TEBAC HP–E2N: E2 Determinant Package on GL(1) and Canonical Normalization

Key Points

• The aim is to develop a canonical heat trace and its corresponding zeta determinant for the GL(1) operator.
• Constructed a canonical centered heat trace for the $GL(1)$ operator.
• Applied Mellin/zeta regularization for the heat trace.
• Developed a scheme-independence theorem for admissible cutoff schemes.
• Formulated a quotient to eliminate constant ambiguity in normalization limits.
• Derived a canonical zeta determinant from the constructed heat trace.
• Established explicit entire correction factors for scheme-independence.
• Demonstrated the effectiveness of the canonical normalization limits.