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Quantization of Carrollian fermions
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Quantization of Carrollian fermions
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We provide the first example of interacting quantized Carrollian Dirac fermions and investigate their discrete symmetries, including charge conjugation (C), parity (P), and time reversal (T) transformations. As a toy model, we couple these fermions to a Carrollian scalar field using Carrollian Yukawa theory and compute the tree-level diagram, revealing an ultralocal interaction between the Carrollian fermions and the scalar field. This interaction, widely known as a Dirac delta interaction with time-dependent factor, frequently appears in quantum physics. We then address the renormalization of the theory by employing the Wilsonian procedure at one-loop order. Furthermore, we analyze the fixed points and stability properties of Carrollian Yukawa theory, comparing them with their relativistic counterparts. Beyond the specific Yukawa model studied here, we expect that our framework will have broader applications in Carrollian physics, particularly in understanding ultralocal interactions and their role in condensed matter systems, where similar phenomena arise in strongly correlated and non-relativistic regimes.
Forward citations
Cited by 7 Pith papers
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Carroll fermions of arbitrary spin
Free massless fermions of arbitrary spin admit two inequivalent Carrollian (c→0) limits, electric and magnetic, derived from the Fang–Fronsdal actions, with the magnetic theory reducible to the projected relativistic ...
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Post-Carroll Algebra, Conformal Extensions, and Field Theories
Introduces the post-Carroll algebra and its conformal extensions, including the Carroll-Schrödinger algebra, and computes two-point functions in post-Carrollian CFTs.
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Carroll fermions from null reduction: A case of good and bad fermions
Carrollian fermionic actions for electric and magnetic sectors are derived from a single Bargmann Dirac action by null reduction, with good and bad fermions as dynamical and constrained modes valid in any dimension.
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Carroll fermions, expansions and the lightcone
Carrollian fermion actions are obtained from relativistic Dirac theory via c-expansion and connected to light-cone dynamics through co-dimension one Carroll subalgebras in the Poincaré algebra.
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Carroll hydrodynamics with spin
Carroll hydrodynamics with spin is obtained as the c→0 limit of relativistic hydrodynamics with spin, extending the description of boost-invariant flows.
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Post-Carroll Algebra, Conformal Extensions, and Field Theories
Defines post-Carroll algebra allowing central charges in higher dimensions, constructs its conformal extension and the Carroll-Schrödinger algebra matching prior theory, and derives two-point functions in post-Carroll...
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The Carrollian Kaleidoscope
A review summarizing Carrollian symmetries, CCFT constructions, and applications in AFS holography, Carroll hydrodynamics, and condensed matter phenomena such as fractons and flat bands.
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