Related papers: Quantum computational path summation for relativis…
The quantum mechanical motion of a relativistic particle in a non-continuous spacetime is investigated. The spacetime model is a dense, rationale subset of two-dimensional Minkowski spacetime. Solutions of the Dirac equation are calculated…
A method is presented which restricts the space of paths entering the path integral of quantum mechanics to subspaces of $C^\alpha$, by only allowing paths which possess at least $\alpha$ derivatives. The method introduces two external…
In this paper we discuss a causal network approach to describing relativistic quantum mechanics. Each vertex on the causal net represents a possible point event or particle observation. By constructing the simplest causal net based on…
A discrete-time Quantum Walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs admit a continuum limit, leading to familiar PDEs (e.g. the Dirac equation). In this paper, we study the…
Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These…
We argue that the Fermi-Hubbard Hamiltonian describing the physics of ultracold atoms on optical lattices in the presence of artificial non-Abelian gauge fields, is exactly equivalent to the gauge theory Hamiltonian describing Dirac…
The Dirac's formalism for constrained systems is applied to the analysis of time-dependent Hamiltonians in the extended phase space. We show that the Lewis invariant is a reparametrization invariant and we calculate the Feynman propagator…
The Dirac method is used to analyze the classical and quantum dynamics of a particle constrained on a circle. The method of Lagrange multipliers is scrutinized, in particular in relation to the quantization procedure. Ordering problems are…
We propose a mathematical model of \textit{quantum} transistor in which bandgap engineering corresponds to the tuning of Dirac potential in the complex four-vector form. The transistor consists of $n$-relativistic spin qubits moving in…
The Dirac equation is a cornerstone in the history of physics, merging successfully quantum mechanics with special relativity, providing a natural description of the electron spin and predicting the existence of anti-matter. Furthermore, it…
A rigorous \textit{ab initio} derivation of the (square of) Dirac's equation for a single particle with spin is presented. The general Hamilton-Jacobi equation for the particle expressed in terms of a background Weyl's conformal geometry is…
We introduce an exact mapping between the Dirac equation in (1+1)-dimensional curved spacetime (DCS) and a multiphoton quantum Rabi model (QRM). A background of a (1+1)-dimensional black hole requires a QRM with one- and two-photon terms…
On a static spacetime, the solutions of the Dirac equation are generated by a time-independent Hamiltonian. We study this Hamiltonian and characterize the split into positive and negative energy. We use it to find explicit expressions for…
A quantum unitary gate is realized in this paper by perturbing a free charged particle in a one-dimensional box with a time- and position-varying electric field. The perturbed Hamiltonian is composed of a free particle Hamiltonian plus a…
A Quantum Walk (QW) simulating the flat $(1 + 2)$D Dirac Eq.\ on a spatial polar grid is constructed. Because fermions are represented by spinors, which do not constitute a representation of the rotation group, but rather of its double…
Requiring physical consistency in a classical flat spacetime geometrisation of fermions is shown to suggest the introduction of torsion. A resulting simple model for that torsion produces a localised quantum-like particle as a solution of a…
A rigorous \textit{ab initio} derivation of the (square of) Dirac's equation for a single particle with spin is presented. The general Hamilton-Jacobi equation for the particle expressed in terms of a background Weyl's conformal geometry is…
It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum…
Discrete-time Quantum Walks (QWs) are transportation models of single quantum particles over a lattice. Their evolution is driven through causal and local unitary operators. QWs are a powerful tool for quantum simulation of fundamental…
We develop a path integral approach to quantum field theory that is defined over the paths of the Le'vy flights possessing a fractal dimension $1<d_f<2$. In standard quantum field theory, the fractality of the Brownian trajectories lead to…