Related papers: Gauge transformations for a driven quantum particl…
The self adjoint operator of time in non-relativistic quantum mechanics is found within the approach where the ordinary Hamiltonian is not taken to be conjugate to time. The operator version of the reexpressed Liouville equation with the…
We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects…
To describe charged particles interacting with the quantized electromagnetic field, we point out the differences of working in the so-called generalized and the true Coulomb gauges. We find an explicit gauge transformation between them for…
In this work we explore the self-adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Newmann for symmetric operators in order to determine whether the…
We address gauge invariance in the statistical mechanics of quantum many-body systems. The gauge transformation acts on the position and momentum degrees of freedom and it is represented by a quantum shifting superoperator that maps quantum…
Some precisions are given about the definition of the Hamiltonian operator H and its transformation properties, for a linear wave equation in a general spacetime. In the presence of time-dependent unitary gauge transformations, H as an…
For quantum mechanics of a charged particle in a classical external electromagnetic field, there is an apparent puzzle that the matrix element of the canonical momentum and Hamiltonian operators is gauge dependent. A resolution to this…
Hamiltonian operators are gauge dependent. For overcome this difficulty we reexamined the effect of a gauge transformation on Schr\"odinger and Dirac equations. We show that the gauge invariance of the operator…
Quantum systems with constraints are often considered in modern theoretical physcics. All realistic field models based on the idea of gauge symmetry are of this type. A partial case of constraints being linear in coordinate and momenta…
Contrary to the conventional view point of quantization that breaks the gauge symmetry, a gauge invariant formulation of quantum electrodynamics is proposed. Instead of fixing the gauge, some frame is chosen to yield the locally invariant…
For the example of the infinitely deep well potential, we point out some paradoxes which are solved by a careful analysis of what is a truly self-adjoint operator. We then describe the self-adjoint extensions and their spectra for the…
Using connection with quantum field theory, the infinitesimal covariant abelian gauge transformation laws of relativistic two-particle constraint theory wave functions and potentials are established and weak invariance of the corresponding…
The quantum measurement axiom dictates that physical observables and in particular the Hamiltonian must be diagonalizable and have a real spectrum. For a time-independent Hamiltonian (with a discrete spectrum) these conditions ensure the…
We are focused on the idea that observables in quantum physics are a bit more than just hermitian operators and that this is, in general, a "tricky business". The origin of this idea comes from the fact that there is a subtle difference…
Understanding which physical processes are symmetric with respect to time inversion is a ubiquitous problem in physics. In quantum physics, effective gauge fields allow emulation of matter under strong magnetic fields, realizing the…
The Hamiltonian for quantum electrodynamics becomes non-Hermitian if the unrenormalized electric charge $e$ is taken to be imaginary. However, if one also specifies that the potential $A^\mu$ in such a theory transforms as a pseudovector…
We consider an unusual singular position=dependent-mass particle in an infinite potential well. The corresponding Hamiltonian is mapped through a point-canonical-transformation and an explicit correspondence between the target Hamiltonian…
Beginning with ordinary quantum mechanics for spinless particles, together with the hypothesis that all experimental measurements consist of positional measurements at different times, we characterize directly a class of nonlinear quantum…
We describe a novel class of quantum mechanical particle oscillations in both relativistic and non-relativistic systems based on $PT$ symmetry and $T^2=-1$ (relevant for fermions), where $P$ is parity and $T$ is time reversal. The…
A system consisting of a point particle coupled to gravity is investigated. The set of constraints is derived. It was found that a suitable superposition of those constraints is the generator of the infinitesimal transformations of the time…