Questions tagged [non-commutative-theory]
The non-commutative-theory tag has no usage guidance.
16
questions
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0answers
8 views
Resource recommendation: Relation between q-deformed groups and non-commutative field theory
I would like to know if non-commutative field theory is related to $q$-deformed groups in any way. There is a relation between non-commutative field theory and group field theory which I understand is ...
-1
votes
0answers
27 views
Relationship between $\star$-products in phase-space quantum mechanics and NC geometry [duplicate]
(NOT a duplicate question)
What exactly is the relationship between $\star$-products in phase-space quantum mechanics, i.e.
$$ (f \star g) (x,p) = f(x,p) e^{\frac{i \hbar}{2} ( \overleftarrow{\...
0
votes
1answer
156 views
What is a fuzzy space?
Can someone give a down-to-earth explanation of what is a fuzzy space? (As known from M-theory and noncommutative geometry)
2
votes
1answer
260 views
Why do position operators in orthogonal directions commute?
In three dimensions, we have $\hat x$, $\hat y$, $\hat z$ as the position operators in the three orthogonal directions. If the components of angular momentum don't commute, why must these all commute? ...
4
votes
2answers
198 views
Solving the *-genvalue equation of a free particle
The background
I want to solve the $\star$-genvalue equation
$$ 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
\...
2
votes
1answer
72 views
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 ...
2
votes
0answers
185 views
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 ...
6
votes
1answer
384 views
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. ...
8
votes
4answers
4k views
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 ...
1
vote
0answers
94 views
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 ...
8
votes
4answers
653 views
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 (up to now) ...
17
votes
2answers
3k views
The physics community's take on noncommutative geometry
Connes's noncommutative geometry program includes an approach to the Standard Model that employs a noncommutative extension of Riemannian metric. In recent years I've heard physicists say that this ...
2
votes
0answers
118 views
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?
11
votes
1answer
157 views
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 ...
7
votes
2answers
2k views
Prerequisites to start the study of noncommutative geometry in physics
What are prerequisites (in mathematics and physics), that one should know about for getting into use of ideas from noncommutative geometry in physics?
15
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2answers
2k views
115 GeV, 170 GeV, and the noncommutative 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 ...
