Ramsey scheme applied to string theoretical processes

Abstract

In this paper, we analyze the evolution of physical quantities due to the interaction of strings with background fields. We will obtain the characteristic function for such a string theoretical process. This will be done by generalize the Ramsey scheme to world-sheet, and using it obtain the information about the evolution of quantity in a string theoretical process, without making two point measurements. We will also use the characteristic function to obtain the average of the difference between the initial and final values such a quantity. Finally, using the characteristic function, we calculate fisher information for the difference of such a quantity.

A Novel Application of Quantum Speed Limit to String Theory

“…Now θ is defined as the unobservable variable probed by this operator [38,39]. Since θ acts as the time for the systems, and M 2 plays the same role as the Hamiltonian [38,39], we can write the θ evolution of a world-sheet mode |ϕ i m 0 ⟩ from θ = 0 to θ as…”

“…According to this equation, θ parameterizes the evolution of a string state to another orthogonal string state. This is expected as the unobservable parameter θ is viewed as time in string theory [38,39]. However, there is a bound on θ, and it is not possible for orthogonal string states to evolve into each other faster than this bound.…”

“…However, such quantities, which are not associated with an observable, can be investigated using Fisher information concept [32][33][34][35][36][37]. It has been recently argued that time in string theory can be defined as an unobservable variable and can only be indirectly probed M 2 [38,39]. The time probed by Hamiltonian does not give any information about the casual ordering of events on the world-sheet due to time reparametrization invariance [40].…”

“…In fact, due to the time reparametrization invariance, the world-sheet Hamiltonian does not contain any information, and cannot be used to study the dynamics of the system [40]. However, the M 2 does contain Fisher information and can be used to study the dynamics of the system [38,39]. We would like to clarify that by time we mean an ordering parameter, which can be used to define the sequences in which events occur.…”

“…This is usually done using a part of the Hamiltonian, to probe change and hence obtain a time variable. The unobservable variable corresponding to this part of Hamiltonian on the world-sheet is θ, and hence it can directly be related to time [38,39]. Here, we will use θ to discuss the evolution of world-sheet string states, as it can be used to define evolution on world-sheet coordinates.…”