Related papers: Dirac and Weyl Fermions -- the Only Causal Systems
We prove the uniqueness theorem for the solutions to the restricted Weyl commutation relations braiding unitary groups and semi-groups of contractions that are close to unitaries. We also discuss related mathematical problems of continuous…
We consider the minimal coupling of a thin film Dirac semimetal Hamiltonian to a generic spin-texture. A simple unitary transformation gauges away the spatial dependence in the exchange term, leading to the generation of effective…
The causal perturbation expansion defines the Dirac sea in the presence of a time-dependent external field. It yields an operator whose image generalizes the vacuum solutions of negative energy and thus gives a canonical splitting of the…
Materials hosting tilted Dirac/Weyl fermions provide an emergent spacetime structure for the solid state physics. They admit a geometric description in terms of an effective spacetime metric. Using this metric that is rooted in the…
The intersections of topology, geometry and strong correlations offer many opportunities for exotic quantum phases to emerge in condensed matter systems. Weyl fermions, in particular, provide an ideal platform for exploring the dynamical…
Non-Hermiticity in Weyl Hamiltonian leads to the realization of Weyl exceptional rings and flat bands inside the Weyl exceptional rings. Recently, the platform of non-Hermitian physics is extended to many-body or disordered systems where…
Understanding Dirac-like Fermions has become an imperative in modern condensed matter sciences: all across its research frontier, from graphene to high T$_c$ superconductors to the topological insulators and beyond, various electronic…
Existing work on quantum causal structure assumes that one can perform arbitrary operations on the systems of interest. But this condition is often not met. Here, we extend the framework for quantum causal modelling to situations where a…
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…
In quantum field theory, we learn that fermions come in three varieties: Majorana, Weyl, and Dirac. Here we show that in solid state systems this classification is incomplete and find several additional types of crystal symmetry-protected…
The expression of causality depends on an underlying choice of chronology. Since a chronology is provided by any Lorentzian metric in relativistic theories, there are as many expressions of causality as there are non-conformally related…
Causal variational principles, which are the analytic core of the physical theory of causal fermion systems, are found to have an underlying Hamiltonian structure, giving a formulation of the dynamics in terms of physical fields in…
The weak localization (WL) contribution to the two-level correlation function is calculated for two-dimensional disordered conductors. Our analysis extends to the nondiffusive (ballistic) regime, where the elastic mean path is of order of…
We derive the spectra of surface states for massive Dirac Hamiltonians with either momentum or energy separation between the left- and right-handed Weyl nodes. Momentum separation between the Weyl nodes corresponds to the explicitly broken…
It is well-known that if one assumes quantum theory to hold locally, then processes with indefinite causal order and cyclic causal structures become feasible. Here, we study qualitative limitations on causal structures and correlations…
We construct a new model of a particle propagating in $4D$, ${\cal N}=1$ superspace that describes the dynamics of a continuous spin irreducible representation of the Poincar\'{e} supergroup. The model is characterized by two-component Weyl…
A new approach to quantum gravity is described which joins the loop representation formulation of the canonical theory to the causal set formulation of the path integral. The theory assigns quantum amplitudes to special classes of causal…
A temporally varying discretization often features in discrete gravitational systems and appears in lattice field theory models subject to a coarse graining or refining dynamics. To better understand such discretization changing dynamics in…
The Dirac equation, in the field of a traveling circularly polarized electromagnetic wave and a constant magnetic field, has singular solutions, corresponding the expansion of energy in vicinity of some singular point. These solutions…
Dirac's equation in the field of a circularly polarized electromagnetic wave and constant magnetic field has exact localized non-stationary solutions. The solutions corresponds relativistic fermions only. Among them singular solutions with…