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.
Questions tagged [non-commutative-geometry]
35 questions
28
votes
5 answers
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 example, just leaving the metric alone, and doing…
Jonathan Gleason
- 8,834
23
votes
0 answers
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 motive related to the theory?
Finally, does this…
22
votes
2 answers
The physics community's take on non-commutative geometry
Connes's non-commutative geometry program includes an approach to the Standard Model that employs a non-commutative extension of Riemannian metric. In recent years I've heard physicists say that this approach does not hold significant interest in…
Jon Bannon
- 1,171
16
votes
4 answers
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 contextuality is to develop an inequality on…
Mateus Araújo
14
votes
2 answers
115 GeV, 170 GeV, and the non-commutative 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 years later.
Meanwhile, for a long time there have…
Mitchell Porter
- 13,692
14
votes
1 answer
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 machinery from algebraic geometry such as étale…
user40276
- 1,043
9
votes
3 answers
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 scalars and needs an entourage of sparticles close…
8
votes
4 answers
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) a sufficient evidence to substantiate the almost…
8
votes
2 answers
Prerequisites to start the study of non-commutative geometry in physics
What are prerequisites (in mathematics and physics), that one should know about for getting into use of ideas from non-commutative geometry in physics?
user5012
- 209
6
votes
1 answer
Impossibility of building quantum gravity theory from the bottom?
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 built directly from Planck-scale elementary degrees…
Mathias
- 410
5
votes
0 answers
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 equation (2.7) on page 9, where they say:
The…
Ralph Mellish
- 274
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5
votes
1 answer
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 plane
Kamal
- 308
5
votes
1 answer
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 and I am now studying manifold theory and geometry…
4
votes
0 answers
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 found Higgs-like particle.
Is it a scalar or a…
4
votes
0 answers
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 involve triples that encode the underlying geometry,…
Carl Bart
- 41