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Galilean fermions: Classical and quantum aspects
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We study the classical and quantum "properties" of Galilean fermions in 3+1 dimensions. We have taken the case of massless Galilean fermions minimally coupled to the scalar field. At the classical level, the Lagrangian is obtained by null reducing the relativistic theory in one higher dimension. The resulting theory is found to be invariant under infinite Galilean conformal symmetries. Using Noether's procedure, we construct the corresponding infinite conserved charges. Path integral techniques are then employed to probe the quantum "properties" of the theory. The theory is found to be renormalizable. A novel feature of the theory is the emergence of mass scale at the first order of quantum correction. The conformal symmetry of the theory breaks at the quantum level. We confirm this by constructing the beta function of the theory.
Forward citations
Cited by 2 Pith papers
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Interacting Galilean and Finite-Energy Carroll Fermions
A c-dependent similarity transformation generates new Galilean and Carrollian fermion actions, including a Carrollian model with non-removable finite energy and a Galilean model with an accidental fermionic gauge symmetry.
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Quantization of Carrollian fermions
A first interacting 4D Carrollian Yukawa theory is constructed, showing ultralocal fermion-scalar interactions and one-loop beta functions with mostly Gaussian fixed points.
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