Questions tagged [non-commutative-theory]
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30 questions
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How do non-commutative fields arise in the low-energy description of the lowest Landau level?
We use quantum field theory in condensed matter physics regularly. Let us focus on bosons. Usually, the field theory picture is motivated using a trotterization of the Hamiltonian using the coherent ...
CommunityBot
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3
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2
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340
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Noncommutative geometry (NCG) in the foundations of physics (SM and QG)
I came across the applications of noncommutative (NCG) geometry to quantum field theory (QFT) and quantum gravity (QG).
I'm trying to understand the status of the field so that I can evaluate if I ...
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Why does $U(1)$ decouple from $SU(N)$ in the infrared in $\mathcal{N}=2$ non-commutative SYM?
In this article, after Equation (2.26), it is claimed that:
Equations (2.26) remarkably show the decoupling of the U(1) component associated with the generator $t^0 ∝ \mathbf{1}$
The non-planar ...
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The non-commutative 1st Chern number is given by ${\rm Im}(Tr(P[X,P][Y,P])$. Want to know the role of ${\rm Re}(Tr(P[X,P][Y,P]))$ and why is it zero?
So I have been doing some numerics on a 2- band disordered Chern insulator model (QWZ) and have been calculating the non-commutative Chern number given by the formula $ \frac{1}{2\pi i} \Im\Tr P[X,P]...
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Why do position operators in orthogonal directions commute?
In three dimensions, we have $\hat x$, $\hat y$, $\hat z$ as the position operators in the three orthogonal directions. If the components of angular momentum don't commute, why must these all commute? ...
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3
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Is string theory a particular non-commutative field theory (whether the commutator of the position coordinates in string theory is non-zero)?
I am just beginning to study string theory, and am reading a bit of literature. Following this, I have a question which is probably not very well framed:
I want to know whether string theory is a ...
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Levinson's theorem in non-commutative quantum mechanics
Levinson's theorem is a fundamental result from the scattering theory of spherically symmetric potentials in ordinary quantum mechanics. It relates the number of bound states $n$ for a given potential ...
- 1,887
16
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4
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Binomial expansion of non-commutative operators
I would like to determine the general expansion of
$$(\hat{A}+\hat{B})^n,$$
where $[\hat{A},\hat{B}]\neq 0$, i.e. $\hat{A}$ and $\hat{B}$ are two generally non-commutative operators. How could I ...
- 224k
8
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4
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Is the 125 GeV Higgs boson some kind of a "almost-commutative graviton" at the electroweak scale?
The clumsy "almost-commutative graviton" is provocative. I use it on purpose, to ask two questions in one :
Is the observation of only one Higgs and no supersymmetric particle below 8 TeV (...
- 2,754
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Function of noncommutative operators: how should the powers in its Taylor expansion be arranged, and how to take partial derivatives?
Let $F:\mathbb R ^n\to\mathbb R$ be a function that has a Taylor expansion, then it can be written (expanded at $a$) as
$$
F(x)=\sum_{\alpha} \frac{(x_1 - a_1)^{\alpha_1}\dots(x_n - a_n)^{\alpha_n}}{\...
- 68k
8
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2
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Prerequisites to start the study of non-commutative geometry in physics
What are prerequisites (in mathematics and physics), that one should know about for getting into use of ideas from non-commutative geometry in physics?
- 224k
14
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2
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115 GeV, 170 GeV, and the non-commutative standard model
Several years ago, noncommutative geometry was used to describe the standard model, somehow yielding a prediction of 170 GeV for the mass of the Higgs boson, a prediction which was falsified a few ...
- 224k
22
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The physics community's take on non-commutative geometry
Connes's non-commutative geometry program includes an approach to the Standard Model that employs a non-commutative extension of Riemannian metric. In recent years I've heard physicists say that this ...
- 224k
1
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1
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Effects of non-locality in the star-product of two fields
My question regards an argument appearing on page 19 of the review: Quantum Field Theory on Non-commutative Spaces - Szabo. The Fourier integral kernel representation of the star-product of two fields ...
- 68k
2
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1
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Seiberg-Witten Map Derivation
In the original paper defining the Seiberg-Witten map, I have been confused about the following step in their derivation. Using the gauge transformation constraint, they write
\begin{align*}
A'_i (A+ \...
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