Questions tagged [non-commutative-geometry]

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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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76 views

Structure of spacetime as a non-commutative algebra

Disclaimer: this question is a cross-posting from mathoverflow.net, as what I expect there is a link to mathematical concepts, while here I'd like an examination of how meaningful it is physically. ...
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Does following kind of commutator arises anywhere in non-commutative geometry of spacetime?

Pauli matrices satisfy following relation $$[\sigma_i,\sigma_j]=2i\epsilon_{ijk}\sigma_k$$ While looking through models of noncommutative geometry of spacetime I have seen people defining following ...
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Equivalence Between the Algebras of the Standard Model and Connes Non-Commutative Geometry Model

I've been watching some lectures on Connes non commutative geometry model and one of the things I don't understand is why the algebra he considers, $M_2(\mathbb{H}) \oplus M_4(\mathbb{C})$, is ...
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61 views

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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Application of non-commutative geometry in quantum mechanics [closed]

What are some of the applications of Connes' non-commutative geometry in quantum mechanics? Is it useful in defining and studying phase structure of a quantum system since we have $[\hat{x},\hat{p}]=...
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2answers
141 views

Relationship between $\star$-products in phase-space QM and NC geometry

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{\partial_x} \cdot \overrightarrow{\...
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1answer
131 views

Implication of the Jacobian map for the structure of the Euclidean space-time

I'm listening to Alain Connes "On the Fine-Structure of Space-Time" around minute 23 saying that it was disappoing that the solution Y to the equation $$ \langle Y[D,Y]^{2m} \rangle= \gamma $...
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95 views

How does Alain Connes NCG compare phenomenologically with superstring theory?

In Veltmans book on QFT, diagrammatica, the full SM Lagrangian is published. There are more than a hundred terms and it looks pretty uninspiring and not quite the kind of equation one would want to ...
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1answer
378 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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79 views

Was $\kappa$-Minkowski model falsified by gamma ray burst measurements?

I'm considering the $\kappa$-Minkowski space – a certain model from non-commutative geometry which reduces to the usual Minkowski space in the limit $\kappa \rightarrow \infty$. The parameter $\kappa$ ...
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270 views

Is there a mathematical connection between Causal Fermion Systems and Noncommutative geometry?

Well, the title says it all. Upon research, many of the ideas in Felix Finster's Causal Fermion Systems (CFS) and Alain Connes' Noncommutative geometry (NCG) struck me as similar. Both theories ...
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177 views

Resources to learn Non-Commutative Geometry

I'm looking for sources on non-commutative geometry and integration theory. I wonder if this theory might replace the standard theorey in the long run, as it seems to be more general. What are ...
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1answer
309 views

Do the canonical commutation relations have any connection to geometry?

I was wondering if the canonical commutation relations have any connection to geometry? If so, could you explain the connection in fairly simple and intuitive terms?
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174 views

Is there an introduction to non-commutative geometry?

I am looking for a simple explanation as how spectral triples give rise to definition of distance using Dirac operators?
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319 views

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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928 views

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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101 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 ...
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0answers
145 views

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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307 views

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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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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106 views

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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3answers
641 views

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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57 views

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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4answers
700 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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1answer
823 views

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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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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156 views

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 ...