What question did this study set out to answer?

To establish a cohesive analytic and geometric framework for principal invariants of Dirac-type operators.

March 15, 2026Open Access

Dirac Spectral Calculus: Heat Kernels, Spectral Actions, Zeta Determinants, Index Theory, Determinant Lines, and Quillen Geometry

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This framework unifies analyses of Dirac-type operators, revealing connections to index theory and spectral actions.

To establish a cohesive analytic and geometric framework for principal invariants of Dirac-type operators.
Derived heat kernel expansions and spectral actions
Analyzed zeta functions and zeta-regularized determinants
Utilized the McKean–Singer index formula and determinant line constructions
Explored the Quillen metric and its implications
Clarified relationships between trace invariants and spectral components
Unified various spectral elements in a coherent framework

Andrew Kim (2026) studied this question.

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March 15, 2026Open Access

View Full Paper

Ask AI

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Authors

This framework unifies analyses of Dirac-type operators, revealing connections to index theory and spectral actions.

To establish a cohesive analytic and geometric framework for principal invariants of Dirac-type operators.
Derived heat kernel expansions and spectral actions
Analyzed zeta functions and zeta-regularized determinants
Utilized the McKean–Singer index formula and determinant line constructions
Explored the Quillen metric and its implications
Clarified relationships between trace invariants and spectral components
Unified various spectral elements in a coherent framework

Andrew Kim (2026) studied this question.

View Full Paper

Ask AI

Bookmark