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We give an introduction to string theory with emphasis on its relation to two-dimensional conformal field theories.
We start by reviewing the classical theory of relativistic particles, before generalising it to relativistic strings based on the Nambu-Goto and Polyakov actions. After reviewing the quantisation of particles and fields, we outline the covariant approach to the quantisation of relativistic strings, and its relation to two-dimensional conformal field theory. We develop the basic elements of two-dimensional conformal field theory, and illustrate them using the special case of the theory of free bosons, corresponding to a string propagating on a flat spacetime. Based on this we present the quantisation of strings in the conformal gauge and in the lightcone gauge. After reviewing the relevant facts and techniques from group and representation theory we provide the space-time interpretation of the physical string states of quantised open and closed strings. We end with an outlook on how to define string scattering amplitudes, effective field theory and the construction of models for particle physics and cosmology by dimensional reduction.
Action principles for relativistic particles.
Action principles for relativistic strings. Nambu-Goto and Polyakov action. Conformal gauge and conformal invariance. Light cone gauge.
Quantisation of particles and strings. Outline of covariant quantisation of strings
Conformal invariance in two dimensions. Witt and Virasoro algebra. Two-dimensional conformal field theories.
Conformal field theory of free bosons and its relation to strings.
Quantisation of strings using conformal field theory of free bosons. Space-time interpretation of states. Momentum and angular momentum. Null states and gauge symmetries.
Analysis of physical states. Examples of physical states: Tachyon, photon, antisymmetric tensor, graviton, dilaton. Elements of the representation theory of the Poincare group.
Outlook: interactions, effective field theory and dimensional reduction..
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The assessment for this course will be released on Monday 11th January 2027 at 00:00 and is due in before Friday 22nd January 2027 at 11:00.
Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period). You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period). If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.
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