Related papers: Magic Fermions: Carroll and Flat Bands
Carroll symmetry is a very powerful characteristic of generic null surfaces, as it replaces the usual Poincar\'e algebra with a vanishing speed of light version thereof. These symmetries have found universal applications in the physics of…
We investigate fermions on Carrollian manifolds. We complement previous intrinsic analysis by deriving Carrollian fermion actions from a relativistic Dirac theory via a systematic expansion in the speed of light ($c$). We then study…
Using carefully chosen projections, we consider different Carroll limits of relativistic Dirac fermions in any spacetime dimensions. These limits define Carroll fermions of two types: electric and magnetic. The latter type transforms as a…
We show how Carrollian symmetries become important in the construction of one-dimensional fermionic systems with all flat-band spectra from first principles. The key ingredient of this construction is the identification of Compact Localised…
A natural approach for constructing a concrete example of flat space holography is to take the flat space limit of a well-understood example of AdS/CFT, such as the one relating M-theory in AdS$_4$ times an orbifolded 7-sphere to a certain…
We derive Carrollian fermionic actions using the null reduction method from Bargmann spacetimes. In the Lorentzian light-cone formulation, the Dirac spinor naturally decomposes into dynamical and constrained degrees of freedom $-$ the…
The Clifford algebra of the endomorphisms of the exterior algebra of a countably dimensional vector space induces natural bosonic shadows, i.e. families of linear maps between the cohomologies of complex grassmannians. The main result of…
Both algebras, Clifford and Grassmann, offer "basis vectors" for describing the internal degrees of freedom of fermions. The oddness of the "basis vectors", transferred to the creation operators, which are tensor products of the finite…
The necessary appearance of Clifford algebras in the quantum description of fermions has prompted us to re-examine the fundamental role played by the quaternion Clifford algebra, C(0,2). This algebra is essentially the geometric algebra…
The exploration of scalar field theories that exhibit Carroll and Galilei symmetries has attracted a lot of attention. In this paper, we generalize these studies to fermionic field theories and construct consistent electric and magnetic…
We study briefly some properties of real Clifford algebras and identify them as matrix algebras. We then show that the representation space on which Clifford algebras act are spinors and we study in details matrix representations. The…
Is there more to Dirac's gamma matrices than meets the eye? It turns out that gamma zero can be factorized into a product of three operators. This revelation facilitates the expansion of Dirac's space-time algebra to Clifford algebra…
This report reviews key developments in Carrollian physics with an emphasis on their role in the emerging framework of holography in asymptotically flat spacetimes. We begin by introducing the Carrollian limit, understood as the…
Magnetic Carrollian theories provide a natural setting for field theories with nontrivial spatial structure in the Carroll limit and are therefore natural candidates for flat-space holographic duals. Embedding such boundary theories into a…
Starting from considerations of Bosons at the real life Compton scale we go on to a description of Fermions, specifically the Dirac equation in terms of an underlying noncommutative geometry described by the Dirac $\gamma$ matrices and…
Carrollian physics provides the natural framework for describing null hypersurfaces. This review explores the geometry of Carrollian manifolds -- spaces endowed with a degenerate metric. We begin with an algebraic overview of the Carroll…
The Carroll group arises in the vanishing speed of light limit of the Poincar\'{e} group and was initially discarded as just a mathematical curiosity. However, recent developments have proved otherwise. Carroll and conformal Carroll…
In this article, we consider some Carrollian dynamical systems as effective models on null hypersurfaces in a Lorentzian spacetime. We show that we can realize Carroll models from more usual ``relativistic'' theories. In particular, we show…
This contribution presents properties of the second quantized not only fermion fields but also boson fields, if the second quantization of both kinds of fields origins in the description of the internal space of fields with the ''basis…
We use Dirac matrix representations of the Clifford algebra to build fracton models on the lattice and their effective Chern-Simons-like theory. As an example we build lattice fractons in odd $D$ spatial dimensions and their $(D+1)$…