What is the meaning of this generic equation in String Theory?

[ZeroZero2]

what is this equation??

I remember an article on String Theory on either Popular Science or Scientific America, and it had this equation:

I no longer have the article and would like to know what this equation means.

Thanks!

 

[ZeroZero2]

no one knows?


not a history of it, just what it represents...
like how E=mc$$^{2}$$ means energy is equal to mass multiplied by the speed of light squared.

 

[ansgar]

It looks like a lagrangian miss-spelled...

g<psi^dagger | psi >^2

it should read

 

[ZeroZero2]

It looks like a lagrangian miss-spelled...

g<psi^dagger | psi >^2

it should read

I don't think so...

I copied it directly from the magazine (I have the actual clipping of the equation).

 

[ZeroZero2]

Found it!
It's Michio Kaku's equation and it describes strings in 10 dimensions

It was on Discover magazine

http://discovermagazine.com/2005/aug/cover/article_view?b_start:int=3"

 

[ansgar]

sorry but that equation is crap

 

[ZeroZero2]

sorry but that equation is crap

haha.. troll

 

[ansgar]

imean they are mixing bra-ket and wavefunction notation, you don't usally write <psi^dagger| since <psi| is the dual correspondence to |psi> ..

 

[diazona]

imean they are mixing bra-ket and wavefunction notation, you don't usally write <psi^dagger| since <psi| is the dual correspondence to |psi> ..

Actually that's right... maybe the magazine mistranscribed it or something. (Unless this is some sort of weird notation unique to string theory, but I have my doubts... I've studied some string theory and never come across that sort of notation)

 

[bradley613]

That equation is using a lot off different equations and comparing them. The derivative of i with respect to a certain time interval and the it, obviously, has the wave function Psi which is the derivative of uppercase gamma and I am pretty sure the g is referring to gravity or some kind of force acting on it. H could be planks constant or like an angular momentum symbol. The i may be an imaginary number which could change the whole format of the equation. As far as L it could be length or momentum or something. The guy who discovered that equation must have done something wrong otherwise we would have heard of it before and there would be no doubts the string theory exists. But there are multiple string theories and not just one so it could pretain to a certain one we haven't heard of before. It could also be saying that when the strings collide and when that happens it creates a force, tourque, which is tau in that equation and it creates angular momentum and they are using it to find the length or shape of the string. Torque is frsin theta so idk there is many ways one could think of it. I really don't know the one Kaku is referring to though.

 

[Ben Niehoff]

The equation has some typos and mixes different kinds of notation...I would write it

$$L = \psi^\dagger (i\partial_t - H) \psi + g(\psi^\dagger \psi)^2$$

Unfortunately, it's hard to guess what Kaku could possibly mean by this, because this is actually something quite generic: It is just the Lagrangian for a quantum field $\psi$ with a quartic self-interaction. H is the Hamiltonian, and g is a coupling constant.

It is completely unspecified what sort of background spacetime the field Psi lives in, or what representations of what groups Psi might carry. This expression could really mean almost anything.

Note: Practically everything in bradley613's post above is complete nonsense.