All Questions
Tagged with noncommutative-geometry mp.mathematical-physics
18 questions
9
votes
1
answer
722
views
Non-commutative complex geometry
I was reading a physics paper where it was mentioned that the basic framework of Connes' differential non-commutative geometry (or actually, a slight modification of Connes in that paper) would need ...
- 5,146
5
votes
0
answers
156
views
Associating noncommutative geometries to 2D conformal field theories
I have recently been reading a bit about noncommutative geometry and string theory and it looked to be an open question (or at least this was open two decades ago) whether there are constructions ...
- 5,146
6
votes
1
answer
504
views
Fermions, their path integrals and effective actions
I just read the nice exposition Fermionic Path Integral on nLab and began to wonder about some details to which references appear to be lacking. Suppose we live on Euclidean space as in the ...
- 651
10
votes
2
answers
2k
views
Why does Riesz's Representation Theorem apply in quantum mechanics?
$\DeclareMathOperator\tr{tr}$One begins with a quantum mechanical system, i.e. a unital $C^*$-algebra $A$.
It is common to begin the discussion with embedding $A$ into the algebra of bounded operators ...
- 2,071
3
votes
1
answer
386
views
What is the precise relationship between real Poisson algebras and commutative $C^*$ algebras?
I've been teaching myself quantum mechanics, and I realized that I'm missing something fundamental. Namely, there are two pictures that I don't know how to reconcile:
Quantum Mechanics generalizes ...
- 2,071
3
votes
0
answers
266
views
Hodge theoretic mirror symmetry and DG-BV algebras
Consider two Calabi-Yau manifold $X$ and $\check{X}$ which are meant to be mirror partners. Motivated by "classical MS", In DGBV Algebras and Mirror Symmetry, the following enhancement is proposed:
...
- 1,981
11
votes
4
answers
1k
views
Geometric or conceptual way to understand supersymmetry algebra
Is there any geometric or more direct conceptual way to understand a supersymmetry algebra, rather than starting from a Lagrangian including boson and fermion fields, deriving all the expressions ...
- 781
3
votes
2
answers
825
views
Reference for de Rham cohomology for physicists
Do you know a basic reference to introduce an undergraduate student with more physical rather than mathematical background to De Rham cohomology?
The Student (from a Bachelors ...
- 2,630
2
votes
2
answers
327
views
Deformation quantization of a closed Riemann surface with genus >1
Quantization of of an elliptic curve can be done in different ways.
In C^*-algebraic version,
one can start with the C^*-algebra ...
- 309
8
votes
0
answers
356
views
Noncommutative geometry and line length
I would like to understand, in some formal sense, the relation between the Dirac operator and the line length introduced by Connes in noncommutative geometry. If $D$ is the Dirac operator, he sets $ds ...
- 1,687
4
votes
1
answer
710
views
Reference request for instantons
I've been researching instantons lately and I'd like to learn more about them but would like some help finding what to read. I have read about the ADHM equations and their noncommutative analogues. ...
- 161
33
votes
1
answer
4k
views
What about nonassociative geometry?
At the conclusion of a conference delivered by Alain Connes in 2000 (video in French at 1:19:25), an audience member posed a question. Below is a polished translated transcription:
Audience:
You have ...
22
votes
3
answers
6k
views
What is quantum Brownian motion?
It seems that the current state of quantum Brownian motion is ill-defined. The best survey I can find is this one by László Erdös, but the closest the quantum Brownian motion comes to appearing is in ...
- 8,502
5
votes
0
answers
547
views
Open question: non-commutative site following Grothendieck, Quillen, Connes and Crane for quantum gravity.
This is an open question and it's to find out who is interested in this kind of thing, who can benefit from thinking about this. It is very brief but hopefully will only be unclear to people who are ...
- 171
7
votes
1
answer
611
views
Extension of the formality theorem?
The following question came up in a discussion the other day and I have been wondering whether something is known about it. Everything below takes place over $\mathbb{C}$. I don't have the expertise ...
- 3,758
21
votes
6
answers
3k
views
Penrose tilings and noncommutative geometry
Are there "elementary" resources on Penrose Tilings in relation to noncommutative geometry? It's all a big blur to me. There are two transformations S and T that can grow the tilings and every ...
- 22.8k
4
votes
1
answer
282
views
Manifolds whose isometry group is Pati-Salam?
By the Pati-Salam group I refer to SU(2) x SU(2) x SU(4). It can be obtained as the group of isometries of the 8 dimensional manifold $S^3 \times S^5$, but I wonder if this is the only 8 dimensional ...
- 437
43
votes
6
answers
9k
views
The 'real' use of Quantum Algebra, Non-commutative Geometry, Representation Theory, and Algebraic Geometry to Physics
In this question, Orbicular made the following comment to Feb7 and my own answers;
Please keep in mind that - even though it is stated very often - noncommutative geometry does not give "real" ...
- 4,842