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Results tagged with quantum-field-theory
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user 61966
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 particle physics. Don’t combine with the [quantum-mechanics] tag.
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What are instanton fugacities?
I have seen this term many times in various papers but I could not find anywhere a good explanation on what instanton fugacity is. Can you explain and provide some reference if possible please?
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Propagator of auxiliary field $D$ in SUSY gauge theory
Consider $4d$ $\mathcal{N}=2$ susy gauge theory. Why is the propagator of the non-dynamical auxiliary field $D$ (the field needed such that the susy algebra is closed off-shell) proportional to a delt …
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Where are the $U(1)$ topological gauge theory zero modes?
In this 1995 paper, Witten claims the following:
The zero modes (i.e. of the gauge field) do not give factors of $\Im \tau$; they are tangent to the space of classical minima, which is a torus of dim …
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Maxwell theory duality problem
I have to show that
$$q \equiv \int d^{3}\vec{x}\, J^0 = -\int d^{3}\vec{x}\ \partial_i F^{0i} = -\int \frac{1}{2} d^{3}\vec{x}\ \varepsilon^{ijk} \partial_{i}G_{jk} \tag{1}$$
(this is exactly what …
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Why does the Higgs field have less energy when it's non-zero than when it's zero?
From the form of the Higgs potential (which is quartic, the famous Mexican hat) you can see that for $\Re \phi =0$ as well as for $\Im \phi=0$ (the real and imaginary parts of the Higgs field), it is …
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0
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165
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Protected operators by SUSY
People say that
In superconformal field theories with extended susy (say 4d, $\mathcal{N}=2$) we have protected local operators
annihilated by some supercharges $Q_I$. Also, upon breaking confo …
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93
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Hypermultiplet as BPS particles
In the third paragraph of page 7 of the paper arxiv:1112.3984 it mentions that we form a basis out of hypermultiplets on the charge lattice $\Gamma$. My questions are:
In what sense do we form such …
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A fundamental question about Seiberg duality
Standard set up and review:
Let us consider $SU(N)$ SQCD with $N_f$ flavors as our electric theory (just like in Seiberg's paper) and also let $N_f \geq N$. This theory is completely Higgsed in the I …
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2
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783
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Understaning Euclidean Green's function
Consider a scalar field coupled to a source
$$(\Box - m^2)\phi(x) = -J(x)\tag{1}.$$
Then, the response of the source is determined by the Green's function $G(x-y)$, which satisfies
$$(\Box - m^2)G(x- …
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Trying to understand the symmetries of higher dimensional $\gamma$-matrices
I am reading that there exists a unitary matrix $C$ (the charge conjugation) matrix such that each matrix $C\Gamma^{A}$ is either symmetric or anti-symmetric. Now, $\Gamma^{A} = \{ {\bf 1}, \gamma^{\m …
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Clarification: Why the gauge symmetry of pure Yang-Mills is $PU(n)$ and not $SU(n)$? [closed]
I am quoting the following from the Wikipedia article on the projective unitary group:
In the pure Yang–Mills $SU(n)$ gauge theory, which is a gauge theory
with only gluons and no fundamental ma …
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1
answer
475
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How to compute this loop integral? [closed]
I have a gauge boson that splits into two scalars and the loop is closed by a gauge boson as shown in the picture. The incoming boson has $\mu$ index while the boson that runs in the loop has momentum …
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Why do we demand $SU(2)$ and $SU(3)$ gauge invariance when we construct the standard model?
We demand our theories to be gauge invariant. By that I mean, we do not pick $G = U(1) \times SU(2) \times SU(3)$ because we "choose so". This pops out due to the bundle nature of the electromagnetic, …
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Higher rank $\gamma$-matrix question
I read that the higher rank $\gamma$ matrices can be written as alternate commutators and anti-commutators. For example, the rank 3 gamma matrix can be written as
$$\gamma^{123} = \frac{1}{2}\{\gamma^ …
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1
answer
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Georgi-Glashow model and the VEV of the scalar field
Consider the Georgi-Glashow model, an $SU(2)$ gauge theory with a real scalar in the adjoint (thus a 3-vector in the colour space) $\phi$. The Lagrangian is
$$ L = -\frac{1}{4g^2} F_{\mu \nu}^{\, a} …
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