We define size and shape in terms of observables, i.e. scattering amplitudes. Excited strings can be measured by scattering ground-state string probes off them. We pick an example where, classically, the ends of the string trace out a circle. Our calculation shows that the radius of the circle is proportional to the mass of the string, M, in agreement with classical expectations. However, on distance scales less than √In M, quantum fluctuations are important and a classical space-time picture becomes questionable.

We extend the work of Mitchell et al., on the decay of highly excited open strings, to closed strings. We use the optical theorem, plus an expansion in level number of the final states, which allows the subtraction of tachyonic processes. Computer results in 26 dimensions, for initial states of level number N up to 70, suggest an asymptotic form of N−12 for the total decay rate. We also consider the truncated theory in d = 4, for comparison with cosmic string calculations of gravity wave emission, and find that massless particle processes dominate in this case. We calculate these processes analytically, leading to an asymptotic decay rate proportional to N−12.

The asymptotic total decay rates for arbitrarily massive states on the leading Regge trajectory for open bosonic strings and SO(32) superstrings are calculated. In the bosonic case, the result corresponds to a local splitting probability per unit length only in d = 26: for fewer than 24 transverse directions the rate is smaller. This provides a new interpretation of the critical dimension. For superstrings there is a splitting probability per unit length, independent of compactification. Compactifying rather than truncating the bosonic string leads to a similar result.

We calculate the decay rates of leading Regge trajectory states for very high level number in open bosonic string theories, ignoring tachyon final states. The optical theorem simplifies the analysis while enabling identification of the different mass level decay channels. Our main result is that (in four dimensions) the greatest single channel is the emission of a single photon and a state of the next mass level down. A simple asymptotic formula for arbitrarily high level number is given for this process. We also calculate the total decay rate exactly up to N = 100. It shows little variation over this range but appears to decrease for larger N. We check our formalism in examples and calculate the decay rate of the first excited level for open superstring theories. The calculation may also have implication for high spin meson resonances.s

To clarify the status of proposed causality arguments limiting the annihilation rate of monopoles, we present a three-dimensional model for the formation of monopoles connected by strings. The length distribution of the strings has been found using a Monte carlo simulation of the phase transition. The result is that long strings connecting monopoles are exponentially suppressed in agreement with the theoretical predictions of Mitchell and Turok [1]. The implications of our results for the monopole problem are discussed.

The statistical properties of a network of cosmic strings in flat space time are analysed using the microcanonical ensemble. This technique, based on the quantised bosonic string shows that the system is characterised by two distinct phases, corresponding to string densities above and below a “critical” density defined in terms of the string tension. The importance of these results for the cosmic string theory of galaxy formation is then discussed. Finally, it is pointed out why the canonical ensemble is not a good description of strings at high densities.

An analytic approach to the phase space for a network of cosmic strings is presented, based on earlier work of Frautschi and Carlitz. It correctly predicts the main features of the network at formation, and is in good agreement with the picture emerging from string simulations. Our results also have important implications for superstrings or heterotic strings in the early Universe.