Related papers: Fermion Systems in Discrete Space-Time
The action of the discrete symmetries on the scalar mode functions of the de Sitter spacetime is studied. The invariance with respect to a combination of discrete symmetries is put forward as a criterion to select a certain vacuum out of a…
We investigate the phenomenon of disorder-free localisation in quantum systems with global permutation symmetry. We use permutation group theory to systematically construct permutation symmetric many-fermion Hamiltonians and interpret them…
This monograph introduces the basic concepts of the theory of causal fermion systems, a recent approach to the description of fundamental physics. The theory yields quantum mechanics, general relativity and quantum field theory as limiting…
Pinning and depinning of wave fronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators…
We study equilibrium statistical mechanics of Fermion lattice systems which require a different treatment compared with spin lattice systems due to the non-commutativity of local algebras for disjoint regions. Our major result is the…
A comparison between the two possible variational principles for the study of a free falling spinless particle in a space-time with torsion is noted. It is well known that the autoparallel trajectories can be obtained from a variational…
In this letter we briefly investigate the mathematical structure of space-time in the framework of discretization. It is shown that the discreteness of space-time may result in a new mechanical system which differ from the usual quantum…
This paper is dedicated to give a concise introduction to the theory of causal fermion systems. After putting the theory of causal fermion systems into the historical context, we recall fundamental physical preliminaries. Afterwards, we…
We consider a four-fermion theory as a simple model of dynamical symmetry breaking in flat space with non-trivial topology, motivated from recent studies in similar considerations in curved space. The phase structure is investigated, by…
Time reversal in quantum or classical systems described by an Hermitian Hamiltonian is a physically allowed process, which requires in principle inverting the sign of the Hamiltonian. Here we consider the problem of time reversal of a…
Pinning and depinning of wavefronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators…
A variational principle enabling one to compute individual Floquet states of a periodically time-dependent quantum system is formulated, and successfully tested against the benchmark system provided by the analytically solvable model of a…
We study the Dirac and the klein-Gordon oscillators in a noncommutative space. It is shown that the Klein-Gordon oscillator in a noncommutative space has a similar behaviour to the dynamics of a particle in a commutative space and in a…
The time-dependent variational principle for many-body trial states is used to discuss the relation between the approaches of different molecular dynamics models to describe indistinguishable fermions. Early attempts to include effects of…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
We show that space-time evolution of one-dimensional fermionic systems is described by nonlinear equations of soliton theory. We identify a space-time dependence of a matrix element of fermionic systems related to the {\it Orthogonality…
We present an approximate solution to the minimally coupled Einstein-Dirac equations. We interpret the solution as describing a massive fermion coexisting with its own gravitational field. The solution is axisymmetric but is time dependent.…
Causal systems describe the localizability of relativistic quantum systems complying with the principles of special relativity and elementary causality. At their classification we restrict ourselves to real mass and finite spinor systems.…
A carefully motivated symmetric variant of the Poisson bracket in ordinary (not Grassmann) phase space variables is shown to satisfy identities which are in algebraic correspondence with the anticommutation postulates for quantized Fermion…
By proposing a paradox between the impossibility of superluminal signal transfer and the normalization condition of wavefunctions, we predict that when a change happens to the conditions that determining the status of a quantum system, the…