Maths HEP Lunchtime Seminars: Finite-temperature form factors in the free Majorana theory
14 October 2005 00:00 in CM221
"I will present a new technique to obtain the large distance expansion of correlation functions in the free massive Majorana theory at finite temperature, alias the Ising field theory at zero magnetic field on a cylinder. This technique mimics the spectral decomposition, or form factor expansion, of zero-temperature correlation functions. In particular, I will introduce the concept of ``finite-temperature form factors''. I will show that the finite-temperature form factors of twist fields (that is, order and disorder fields and their descendants) satisfy a Riemann-Hilbert problem, and I will solve it for the order and disorder fields. I will show that this leads to a Fredholm determinant representation for finite-temperature correlation functions. I will also show that finite-temperature form factors of free fields are given by a mixing of their zero-temperature form factors, and I will describe explicitly the mixing matrix. This mixing matrix, in some sense, generalizes to this massive model the operator performing a transformation to the cylinder in conformal field theory. Finally, I will show that an appropriate analytical continuation of the finite-temperature form factors in rapidity space reproduces form factors in the quantization on the circle. Hence, my technique provides a new, analytical way of evaluating the form factors in the quantization on the circle. I will discuss briefly the possible extension to interacting integrable models and the difficulties to overcome. "