Questions tagged [non-commutative-theory]

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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}}{\...
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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 ...
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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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Loop-correction for non-commutative quartic theory

What is the meaning of the second, third and fourth graph? The image is from arXiv:hep-th/9912072.
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Generalisation of Seiberg-Witten Map?

Given the following algebra, $$[\hat{x}_i,\hat{p}_j] = i\hbar\delta_{ij};~[\hat{x}_i,\hat{x}_j] = i\theta_{ij};~[\hat{p}_i,\hat{p}_j] = i\eta_{ij}$$ in a space, where $\theta_{ij},\eta_{ij}$ are ...
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Interaction vertex in non-commutative QFT

If $\hat{S}_{1}=i \int d^{d} x \mathcal{L}_{I}$ and $$ \begin{aligned} V\left(x_{1}, x_{2}, \ldots, x_{n}\right) & \equiv \int\left[\prod_{j=1}^{n} \frac{d k_{j}}{(2 \pi)^{d}}\right] e^{i k_{\mu}^{...
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Why does a phase shift in a light pulse imply a non-commutative structure of space (which implies gravity has a quantum structure)?

In the news report Physicists propose test of quantum gravity using current technology (Lisa Zyga, Phys.org, 27 October 2017), a test is proposed to determine if gravity has a quantum structure. From ...
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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 \...
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Non-commutative field theory vs Non-commutative geometry

In the literature I have read about non-commutative field theory where the spacetime coordinates obey $$[x_i, x_j] = \theta_{ij}, \quad \theta_{ij} \neq 0.$$ However, I have also non-commutative ...
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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 ...
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What is a fuzzy space?

Can someone give a down-to-earth explanation of what is a fuzzy space? (As known from M-theory and noncommutative geometry)
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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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2 answers
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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 \...
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Snyder spacetime: are position and time true (quantum) operators there?

Snyder spacetime is generally considered one of the first models of non-commutative and quantum spacetime. There is no time operator in Quantum Mechanics. Is time in quantized Snyder space a true ...
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Partial Derivatives in Noncommutative Spacetime

Will the order of taking partial derivatives matter in a noncommutative spacetime? If so, what implications will that have on the way we do gauge theory? For example, will our Lagrangian now contain ...
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Feynman graphs in noncommutative quantum field theory

I learn noncommutative quantum field theory now. Here, this topic is treated: arXiv:hep-th/0109162 I understood basic equations, but I don't really understand Feynman rules for noncommutative case. ...
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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 ...
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Noncommutative Field Quantization

I'm studying noncommutative (quantum) field theory, and I have confusion need to be clear. I'm reading Szabo's and Douglas's .pdf of noncommutative QFT. As I understand, in the book they just ...
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4 answers
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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 (...
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21 votes
2 answers
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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 ...
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Why are interacting noncommutative quantum field theories with space-time noncommutativity unitary?

Can anyone explain in a simple manner why interacting noncommutative quantum field theories with space-time noncommutativity of the Moyal bracket sort are unitary?
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Metric interpretation of self-adjoint extensions?

I am wondering if beyond physical interpretation, the one dimensional contact interactions (self-adjoint extensions of the the free Hamiltonian when defined everywhere except at the origin) have a ...
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8 votes
2 answers
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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?
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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 ...
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