Finite-temperature form factors in the free Majorana theory

• Main Author: Doyon, Benjamin
• Format: Journal Article
• Language: English
• Published: 14.06.2005
• Subjects: Physics - High Energy Physics - Theory; Physics - Strongly Correlated Electrons
• DOI: 10.48550/arxiv.hep-th/0506105

J.Stat.Mech.0511:P11006,2005 We study 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. We develop a method that mimics the spectral decomposition, or form factor expansion, of zero-temperature correlation functions, introducing the concept of "finite-temperature form factors". Our techniques are different from those of previous attempts in this subject. We show that an appropriate analytical continuation of finite-temperature form factors gives form factors in the quantization scheme on the circle. We show that finite-temperature form factor expansions are able to reproduce expansions in form factors on the circle. We calculate finite-temperature form factors of non-interacting fields (fields that are local with respect to the fundamental fermion field). We observe that they are given by a mixing of their zero-temperature form factors and of those of other fields of lower scaling dimension. We then calculate finite-temperature form factors of order and disorder fields. For this purpose, we derive the Riemann-Hilbert problem that completely specifies the set of finite-temperature form factors of general twist fields (order and disorder fields and their descendants). This Riemann-Hilbert problem is different from the zero-temperature one, and so are its solutions. Our results agree with the known form factors on the circle of order and disorder fields.