String theory for undergraduates

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String theory is a mathematical model in physics. It is still under heavy construction. It is an extension of quantum field theory, which is also in many senses incomplete.

The basic theme in the work of a string theorist is:

  • pick a classical space (manifold, to be specific)
  • define an action for a classical string to move in the space
  • quantize your system
  • From here you may
    • study the phenomena in it and compare what you get to the real world
    • compare your system to other mathematical structures known or unknown

However, all these are often much easier said than done. Quantization is often a difficult problem. Another fundamental problem is that, if string theory is to be a fundamental physical theory, we would really want to start from a quantum definition and derive the classical analogue, which is opposite to what can be done at the moment. So we still don't know what string theory is (but see M-theory). Another problem is to construct a 4-dimensional model with all the particles and interactions we can observe in our accelerators. The candidate models are so numerous (the so-called "landscape") that it is almost impossible to pick out "the one" without additional insights.

However, since the standard model predicts the Higgs bosons and string theory requires supersymmetric particles on top of that, experiments may provide new clues to another breakthrough - or resignation.

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