (\tau) \psi_l (\tau) + ...
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Renormalization group equation of 1D charge susceptibility
I am readng the famous book Quantum Physics in One Dimension by Thierry Giamarchi ,where I have a subtle question about the Renormalization group equation of 1D charge susceptibility at the end of ...
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Helicity dependence in loop diagrams
I am trying to evaluate a diagram that looks like
The middle of the diagram is a fermion loop. I know that the coupling between the $Z^0$ and fermions depends on the fermions' helicities, so it ...
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63 views
Categorizing solutions to Hierarchy problem
We know that no gauge symmetry can prevent a term $m_\phi^2|\phi|^2$ for a scalar field, and that, given the quadratic loop corrections, the natural scale is $m_\phi \sim M_P$. This is related to the ...
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Bosonic-Fermionic interactions in supersymmetry
There are a lot of supersymmetric theories, and, sometimes,in the Lagrangian, there are interacting terms between bosonic and fermionic degrees of freedom, and sometimes not. Why ?
For instance, for ...
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``integrated vertex operators" in 1-loop open/closed bosonic string amplitude
This question is in reference to the first ~15 minutes of this String Theory lecture by Prof.Shiraz Minwalla,
http://theory.tifr.res.in/Videos/strings28_24sep08.mp4
Can one give a reference ...
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56 views
A particlar normal ordering problem
Say we have an expression of the form:
$$
\left<0\right|:\phi(x)^2: : \phi(y)^2:\left|0\right>,
$$
where $\phi$ is some scalar field. I have heard the claim several times, that in evaluating ...
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$U(N)$ gauged quantum mechanics
I'm studying the $U(N)$ gauge theory theory in 0+1 dimensions. The aim is to show that this is equivalent to a matrix model. Is there any literature on this topic?
The action I am interested in is
...
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Questions about classical and quantum scale invariance
This is kind of a continuation of this and this previous questions.
Say one has a free "classical" field theory which is scale invariant and one develops a perturbative classical solution for an ...
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60 views
How does one write eigenstates of field operators in terms of particle states in scalar field theory?
I am reading the first paper in Schwinger's QED anthology, where he discusses his action principle. In this, he writes down states that are simultaneous eigenkets of the field operators at all points ...
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Contact Term and Schwinger Term
In field theory, when 4-divergences of time-ordered Green's functions are computed, there are extra terms known as 'Schwinger terms'.
When deriving the quantum equations of motion for time-ordered ...
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105 views
Quantum Electrodynamics
I was wondering if anyone could give a simple explanation of how light interacts with matter. From what I have read in QED, electrons will repel each other because of their ability to emit and ...
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123 views
Zeta regularization gone bad
This may sound as a mathematical question, but it should be very familiar to physicists. I am trying to perform an expansion of the function $$f(x) = \sum_{n=1}^{\infty} \frac{K_2(nx)}{n^2 x^2},$$ for ...
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63 views
Finding symmetry of a part of an equation, given the group transformation property of another part
I am reading this paper on Dyons and Duality in $\mathcal{N}=4$ super-symmetric gauge theory. The author finds the zero modes or a dirac equation obtained by considering first order perturbations to ...
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80 views
Isospin and Hypercharge of the SU(2) bps monopole embedding
I am reading the paper Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups - Weinberg, Erick J .
In appendix C of this paper the author states, that the solution ...
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41 views
Linear combination of anomalous dimensions in effective potential on pseudomoduli space
In the paper of Intriligator, Seiberg, and Shih from 2007, they give an expression for the effective potential on the pseudo-moduli space $X$, estimated at large $X$ (equation 1.3).
In this equation, ...
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88 views
Asymptotic limit of the two kink solution of the sine-gordon equation
I am reading a paper on the sine-gordon model. The solution for a two kink solution is given as:
...
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Divergence calculation of a lie algebra valued quantity having spinor indices
I am reading this paper by E. Weinberg - Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups.
I am having a problem with a calculation. I don't have much experience ...
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About the gauge invariance of Chern-Simons' theory (in local coordinates)
I am aware of the differential form language proof of the fact that for arbitrary gauge transformations the Chern-Simons' term shifts by a WZW term (on the boundary).
But I am getting confused if ...
