Related papers: Free Fermions on causal sets
We develop relativistic causality theory in the setting of point-free topology by introducing a notion of causal coverage in ordered locales, generalising their canonical coverage relation to incorporate causal structure. This improves…
Understanding the causal influences that hold among parts of a system is critical both to explaining that system's natural behaviour and to controlling it through targeted interventions. In a quantum world, understanding causal relations is…
A central question for causal inference is to decide whether a set of correlations fit a given causal structure. In general, this decision problem is computationally infeasible and hence several approaches have emerged that look for…
The infrared effective theory of adjoint QCD with one Dirac flavour is still under debate. The theory could be confining, conformal, or with a massless fermion in the infrared. The study of chiral symmetry seems to be important to answer…
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…
It was known that a free, nonrelativistic particle in a superposition of positive momenta can, in certain cases, bear a negative probability current --- hence termed quantum backflow. Here, it is shown that more variations can be brought…
There are numerous indications that a discrete substratum underlies continuum spacetime. Any fundamentally discrete approach to quantum gravity must provide some prescription for how continuum properties emerge from the underlying…
After sketching a context in which to seek observable signals of spatio-temporal discreteness, I briefly review the status of the causal set program for quantum gravity, concluding with a simple model for the field produced by a moving…
In the theory of causal fermion systems, the physical equations are obtained as the Euler-Lagrange equations of a causal variational principle. Studying families of critical measures of causal variational principles, a class of conserved…
In the causal set approach, spacetime is a continuous approximation of a faithful embedded causal set. But the faithful embedded causal set describes the empty spacetime and cannot describe matter. Only faithful embedding of coarse grained…
One route towards understanding both fractional charges and chiral anomalies delves into Dirac's negative energy sea. Usually we think of Dirac's negative energy sea as an unphysical construct, invented to render quantum field theory…
We show that a class of fermion theory formulated on a compact, curved manifold will generate a condensate whose magnitude is determined only by the volume and Euler characteristic of the space. The construction requires that the fermions…
I discretize axion string configuration coupled to a Dirac fermion, which in the continuum binds a massless chiral fermion in its core when the winding is one. I show that such a configuration can host one or more chiral fermions when…
We describe the occurrence and physical role of zero-energy modes in the Dirac equation with a topologically non-trivial background.
We discuss the generalization of the Dirac equations and spinors in momentum space to free unstable spin-$1/2$ fermions taking into account the fundamental requirement of Lorentz covariance. We derive the generalized adjoint Dirac equations…
The notion of causal effect is fundamental across many scientific disciplines. Traditionally, quantitative researchers have studied causal effects at the level of variables; for example, how a certain drug dose (W) causally affects a…
The mean arrival time of free particles is computed using the quantum probability current. This is uniquely determined in the non-relativistic limit of Dirac equation, although the Schroedinger probability current has an inherent…
We extend the recently proposed Time-Dependent Multi-Determinant approach (ref.[1]) to the description of fermionic propagators. The method hinges on equations of motions obtained using variational principles of Dirac type. In particular we…
There is growing interest in the study of causal methods in the Earth sciences. However, most applications have focused on causal discovery, i.e. inferring the causal relationships and causal structure from data. This paper instead examines…
We develop a new formalism for constructing probabilities associated to the causal ordering of events in quantum theory, where by an event we mean the emergence of a measurement record on a detector. We start with constructing probabilities…