Energy of a String: Understanding the Various Forms of Energy in String Theory

[Legend-of-Nub]

Hi I'm new to Physics Forum but not Physics. I am well versed with the theories of Quantum Mechanics and String Theory. And I have a question, exactly what "type" of energy do strings posses? In other words when we say a string is a "loop" of energy what kind of energy are we referring to; Kinetic, electromagnetic, electric, nuclear or something else? And is there any "generic" state of energy. I mean can we have energy in no specific form just as energy itself or "pure energy"? Thanks for all your help.


Legend-of-Nub.

 

[humanino]

It's kinetic energy of a string.

 

[Legend-of-Nub]

It's kinetic energy of a string.

But if it's the "kinetic energy of a string" you're implying that the string itself is not made of energy but rather it is made of something else that possesses kinetic energy or a form of energy. How is that so? Thanks for all your help.

 

[humanino]

No, I'm just saying that this is the formal lagrangian of a string with purely kinematical energy. I don't need to assume that the string is made of anything, I don't know what it is made of, and I think stating "it is made of pure energy" is a useless, void, affirmation (it is neither wrong nor true, and most importantly it does not help me whatsoever). What is remarkable, is that you get interactions from a purely free lagrangian. This is quite different from gauge fields in the standard model.

 

[arivero]

Let me to consider an spring moving freely in space. Do you claim that its free hamiltonian is "the kinetic energy of the spring"? It is, as a minimum, a bizarre name. But I agree that in any case the formal name is useless as a physics concept. And even more if you consider the relativistic aspects.

 

[robousy]

Well, in the simple example of the bosonic open string the Polyakov action reads

$$S_P = -\frac{1}{4 \pi \alpha'}\int_W d \tau d \sigma \sqrt{ \gamma}\gamma^{ab} \partial_a X^{\mu} \partial_b X_{\mu}$$

and the Lagrangian contains the standard kinetic term. I don't really think there is a good classical analogy of the kinetic term in an quantum theoretic action.

 

[Demystifier]

In a non-relativistic terminology, only the time-derivative (I am talking about the world-sheet time tau) of X is naturally interpreted as kinetic energy, while the derivative with respect to sigma is more naturally interpreted as a potential energy. Hence, the energy of the string is a sum of the kinetic and the potential energy.

 

[humanino]

In a non-relativistic terminology, only the time-derivative (I am talking about the world-sheet time tau) of X is naturally interpreted as kinetic energy, while the derivative with respect to sigma is more naturally interpreted as a potential energy. Hence, the energy of the string is a sum of the kinetic and the potential energy.

I never saw it that way, and counting the number of derivative in time (two) does not match here (only one).

In relativistic physics, the kinetic action is given by the length of the worldline, here the kinetic action is given by the surface (generalized length) of the worldsheet.

But again, to me all that matters is the difference between free and interacting theory of point particle vs string. It was especially relevant in the early days of string theory to explain hadronic duality and the double counting of s-channel and t-channel diagrams.

 

[Toastus]

So, really nobody knows exactly what a string is made of, right? What if it isn't actually made of anything, but is a vibrating point of space-time?