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Question 1

5votes

2answers

164views

Algebraic Geometric Approach to Physical Systems

Is it common to use algebraic geometry for statistical mechanics?More specifically, can we consider the phase space hypersurface consistent with a level of energy as a variety in the affine space and ...

VVM

593

askedJan 9 at 15:59

Question 2

1vote

1answer

428views

How can I find the unitaries for the Bloch-Messiah decomposition?

I'm currently trying to understand the Bloch-Messiah decomposition in quantum optics, which basically states that every second-order nonlinear quantum optical circuit can be decomposed into a ...

Luca Bianchi

73

askedNov 1, 2024 at 10:08

Question 3

3votes

1answer

222views

Is the Godel universe Wick rotatable?

Take Wick Rotatability being as the way defined in the article by Helleland:Wick rotations and real GITIs the Gödel universe Wick rotatable according to this definition?

Bastam Tajik

1,330

askedJan 23, 2024 at 13:38

Question 4

4votes

1answer

287views

Decomposition of vector bundle in $M$-theory

I was studying this paper where the authors construct some field theory solutions by wrapping M5-branes on holomorphic curves on Calabi-Yau. I have some questions about their construction.What they ...

Quiver

4,180

askedOct 14, 2023 at 10:32

Question 5

1vote

0answers

101views

Resource recommendation for geometrical viewpoint of physics [closed]

I am interested in seeing the geometrical viewpoint of the formulation of quantum field theory and related fields. I have been studying The Geometry of Quantum States and find it a very good approach ...

Community wiki

2 revs, 2 users 100%
Lelouch

Question 6

1vote

1answer

255views

Shankar Monopole belonging to the class $-1$ of $\pi_3(\mathbb{R}P^3)$

I am having a lot of trouble trying to understand how the classes of homotopy groups relate to point-defects in physics (and how they can be used/represent in general). This is a problem from Nakahara'...

MathZilla

1,212

askedAug 18, 2022 at 20:27

Question 7

1vote

0answers

69views

Are there examples of harmonic differential forms in non-singular projective algebraic varieties that appear in general relativity or quantum physics?

I would like to study some real physical examples of harmonic differential forms in non-singular projective algebraic varieties. As Calabi - Yau and Kahler manifolds are used in supersymmetry theories ...

Rajaram Venkataramani

27

askedMar 11, 2022 at 14:44

Question 8

1vote

0answers

91views

Does $\mathcal{N}=1$ SCFTs have geometric constructions?

There are class S theories which are 4d $\mathcal{N}=2$ SCFTs by compactifying 6d $\mathcal{N}=(2,0)$ SCFT on a Riemann surface.Does similar geometric constructions exist for 4d $\mathcal{N}=1$ SCFTs?...

Nugi

551

askedDec 20, 2021 at 18:02

Question 9

2votes

1answer

142views

Positive geometry and log singularities

In order to define a positive geometry it is a requirement that has to be a logarithmic singularities on the boundaries, for example for an interval (endpoints $a$ and $b$) the canonical form is$$\...

MZperX

183

askedAug 10, 2021 at 14:25

Question 10

3votes

0answers

72views

Is there any physical significance for the Cremona group / birrational transformations on the projective plane?

In algebraic geometry, the Cremona group is the group of birational transformations on the projective plane.I would like to know:Is there any physical interpretation for this group?Does this group ...

Byron Andrade

61

askedApr 6, 2021 at 12:28

Question 11

8votes

3answers

744views

Why do you need to count curves on Calabi-Yau manifolds in string theory?

One of the mathematical fields that string theory is said to have had a large bearing on is enumerative geometry which, roughly, deals with counting rational curves on hypersurfaces and its ...

Nihar Karve

8,732

askedMar 25, 2021 at 15:02

Question 12

0votes

2answers

97views

Gaussian beam reflection derivation

In this PhD thesis I found a good treatment of refraction and reflection of Gaussian beams at a curved surface.My doubt is from where does it come the cube in the cosine at the denominator of $x^2$ ...

Massimo Valerio Preite

29

askedFeb 22, 2021 at 17:47

Question 13

5votes

1answer

647views

References on mathematical stacks for a string theory student

This question was posted on mathoverflow (here) without too much success.I'm hoping to read the famous Kapustin-Witten Paper "Electric-magnetic duality and the geometric Langlands program" ...

Community wiki

6 revs, 2 users 97%
Ramiro Hum-Sah

Question 14

0votes

1answer

174views

Application of algebraic geometry in studying geodesic and hypersurface

Hypersurface and geodesic can, in principle be written as function of spacetime co-ordinates but not all of them can be written as a polynomial therefore my question is: does algebraic geometry finds ...

aitfel

3,163

askedOct 29, 2020 at 11:59

Question 15

2votes

1answer

214views

Four dimensional massless spectra of type IIA/B compactified on $\mathcal{M}_{4} \times {\rm CY}_3$

I am following “String Theory and M-Theory” by Becker, Becker, and Schwarz and I am currently studying chapter 9. I have a question - or better yet a point of confusion - regarding the derivation of ...

user172341

askedApr 10, 2020 at 17:14

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Stack Exchange Network

Questions tagged [algebraic-geometry]

Algebraic Geometric Approach to Physical Systems

How can I find the unitaries for the Bloch-Messiah decomposition?

Is the Godel universe Wick rotatable?

Decomposition of vector bundle in $M$-theory

Resource recommendation for geometrical viewpoint of physics [closed]

Shankar Monopole belonging to the class $-1$ of $\pi_3(\mathbb{R}P^3)$

Are there examples of harmonic differential forms in non-singular projective algebraic varieties that appear in general relativity or quantum physics?

Does $\mathcal{N}=1$ SCFTs have geometric constructions?

Positive geometry and log singularities

Is there any physical significance for the Cremona group / birrational transformations on the projective plane?

Why do you need to count curves on Calabi-Yau manifolds in string theory?

Gaussian beam reflection derivation

References on mathematical stacks for a string theory student

Application of algebraic geometry in studying geodesic and hypersurface

Four dimensional massless spectra of type IIA/B compactified on $\mathcal{M}_{4} \times {\rm CY}_3$

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