Reference no: EM13985401
Some cases to ponder over.
A closed string splits into two closed strings, which then merge again into a single closed string. The overall string worldsheet has the topology of a torus. There is an SL(2,Z) group of large diffeomorphisms acting upon this worldsheet. The contribution to the partition function comes from summing up over all contributions with this topology. Suppose you insist upon a canonical description of this process. In the loop part in the middle, there is a different slicing associated with each of the SL(2,Z) elements. We have to sum up over all such contributions. Each such choice gives the same contribution, but there is no canonical choice of which slicing. If you consider summing up over all possible slicings, there is the possibility of "interference" between different choices of slicings because the configurations you get from a different slicing might be continuously deformable into that of a different slicing. So, you can't just insist that we sum up over one possible slicing only. However, if you sum up over all possible intermediate slicings, you pick up an infinite multiplicative factor compared to the no string interaction case.
The other case is a "tree level" worldsheet with two incoming closed strings, and two outgoing ones. There are the s-, t- and u-channels. They correspond to different possible slicings. Each by itself gives the same contribution. Each tells a different splitting story. You don't sum up over all channels. The problem comes when the two outgoing strings are identical. Then, you can't even distinguish between the s- and t-channels.
The moral of the story is, there is no canonical description of string interactions.
How to deal with crossing duality and modular invariance in string field theory?
|
Don williams uses his small motorboat
: Don Williams uses his small motorboat to go 3 miles upstream to his favorite fishing spot. Against the current, the trip takes 1/2
|
|
Poisson process with intensity
: At the center of espionage in Kznatropsk one is thinking of a new method for sending Morse telegrams. Instead of using the traditional method, that is, to send letters in groups of 5 according to a Poisson process with intensity 1, one might send ..
|
|
What is the probability
: In your math class there are 17 boys and 23 girls. 10 of the boys and 10 of the girls are freshmen. If you randomly choose a student in your class, what is the probability
|
|
Fredrik machine produces the first bubble
: Fredrik and Ulrich both received soap bubble machines for Christmas. The machines emit bubbles according to independent Poisson processes with intensities 3 and 2 (bubbles per minute), respectively. Suppose they turn them on at the same time.
|
|
How to deal with crossing duality and modular invariance
: The moral of the story is, there is no canonical description of string interactions. How to deal with crossing duality and modular invariance in string field theory?
|
|
Find out distributed random variables
: Suppose that X1, X2, . . . are independent, identically Linnik(α)-distributed random variables, that N ∈ Fs(p), and that N and X1, X2, . . . are independent. Show that p1/α(X1 + X2 + · · · + XN ) is, again, Linnik(α)- distributed.
|
|
What index of refraction does the cladding need
: Suppose you wanted the largest angle at which total internal reflection occurred to be θ'c = 5 degrees. What index of refraction does the cladding need if the core is unchanged?
|
|
Explain in words whether this additional force works
: Draw a second IS/LM curve that depicts what would occur in the short-run, if in addition to the shock in part A, agents also tend to demand more money the larger the government budget deficit. Explain in words whether this additional force works to a..
|
|
Determine what type of lease this would be for the lessee
: The lease is noncancelable with no renewal option. The lease term is 10 years (the same as the estimated economic life).
|