Questions tagged [non-commutative-theory]
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30 questions
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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 ...
- 1,330
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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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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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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 ...
- 1,206
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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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4
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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? ...
- 293
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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 ...
- 347
4
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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
2
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3
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Quantum Probability, what makes quantum characteristic functions quantum?
I'm trying to understand how $[Q,P] \neq 0$ leads to the conclusion that no probability distribution can be established for $A$ and $B$.
Classically if we had two random variables $Q$ and $P$ we ...
- 16.4k
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 ...
- 1,171
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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
$$
F(x)=\sum_{\alpha} \frac{(x_1 - a_1)^{\alpha_1}\dots(x_n - a_n)^{\alpha_n}}{\...
- 903
4
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1
answer
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Is The Seiberg-Witten Map Unique?
From my understanding the Seiberg-Witten map is a way to convert a non-commutative field theory into a commutative field theory. For example for the commutative relation between positions $[x, y]=i \...
- 179
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1
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Effects of non-locality in the star-product of two fields
My question regards an argument appearing on page 19 of the review: Quantum Field Theory on Non-commutative Spaces - Szabo. The Fourier integral kernel representation of the star-product of two fields ...
user195631
2
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1
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188
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Seiberg-Witten Map Derivation
In the original paper defining the Seiberg-Witten map, I have been confused about the following step in their derivation. Using the gauge transformation constraint, they write
\begin{align*}
A'_i (A+ \...
- 3,059
5
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2
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Solving the *-genvalue equation of a free particle
The background
I want to solve the $\star$-genvalue equation
$$ H(x,p) \star \psi(x,p) = E~\psi(x,p),$$
where $\star$ denotes the Moyal star product given by
$$
\star \equiv \exp \left\lbrace
\...
- 1,090