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Moyal Product in Non Commutative Quantum Mechanics

Can someone please explain me what is a Moyal product? Also, how does putting $$X_a(\psi) ~=~ x_a\star\psi$$ realise $$[X_a,X_b]=i\theta_{ab}{\bf 1}?$$ Ref: Quantum mechanics on non-commutative ...
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Questions about Quantization and Noncommutative Geometry

I am trying to orient myself among the vast amount of literature, trying to study the prerequisites necessary for gauge theory and theoretical physics. I have an undergraduate degree in mathematics ...
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TQFTs and Feynman motives

Questions Is a topological quantum field theory metrizable? or else a tqft coming from a subfactor? For a given metric, are there always renormalization and Feynman diagrams? Is there always a Feynman ...
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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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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 ...
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How should I understand the Hilbert space of field theory on non-commutative spaces?

I have a naive question about quantum field theory on non-commutative spaces. I apologize if my question is somewhat vague. Also, I have a weak mathematical background, and I apologize if my question ...
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Commutator as a time-ordered product

I'm reading through Seiberg and Witten's paper "String Theory and Noncommutative Geometry," and one part in $\S$2.1 isn't quite clear to me. (Sorry, in advance, for the length.) My question is about ...
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What is the most natural new physics one can expect at the TeV scale: new (supersymmetric)particles or some new (non-commutative) spacetime structure?

Up to now, nothing else than one Standard Model (SM) Higgs boson-like resonance has been found at the LHC while many predictions based on effective theories using supersymmetry require several Higgs ...
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How algebraic geometry and motives appears in physics?

First, I'm not a physicist so I have just a little background in physics. I have been reading some noncommutative geometry books and papers (Connes, Rosenberg, Kontsevich etc) and a lot of high ...
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Is the conjectured noncommutative heavy scalar “brother” of the already detected Higgs boson is a pseudo scalar?

This is a technical (may be trivial?) question about this sigma scalar field advertised by Chamseddine and Connes to improve the electroweak vacuum stability involved by the weak mass of the already ...
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Is a dynamical extension of non-commutative black holes feasible?

Non-commutative (sometimes called "fuzzy") black holes are solutions of Einstein's equations obtained with a previous basic assumption of non-commutativity of the coordinates $[x^{\mu},x^{\nu}]=i\, ...
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Is the quantization of gravity necessary for a quantum theory of gravity?

The other day in my string theory class, I asked the professor why we wanted to quantize gravity, in the sense that we want to treat the metric on space-time as a quantum field, as opposed to, for ...
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Why can't noncontextual ontological theories have stronger correlations than commutative theories?

EDIT: I found both answers to my question to be unsatisfactory. But I think this is because the question itself is unsatisfactory, so I reworded it in order to allow a good answer. One take on ...