Questions tagged [non-commutative-theory]

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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 ...
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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{\...
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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)
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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? ...
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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 \...
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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 ...
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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
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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. ...
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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 ...
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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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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) ...
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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 ...
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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?
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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 ...
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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?
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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 ...