TL;DR
This paper explores the concept of anomalies in quantum field theories, framing them as projective phenomena and linking them to invertible field theories, culminating in a formula for free spinor field anomalies.
Contribution
It introduces a novel perspective by connecting anomalies to projective and categorified invertible theories, providing a general formula for free spinor field anomalies.
Findings
Anomalies are manifestations of projectivity in quantum theories.
Anomalies can be described as categorified invertible field theories.
A general formula for the anomaly of a free spinor field is derived.
Abstract
The anomaly of a quantum field theory is an expression of its projective nature. This starting point quickly leads to its manifestation as a special kind of field theory: a once-categorified invertible theory. We arrive at this statement through a general discussion of projectivity and a discussion of projectivity in quantum mechanics. We conclude with a general formula for the anomaly of a free spinor field.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Black Holes and Theoretical Physics · Quantum Mechanics and Applications