Quantum Field Theory Applications of Heun Type Functions

Abstract

After a brief introduction to Heun type functions we note that the actual solutions of the eigenvalue equation emerging in the calculation of the one loop contribution to QCD from the Belavin-Polyakov-Schwarz-Tyupkin instanton and the similar calculation for a Dirac particle coupled to a scalar $C{P}^1$ model in two dimensions can be given in terms of confluent Heun equation in their original forms. These equations were previously modified to be solved by more elementary functions. We also show that polynomial solutions with discrete eigenvalues are impossible to find in the unmodified equations.

arXiv comment6 pages. Matches the published version

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Cited by in corpus (9)

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• Non-commutativity and non-inertial effects on the Dirac oscillator in a cosmic string space-time
• Elementary Integral Series for Heun Functions. With an Application to Black-Hole Perturbation Theory
• Symbolic and Numerical Analysis in General Relativity with Open Source Computer Algebra Systems
• Fermion scattering on topological solitons in the ${\mathbb{CP}}^{N-1}$ model
• Three-Dimensional Eigenvalues of Harmonic Oscillator- and Coulomb-type Potentials from One-Dimensional Generalized Morse Potential: Perturbative Analyse based on Generalized Laguerre Polynomials
• Computations of general Heun functions from their integral series representations