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Questions tagged [non-commutative-geometry]

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Non-commutative geometry deals with spaces where the uncertainty principle of quantum mechanics thwarts even one's ability to simultaneously measure two position co-ordinates. It finds applications in models where geometry is emergent including the matrix model approach to string theory.

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In mathematics Callias-type operator is defined as follow. Let $M$ be a complete manifold and $E$ a Clifford bundle. Let $D$ be the Dirac operator acting on section if $E$ and let $A$ be a self-...
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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 ...
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I heard recently in a talk by Alain Connes that a certain Woodword (or Woodward or Woodard, not sure with reccording quality) showed an important result that a quantum theory of gravity cannot be ...
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I'm reading a book by Szekeres P (2004) A modern course in Mathematical Physics and it has an excerpt here that goes: We have good reason to believe that on time scales less than the Planck time [...]...
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My question concerns fuzzy sphere solutions and how they fit into the large-$N$ limit of gauge theory. The Berenstein-Maldacena-Natasse (BMN) model is a matrix model that arises in string theory. The ...
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I know this is a very broad question with few references but what is kappa deformation in the context of quantum gravity and non-commutative QFT (https://doi.org/10.1016/j.physletb.2019.01.063)?, I ...
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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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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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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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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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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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What exactly is the relationship between $\star$-products in phase-space quantum mechanics, i.e. $$ (f \star g) (x,p) = f(x,p) e^{\frac{i \hbar}{2} ( \overleftarrow{\partial_x} \cdot \overrightarrow{\...
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I'm listening to Alain Connes "On the Fine-Structure of Space-Time" around minute 23 saying that it was disappoing that the solution $Y$ to the equation $$ \langle Y[D,Y]^{2m} \rangle= \...
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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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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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