Learning String Theory in high school

[Berislav]

I am currently reading these lecture notes about string theory:

http://www.phys.uu.nl/~thooft/lectures/string.html

I think that I understand the general idea. After that it's simply applying QFT formalism, which I'm more or less familiar with (or so I thought). But in Chapter 7. - BRST quantization of the notes (p. 31) I encountered a few concepts and terms that I don't what mean: What's the D in equation (7.1) (does it have anything to do with the covariant derivative?) and what are "gauge orbits"?

I haven't found anything about BRST quantization in Landau and Lif****z's Quantum Electrodynamics, which is the only book I have on the subject. Google only gave me links to scientific papers exploring the procedure.

Also on page 34, they associate the world sheet of two interacting closed strings with the topology of a sphere, and the strings being topological "holes" in the sheet. It was my impression that the world sheet of a string was the string itself (p. 8); the two dimensional world sheet (proper time and a spatial coordinate along the string) is located in a higher dimensional space-time.

I thank you in advance for your help.

 

[selfAdjoint]

BRST quantization postdate L&L by several decades. The eponymous suspersymmetry was discovered in ordinary non-supersymmetric Yang-Mills theory in the 1960s, and the whole BRST thing has just taken off and expanded into seemingly every corner of physics. Nearest hint I can give you is that BRST provides a kind of super-powered analog of Lagrange multipliers in a simplectic context.

I don't know how you got the wrong idea from this standard explanation of the string world sheet:

In Minkowski space-time, a string sweeps out a 2-dimensional surface called the “world sheet”. Introduce two coordinates to describe this sheet: $$\sigma$$ is a coordinate along the string, and $$\tau$$ a timelike coordinate. The world sheet is described by the functions $$X^i(\sigma;\tau)$$, where i runs from 0 to d, the number of space dimensions.

('t Hooft p.8)

 

[Berislav]

Nearest hint I can give you is that BRST provides a kind of super-powered analog of Lagrange multipliers in a simplectic context.

I think I understand; the gauge symmetries being analogous to the constraints imposed on the field configurations and the amplitude to the extremum?

I don't know how you got the wrong idea from this standard explanation of the string world sheet:

The "sweeps out" part confused me. English is not my primary language.

Thank you again for taking the time to help me understand this complex theory.

 

[selfAdjoint]

The "sweeps out" part confused me. English is not my primary language.

Aah. Think of the sweeping edge of a broom, as the broom is moved it leaves a track. We say of anything similar that it is sweeping out such a track. If the object is one-dimensional like a string, we would expect the track swept out to be two dimensional. Now allow the string to wiggle as it moves, and this spacetime track becomes a general two dimensional manifold; in fact, as will be shown in the Notes, it is a conformal complex manifold: a Riemann Surface.

 

[dextercioby]

The bible on BRST & Batalin-Vilkovisky quantization is still
Marc Henneaux & Claudio Teitelboim,"Quantization of Gauge Systems"

Daniel.

 

[selfAdjoint]

The bible on BRST & Batalin-Vilkovisky quantization is still
Marc Henneaux & Claudio Teitelboim,"Quantization of Gauge Systems"

Daniel.

75 smackers used at alibris is a bit steep, even for something that interesting.

 

[misogynisticfeminist]

Learning string theory in high school ??

 

[dextercioby]

Learning string theory in high school ??

Yeah,why not?Who cares about the knowledge on QM & GR?It's nice that one gets to know what a heterotic string is and how they are quantized via BRST techniques,while still in HS.

Daniel.

 

[selfAdjoint]

Yeah,why not?Who cares about the knowledge on QM & GR?It's nice that one gets to know what a heterotic string is and how they are quantized via BRST techniques,while still in HS.

Daniel.

Let the kid alone. Life isn't all about being soundly grounded; maybe BRST quantization can be "hyacinths for the soul" too.

 

[marcus]

Let the kid alone. Life isn't all about being soundly grounded; maybe BRST quantization can be "hyacinths for the soul" too.

The twelfth-century Persian poet, Moslih Eddin Saadi, wrote:

"When of thy worldly goods
Thou find thyself bereft,
And from the goodly store
Two loaves alone are left...
Sell one, and with the dole
Buy hyacinths to feed thy soul."

 

[dextercioby]

Let the kid alone. Life isn't all about being soundly grounded;

True,but you got to admit the feeling you have when you're able to justify your every statement is unique...

maybe BRST quantization can be "hyacinths for the soul" too.

True,but it still provides a supersymmetric algebra within QED...

Daniel.

 

[Berislav]

Aah. Think of the sweeping edge of a broom, as the broom is moved it leaves a track. We say of anything similar that it is sweeping out such a track. If the object is one-dimensional like a string, we would expect the track swept out to be two dimensional. Now allow the string to wiggle as it moves, and this spacetime track becomes a general two dimensional manifold; in fact, as will be shown in the Notes, it is a conformal complex manifold: a Riemann Surface.

I understand. Thank you.

Originally Posted by dextercioby
The bible on BRST & Batalin-Vilkovisky quantization is still
Marc Henneaux & Claudio Teitelboim,"Quantization of Gauge Systems"

Daniel.

75 smackers used at alibris is a bit steep, even for something that interesting.

I'll ask my parents can I buy the book. Thank you for the advice.

Yeah,why not?Who cares about the knowledge on QM & GR?

Of course, I studied QM and GR before I even thought about learning String Theory. True, I still feel that I'm not all that well grounded, here's a list of books I read on the subjects; if you would, please, recommend further reading:

B.F. Schutz: "A first course in General Relativity"
R. Wald: "General Relativity"
Martin & Shaw: "Particle Physics"
Landau & Lif****z: "Quantum Mechanics: Non-relativistic theory"
Landau & Lif****z: "Quantum Electrodynamics"
Riley, Hobson & Bence: "Mathematical Methods for Physics and Engineering"
S. Hassani: "Mathematical Physics"

 

[dextercioby]

Berislav,are u a chess champion...?

Daniel.

 

[selfAdjoint]

Berislav, here is an online survey paper on BRST Quantization which I have found useful and you might too. "Aspects of BRST Quantization", by J.W. van Holten

 

[Berislav]

Berislav, here is an online survey paper on BRST Quantization which I have found useful and you might too.

Thank you, thank you very much. It seems like a very interesting paper. It will be of great help.

Berislav,are u a chess champion...?

No. Just very enthusiastic.

 

[misogynisticfeminist]

btw, berislav, how old are you? Cos' if you're indeed a high school student who can understand stuff such as QFT and tensor analysis, i am very very much impressed.

 

[Berislav]

btw, berislav, how old are you?

I'm 18 years old.

Cos' if you're indeed a high school student who can understand stuff such as QFT and tensor analysis, i am very very much impressed.

It hasn't been easy, mostly because of the complexity of the subjects at hand, but also due to the fact that almost all of the material I studied is in English and due to the fact that I couldn't find anyone to help me (until I found this board, that is).

 

[Mark_W_Ingalls]

Dear Berislav--

I am old. It is not easy for me to understand these subjects either. (String theory was just being dreampt of when I was your age.) I want you to know two things. First, you have helped me. Second, your life is not a sprint. If you must work a long time to understand something, that is OK, you will succeed. Thanks for making me smile, buddy!

Mark