Nature's Laws


B. E. Baaquie and Marakani Srikant, Department of Physics, National University of Singapore

A classical string is a one-dimensional extended object existing in four-dimensional space-time. A typical example of a classical string is a piece of thread.

A classical string is specified by the string tension T, and can exist in a space-time of arbitrary dimension. Quantum strings can only exist in certain critical space-time dimensions such as 26 and 10. Quantum bosonic strings can be made supersymmetric yielding the superstring.

Fundamental Postulate

All of physical reality is made out of different states of the superstring. Roughly speaking, each vibrational mode of the string can be thought of as a point particle. Hence, one superstring gives rise to infinitely many local fermion and boson fields. All of the observed bosons and fermions can be cosidered as a vibrational mode of the fundamental superstring. It must be noted that the string is both constituent and interaction. Superstrings can be either open or closed.

World Sheets
Open and Closed Strings

Quantum strings inherently contain a quantum theory of gravity! For this purpose, the size of the strings must be of Planck length scale.

Consider a particle at the point x0. Conventionally, the properties of the point-particle are then specified by a field A(x0).

However, for a string, we have to determine infinitely many points (along the whole string). This is fundamentally the reason why a single string in effect yields infinitely may point-like particles.

How long is a superstring?

Length Scales

According to the big bang theory, we have the following scenario : Universe starts from a point -> Strings -> Inflation -> Gravity differentiates -> Further differentiation. Since strings occur before any differentiation, they must of Planck scale (10-35m), the distance at which all the forces are equally strong.

Unification Scale
Note : Distances are inversely related to energy by the uncertainty principle (the smaller the distance, the higher the energy scale).

* Quantized Strings

* D-Branes

* Superstring Particle Spectrum

* String Interaction : Topology vs Geometry

Last updated: 03 March, 2000

NUS Core Curriculum Nature's Laws Physics String Theory