Techniques are presented for calculating directly the scalar functional determinant on the Euclidean d-ball. General formulae are given for Dirichlet and Robin boundary conditions when d is even and the field is massless. The method involves a large mass asymptotic limit which is carried out in detail for d = 2 as an exercise, incidentally producing some specific summations and identities. Extensive use is made of the Watson - Kober summation formula. The calculation of the finite-mass determinant is also briefly considered.
Classical and Quantum Gravity
- Pub Date:
- April 1996
- High Energy Physics - Theory;
- General Relativity and Quantum Cosmology
- 36p,JyTex, misprints corrected and a section on the massive case added