Is String Theory Mathematically Rich and Diverse?

In summary: Experts, tons of them. In the math field: Sergei Gukov, Edward Witten (cmon you got to count him), Ron Donagi, David Morrison, etc, etc.I don't know what you mean by the mathematics of string theory. For one thing they are done by different communities of people so there's got to be some difference?For one thing they are done by different communities of people so there's got to be some difference?
  • #1
pivoxa15
2,255
1
How is this field looking?

What topics does it have?

Who are the experts in this field?
 
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  • #2
pivoxa15 said:
Who are the experts in this field?

Barton Zwiebach at MIT

I am just learning the basics, but from what I can tell ST is thriving and it remains the best solution to the GR-QM inconsistencies.

Check out Zwiebach's A First Course in String Theory if you want the details.
 
  • #3
ehrenfest said:
Barton Zwiebach at MIT

I am just learning the basics, but from what I can tell ST is thriving and it remains the best solution to the GR-QM inconsistencies.

Check out Zwiebach's A First Course in String Theory if you want the details.

I assume the mathematics of string theory is different to string theory?

For one thing they are done be different communities of people so there's got to be some difference?
 
  • #4
ehrenfest said:
Barton Zwiebach at MIT

I am just learning the basics, but from what I can tell ST is thriving and it remains the best solution to the GR-QM inconsistencies.

Check out Zwiebach's A First Course in String Theory if you want the details.

I assume the mathematics of string theory is different to string theory?

For one thing they are done by different communities of people so there's got to be some difference?
 
  • #5
pivoxa15 said:
For one thing they are done by different communities of people so there's got to be some difference?

I've never heard this, but then I don't know what you mean by the mathematics of string theory. I'd be very suprised if a string theorist did not use the "mathematics of string theory" though.
 
  • #6
Algebraic geometry, mirror symmetry, Calabi-Yau manifolds, generalized geometry, BRST, super-"mathematics" - i.e. mathematics with the anticommutative property

Experts, tons of them. In the math field: Sergei Gukov, Edward Witten (cmon you got to count him), Ron Donagi, David Morrison, etc, etc.
 
  • #7
cristo said:
I don't know what you mean by the mathematics of string theory.

Pursuing string theory only as a maths theory.

If that dosen't make sense then it would be doing maths that was motivated by string theory.
 
  • #8
JasonJo said:
Algebraic geometry, mirror symmetry, Calabi-Yau manifolds, generalized geometry, BRST, super-"mathematics" - i.e. mathematics with the anticommutative property

Experts, tons of them. In the math field: Sergei Gukov, Edward Witten (cmon you got to count him), Ron Donagi, David Morrison, etc, etc.

Would Ed Witten be in the physics field?
 
  • #9
pivoxa15 said:
Would Ed Witten be in the physics field?
But most people working in quantum gravity are mathematicians. It, again, comes down to where you draw this line between theoretical physics and maths-- I don't think one needs to draw the line.
 
  • #10
I think there is a difference between mathematical physics and theoretical physics. Witten is for sure not theoretical physicist, if anything, he is a mathematical physicist.
 
  • #11
timur said:
I think there is a difference between mathematical physics and theoretical physics. Witten is for sure not theoretical physicist, if anything, he is a mathematical physicist.

Ed Witten does physics. Ed Witten does theory. Thus, he's a theorist.
All physicists use math.
 
  • #12
pivoxa15 said:
Pursuing string theory only as a maths theory.

I could be wrong here, but I don't think there are any string theory experimentalists. They're all pretty much theoreticians.
 
  • #13
pivoxa15 said:
Would Ed Witten be in the physics field?

He is a very special case; can you name any physicist that wrote a paper on Geometric Langlands conjecture?
 
  • #14
JasonJo said:
He is a very special case; can you name any physicist that wrote a paper on Geometric Langlands conjecture?

Actually, he is a Fields medalist but no Nobel prize:) so we should put him in the maths camp. Imagine if string theory was connected to nature in a deep way then he would also line up for the nobel prize?

Although what kind of journals does he publish in? Are they more maths or physics journals?
 
  • #15
In this site http://superstringtheory.com/math/math2.html there is no mention of integrable models but string theory is an integrable model?
 
  • #16
How much representation theory is in string theory?
 
1.

What is string theory and how does it relate to mathematics?

String theory is a theoretical framework in physics that attempts to reconcile the fundamental forces of nature, including gravity, into a single theory. It posits that particles are not point-like objects, but rather tiny strings vibrating at different frequencies. The mathematics of string theory involves advanced concepts from fields such as differential geometry, algebraic topology, and quantum field theory.

2.

What is the significance of extra dimensions in string theory?

String theory predicts that there are more than the four dimensions (3 spatial dimensions and 1 time dimension) that we observe in our everyday lives. These extra dimensions are compactified, meaning they are curled up and imperceptible to us. The mathematics of string theory allows for the existence of these extra dimensions, providing a possible explanation for their presence.

3.

How does string theory approach the unification of quantum mechanics and general relativity?

One of the main goals of string theory is to unify quantum mechanics and general relativity, two of the most successful theories in modern physics. The mathematics of string theory allows for the consistent incorporation of both theories by describing particles as vibrating strings and incorporating the concept of spacetime curvature into its equations.

4.

What is the role of symmetry in string theory?

Symmetry plays a crucial role in string theory and its mathematics. The theory requires the existence of symmetries, both at the macroscopic and microscopic levels, to maintain its consistency. Additionally, the mathematical tools used in string theory, such as group theory and Lie algebras, heavily rely on symmetry principles.

5.

What are some applications of string theory in practical science?

Although string theory is still a highly theoretical and speculative field, it has already had some practical applications. For example, the mathematics of string theory has been used to study certain properties of black holes and to make predictions about the behavior of matter at high energies. It has also provided insights into other areas of physics, such as condensed matter physics and cosmology.

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