Related papers: Dimensionless equations in non-relativistic quantu…
We discuss a systematic construction of dimensionless quantum-mechanical equations. The process reduces the number of independent model parameters to a minimum and, at the same time, provides the natural units of length, energy, etc. in a…
We present a self-contained formulation of spin-free nonrelativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories,…
A generalized formulation of non-relativistic quantum mechanics is developed within multidimensional geometric (NG) frameworks characterized by a power-law dispersion relation \(E \propto |p|^{j}\), where \(j = N - 1\). Starting from the…
The non perturbative construction of quantum field models with nontrivial scattering in arbitrary dimension $d$ of the underlying Minkowski space-time is much more simple in the framework of quantum field theory with indefinite metric than…
Non-relativistic quantum mechanics was originally formulated to describe particles. Using ideas from the geometric quantization approach, we show how the concept of antiparticles can and should be introduced in the non-relativistic case…
It is shown that regularisation by dimensional reduction is a viable alternative to dimensional regularisation in non-supersymmetric theories.
On the basis of a 5-dimensional form of space-time transformations non-relativistic quantum mechanics is reformulated in a manifestly covariant manner. The resulting covariance resembles that of the conventional relativistic quantum…
Relational particle mechanics are models in which there is, overall, no time, position, orientation (nor, sometimes, scale). They are useful for whole-universe modelling - the setting for quantum cosmology. This note concerns 3 particles in…
One-dimensional nonrelativistic systems are studied when time-independent potential interactions are involved. Their supersymmetries are determined and their closed subsets generating kinematical invariance Lie superalgebras are pointed…
Dynamic equations of non-relativistic mechanics are written in covariant-coordinate form in terms of relative velocities and accelerations with respect to an arbitrary reference frame. The notions of the non-relativistic reference frame,…
Stabilizing, by deformation, the algebra of relativistic quantum mechanics a non-commutative space-time geometry is obtained. The exterior algebra of this geometry leads to an extended massless Dirac equation which has both a massless and a…
Dimensionless numbers and scaling laws provide elegant insights into the characteristic properties of physical systems. Classical dimensional analysis and similitude theory fail to identify a set of unique dimensionless numbers for a…
Nonlinear quantum mechanics at the Planck scale can produce nonlocal effects contributing to resolution of singularities, to cosmic acceleration, and modified black-hole dynamics, while avoiding the usual causality issues.
A novel manifestation of nonlocality of quantum mechanics is presented. It is shown that it is possible to ascertain the existence of an object in a given region of space without interacting with it. The method might have practical…
We outline an approach that streamlines considerably the construction and analysis of well-behaved nonlinear quantum dynamics, with completely positive extensions to entangled systems. A few notes are added on the issue of quantum…
Equations are ubiquitous in most mathematical activities. Nevertheless, in this paper it is shown how to do standard mathematics without any equation at all. More than that, it is proven there is a foundational framework for standard…
General non-commutative supersymmetric quantum mechanics models in two and three dimensions are constructed and some two and three dimensional examples are explicitly studied. The structure of the theory studied suggest other possible…
We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for…
The advantageous points of ERG in applications to non-perturbative analyses of quantum field theories are discussed in comparison with the Schwinger-Dyson equations. First we consider the relation between these two formulations specially by…
When faced with a mathematical model, often the first step is to reduce the complexity of the model by turning variables and parameters into dimensionless quantities. This process is often performed by hand, relying on a skill practiced…