Related papers: Fermionic Fock Spaces and Quantum States for Causa…

We provide a Hilbert space approach to quantum mechanics where space and time are treated on an equal footing. Our approach replaces the standard dependence on an external classical time parameter with a spacetime-symmetric algebraic…

We construct the causal fermion system for globally hyperbolic spacetimes starting in the framework of algebraic quantum field theory. The fermionic projector is identified with the one-particle density operator of a quasi-free Hadamard…

Zombie States are a recently introduced formalism to describe coupled coherent Fermionic states which address the Fermionic sign problem in a computationally tractable manner. Previously it has been shown that Zombie States with fractional…

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…

A relativistic statistical field theory is constructed for a fluctuating complex-valued scalar field on a discretized Minkowski lattice. A Hilbert space of observables is then constructed from functionals of the fluctuating complex-valued…

As toy models for space-time on the Planck scale, we consider examples of fermion systems in discrete space-time which are composed of one or two particles defined on two up to nine space-time points. We study the self-organization of the…

We show that and specify how space-time symmetries give rise to corresponding symmetries of the fermionic signature operator and generalized fermionic projector states.

We formulate a general multi-mode Gaussian operator basis for fermions, to enable a positive phase-space representation of correlated Fermi states. The Gaussian basis extends existing bosonic phase-space methods to Fermi systems and thus…

This work deals with the behavior of fermions in the background of kinklike structures in the two-dimensional spacetime. The kinklike structures appear from bosonic scalar field models that engender distinct profiles and interact with the…

Symmetric Hilbert spaces such as the bosonic and the fermionic Fock spaces over some `one particle space' $\K$ are formed by certain symmetrization procedures performed on the full Fock space. We investigate alternative ways of…

A simplified Walecka-type model is investigated in a cosmological scenario. The model includes fermionic, scalar and vector fields as sources. It is shown that their interactions, taking place in a Robertson-Walker metric, could be…

We consider the time evolution of systems in which a spatially homogeneous scalar field is coupled to fermions. The quantum back-reaction is taken into account in one-loop approximation. We set up the basic equations and their…

Based on a mechanism originally suggested for causal fermion systems, the present paper paves the way for a rigorous treatment of baryogenesis in the language of differential geometry and global analysis. Moreover, a formula for the rate of…

We discuss the origin of causal set structure and the emergence of classical space and time in the universe. Given that the universe is a closed self-referential quantum automaton with a quantum register consisting of a vast number of…

Causal set theory provides a model of discrete spacetime in which spacetime events are represented by elements of a causal set---a locally finite, partially ordered set in which the partial order represents the causal relationships between…

We revisit the quantum oscillator model of the electromagnetic field and conclude that, while the nonlocal positive and negative frequency ladder operators generate a photon Fock basis, the Hermitian field operators obtained by second…

We present a new variational method for investigating the ground state and out of equilibrium dynamics of quantum many-body bosonic and fermionic systems. Our approach is based on constructing variational wavefunctions which extend Gaussian…

We study several issues related to the different choices of time available for the classical and quantum treatment of linearly polarized cylindrical gravitational waves. We pay especial attention to the time evolution of creation and…

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…

Application of the so-called refined algebraic quantization scheme for constrained systems to the relativistic particle provides an inner product that defines a unique Fock representation for a scalar field in curved space-time. The…