Quantum consistency from topological symmetry: resolving the single Weyl fermion anomaly

Andrei Tudor Patrascu ()
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Andrei Tudor Patrascu: FAST Foundation

The European Physical Journal B: Condensed Matter and Complex Systems, 2025, vol. 98, issue 10, 1-12

Abstract: Abstract Quantum anomalies impose profound constraints on our fundamental descriptions of nature, traditionally forbidding the existence of isolated Weyl fermions due to gauge inconsistencies. Here, we introduce a novel quantisation method based on Becchi–Rouet–Stora–Tyutin (BRST) symmetry and cohomological field theory, explicitly demonstrating that a single Weyl fermion doublet under an SU(2) gauge symmetry can be consistently quantised without anomalies. This approach introduces auxiliary BRST-exact fields that shift the anomalous fermionic measure into a trivial cohomological class, explicitly removing the anomaly while leaving no residual physical degrees of freedom. By bridging topological field theory and quantum consistency, this method not only overturns long-standing theoretical constraints but also opens experimental pathways to detecting standalone Weyl fermions. Our results significantly broaden the landscape of quantum field theories and highlight a deep interplay between topology, anomalies, and quantum gauge invariance. Graphic abstract

Date: 2025
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DOI: 10.1140/epjb/s10051-025-01061-7

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