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Gauge-invariance of pole mass using Ward Identity
I am able to explicitly verify to one-loop order that pole masses are independent of the choice of gauge paramter.
But how do I use the Ward-Identity/Taylor-Slavnov identity show that the position of ...
3
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112 views
Wilson lines, boundary conditions, surface defects of TQFTs
I asked the following question in mathematics stack exchange but I'd like to have answers from physicists too;
I have been studying (extended) topological quantum field theories (in short TQFTs) from ...
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139 views
Spin polarization of decay products
A relativistic moving particle, e.g. muon $\mu^+$, described by its four-momentum vector $p_\mu$, charge $e$ and with a given spin polarization, ${\bf S}=(S_x,S_y,S_z)$, decays into three particles, ...
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118 views
Dual Resonance Model: Fermions
I am going through Ramond's 1971 paper Dual Theory for Free Fermions Phys Rev D3 10, 2415 where he first attempts to introduce fermions into the conventional dual resonance model.
I get the 'gist' of ...
3
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49 views
uncertainty deviations for vacuum astronomy
Since i've done this question, i've been trying to improve and make more precise the statements regarding cosmic squeezed states and how different uncertainties affect the vacuum energy, but as it ...
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280 views
On the naturalness problem
I know that there are several questions about the naturalness (or hierarchy or fine-tunning) problem of scalars masses in physics.stackexcange.com, but I have not found answers to any of the following ...
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137 views
Gauge invariance of gg->gg scattering amplitude?
I'm trying to calculate the spin and color averaged gg->gg cross section, and I am stumbling upon gauge invariance:
Must the amplitude not be invariant under replacements $\epsilon_i \to \epsilon_i + ...
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103 views
Polyakov action as broken symmetry effective action
I would like to ask if it is possible to regard the Polyakov action as an effective action that describes the broken symmetric phase of a more general model.
Could someone draw an analogy with O(N) ...
3
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126 views
Stability of the vacuum state of interacting quantum fields
"Stability" is generally taken to be the justification for requiring that the spectrum of the Hamiltonian should be bounded below. The spectrum of the Hamiltonian is not bounded below for thermal ...
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154 views
Transition of electric charge to “magnetic charge” when $\alpha$ gets >> 1 in QED?
I`ve just learned that electrically charged particles and magnetically charged monopoles in QED are S-dual to each other such that it depends on the value of the fine structure constant which of the ...
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72 views
Seeking chiral anomaly EFT example
If an effective field theory has a chiral anomaly it means that chiral symmetry isn't a symmetry of the underlying theory which has been cut off to make the EFT. My question is whether there's a good ...
3
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173 views
Descent equation and anomaly polynomial
I am just reading Ryu, Moore and Ludwig's paper on classifications of topological insulators and quantum anomaly(arXiv:1010.0936v1). They are trying to relate the quantum anomaly as a signal of the ...
3
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338 views
An alternative, algebraic way to introduce interactions. Are there other ways out there?
An opening paragraph:
The usual approach to introducing interactions in quantum field theory
is to make the constraint on the
amplitude of the field towards smaller
values more forceful than ...
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Quantum field theory meson scattering calculation (scalar yukawa theory)
Please see this question for a clear background of the notation I use. My issue is that I want to use Wick's theorem to calculate the amplitude of meson ...
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Why isn't there a Heterotic string theory which tensors the fermionic state with the Type II state?
The Heterotic (HO and HE) string is found by tensoring the left movers of the bosonic string theory state and the right movers of the Type II string theory state:
...
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Alternative interpretation of Off-shell internal QFT propagators?
In Quantum Field Theory in a (1, D - 1) space-time, to calculate transition amplitudes, we are using Feynman diagrams, where internal lines (internal propagators) corresponds to momenta which are said ...
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Relevant operators in two dimensional O(n) models
The most general hamiltonian of a two dimensional $O(n)$ and $Z_2$ invariant statistical model can be written:
$$
H=\int d^2 x \left[\frac{\nabla \mathbf{\phi}^2}{2} + \frac{m_0^2}{2}\mathbf{\phi}^2 ...
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de Sitter versus Minkowski QFT and cosmological constant
WMAP/Planck results confirm than we live in a de Sitter-like phase, i.e., a Universe with positive acceleration or positive cosmological constant! Therefore, I believe that a way to solve the ...
