Related papers: No Drama Quantum Theory? A Review
The Dirac equation is one of the most fundamental equations of modern physics. It is a spinor equation, but some tensor equivalents of the equation were proposed previously. Those equivalents were either nonlinear or involved several…
We show that the principal part of the Dirac Hamiltonian in 3+1 dimensions emerges in a semi-classical approximation from a construction which encodes the kinematics of quantum gravity. The construction is a spectral triple over a…
Transition to a nonrelativistic Pauli equation in Riemann space of constant positive curvature for a Dirac particle in presence of the Coulomb field is performed in the system of radial equations, exact solutions are constructed in terms of…
We propose to represent both $n$--qubits and quantum gates acting on them as elements in the complex Clifford algebra defined on a complex vector space of dimension $2n.$ In this framework, the Dirac formalism can be realized in…
Generalized solutions of the standard gauge transformation equations are presented and discussed in physical terms. They go beyond the usual Dirac phase factors and they exhibit nonlocal quantal behavior, with the well-known Relativistic…
Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of…
We show that additional solutions must be ignored (in differences of the Schrodinger and Klein-Gordon equations) in the Dirac equation, where usually passed the second order radial equation, called the reduced equation, instead of a system.…
In terms of the relational approach to space-time geometry and physical interactions, we show that the Dirac equation for a free fermion in the momentum representation can be obtained starting from a binary system of complex relations…
We perform a reduced phase space quantization of gravity using four Klein-Gordon scalar fields as reference matter as an alternative to the Brown-Kuchar dust model in [1], where dust scalar fields are used. We compare our results to an…
The system of gravity coupled to the non-rotational dust field is studied at both classical and quantum levels. The scalar constraint of the system can be written in the form of a true physical Hamiltonian with respect to the dust time. In…
Unifying quantum theory and gravity remains a fundamental challenge in physics. While most existing literature focuses on the ultraviolet (UV) modifications of quantum theory due to gravity, this work shows that generic infrared (IR)…
We consider the adiabatic evolution of the Dirac equation in order to compute its Berry curvature in momentum space. It is found that the position operator acquires an anomalous contribution due to the non Abelian Berry gauge connection…
The formalism based on the equal-time Wigner function of the two-point correlation function for a quantized Klein--Gordon field is presented. The notion of the gauge-invariant Wigner transform is introduced and equations for the…
We show that the Dirac equation for real spinors can be naturally decomposed into a system of two first-order relativistic wave equations. The decomposition separates in a transparent way the real and imaginary parts of the Dirac equation…
Over the past decades, many authors advertised models on complexified spacetime algebras for use in describing gravity. This work aims at providing phenomenological support to such claims, by introducing a one-parameter real phase $\alpha$…
This article is a pedagogical introduction to relativistic quantum mechanics of the free Majorana particle. This relatively simple theory differs from the well-known quantum mechanics of the Dirac particle in several important aspects. We…
It is shown the central field Dirac equation can be simplified through the use of real conjugate spinors to substitute for the upper and lower components of the bi-spinor eigensolutions. This substitution reduces the Dirac equation for the…
Gauge fields associated to the Dirac matrix algebra used with the standard quadratic gauge field Lagrangian lead to an extended gravitational Lagrangian which includes the Einstein-Hilbert one, plus quadratic, cosmological constant and…
We investigate whether the spinor field can be differential-algebraically eliminated from the Maxwell--Dirac equations in a particular gauge. To this end, we construct a generic truncated power-series solution and linearize the prolonged…
We suggest an alternative mathematical model for the electron in which the dynamical variables are a coframe (field of orthonormal bases) and a density. The electron mass and external electromagnetic field are incorporated into our model by…