Questions tagged [non-commutative-theory]
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28 questions
3votes
1answer
103views
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 ...
3votes
1answer
231views
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 ...
- 445
7votes
1answer
537views
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 ...
- 1,121
4votes
0answers
76views
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 ...
- 1,781
0votes
0answers
100views
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 $$ F(x)=\sum_{\alpha} \frac{(x_1 - a_1)^{\alpha_1}\dots(x_n - a_n)^{\alpha_n}}{\...
- 859
1vote
1answer
85views
Effects of non-locality in the star-product of two fields
My question regards an argument appearing on page 19 of the review: Quantum Field Theory on Non-commutative Spaces - Szabo. The Fourier integral kernel representation of the star-product of two fields ...
user195631
2votes
1answer
123views
Seiberg-Witten Map Derivation
In the original paper defining the Seiberg-Witten map, I have been confused about the following step in their derivation. Using the gauge transformation constraint, they write \begin{align*} A'_i (A+ \...
- 2,999
2votes
1answer
68views
Loop-correction for non-commutative quartic theory
What is the meaning of the second, third and fourth graph? The image is from arXiv:hep-th/9912072.
1vote
0answers
40views
Generalisation of Seiberg-Witten Map?
Given the following algebra, $$[\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}$$ in a space, where $\theta_{ij},\eta_{ij}$ are ...
- 3,636
2votes
0answers
78views
Interaction vertex in non-commutative QFT
If $\hat{S}_{1}=i \int d^{d} x \mathcal{L}_{I}$ and $$ \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}^{...
0votes
1answer
121views
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 ...
4votes
1answer
212views
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 \...
1vote
0answers
109views
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 ...
- 1,552
2votes
3answers
1kviews
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 ...
- 15.8k
1vote
1answer
1kviews
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)
user122089
