Related papers: Quantum mechanics with quaternionic mass
We extend a recent formulation of quantum continuum mechanics [J. Tao et. al, Phys. Rev. Lett. {\bf 103}, 086401 (2009)] to many-body systems subjected to a magnetic field. To accomplish this, we propose a modified Lagrangian approach, in…
We obtain the effective action of four dimensional quantum gravity, induced by N massless matter fields, by integrating the RG flow of the relative effective average action. By considering the leading approximation in the large N limit,…
The semiclassical interaction of the gravitational with a quantum scalar field is considered, in view of the renormalizability of the associated energy-momentum tensor in a n-dimensional curved spacetime resulting from a quadratic…
Since the particles such as molecules, atoms and nuclei are composite particles, it is important to recognize that physics must be invariant for the composite particles and their constituent particles, this requirement is called particle…
The complex-valued quantum mechanics considers quantum motion on the complex plane instead of on the real axis, and studies the variations of a particle complex position, momentum and energy along a complex trajectory. On the basis of…
The equivalence postulate of quantum mechanics offers an axiomatic approach to quantum field theories and quantum gravity. The equivalence hypothesis can be viewed as adaptation of the classical Hamilton-Jacobi formalism to quantum…
Expanding the ordinary Dirac's equation in quaternionic form yields Maxwell-like field equations. As in the Maxwell's formulation, the particle fields are represented by a scalar, $\psi_0$ and a vector $\vec{\psi}$. The analogy with…
We consider for the first time the solutions of Klein-Gordon equation in gravitational field of {\em a massive} point source in GR. We examine numerically the basic bounded quantum state and the next few states in the discrete spectrum for…
The non-commutativity of the position and momentum operators is formulated as an effective potential in classical phase space and expanded as a series of successive many-body terms, with the pair term being dominant. A non-linear partial…
Different quantum Langevin equations obtained by coupling a particle to a field are examined. Instabilities or violations of causality affect the motion of a point charge linearly coupled to the electromagnetic field. In contrast, coupling…
A common assumption in quantum field theory is that the energy-momentum 4-vector of any quantum state must be time-like. It will be proven that this is not the case for a Dirac-Maxwell field. In this case quantum states can be shown to…
Four-dimensional mass is determined in four-dimensional pseudo-Euclidean space as a physical invariant of that space. That invariant is discussed as an invariant of electromagnetic type. Finally, equations of Maxwell type are obtained for…
Some connections between quantum mechanics and classical physics are explored. The Planck-Einstein and De Broglie relations, the wavefunction and its probabilistic interpretation, the Canonical Commutation Relations and the Maxwell--Lorentz…
Massive scalar particle production, due to the anisotropic evolution of a five-dimensional spacetime, is considered in the context of a quadratic Lagrangian theory of gravity. Those particles, corresponding to field modes with non-vanishing…
Quantum mechanics postulates the existence of states determined by a particle position at a single time. This very concept, in conjunction with superposition, induces much of the quantum-mechanical structure. In particular, it implies the…
This article develops a variational formulation of relativistic nature applicable to the quantum mechanics context. The main results are obtained through basic concepts on Riemannian geometry. Standards definitions such as vector fields and…
There must exist a reformulation of quantum field theory, even at low energies, which does not depend on classical time. The octonionic theory proposes such a reformulation, leading to a pre-quantum pre-spacetime theory. The ingredients for…
Despite the fact that it is not integrable, the 1 + 2-dimensional Sine-Gordon equation has N-soliton solutions, whose velocities are lower than the speed of light (c = 1), for all N greater than or equal to 1. Based on these solutions, a…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
A new quantum mechanical wave equation describing a particle with frictional forces is derived. It depends on a parameter $\alpha$ whose range is determined by the coefficient of friction $\gamma$, that is, $0 \leq \alpha \leq \gamma$. For…