Related papers: Are Constants Constant?
In the first days of quantum mechanics Dirac pointed out an analogy between the time-dependent coefficients of an expansion of the Schr\"odinger equation and the classical position and momentum variables solving Hamilton's equations. Here…
We exactly solve the (2+1)-dimensional Dirac equation in a constant magnetic field in the presence of a minimal length. Using a proper ansatz for the wave function, we transform the Dirac Hamiltonian into two 2-dimensional non-relativistic…
The cosmological solution with a long-term bouncing off time is presented. The solution has a preceding contracting and a subsequent expanding phases and between them there exists a bouncing off phase with arbitrary time duration.
In the standard procedure for calculating the decay rate of a metastable vacuum the solution of the classical Euclidean equation of motion of the background field is needed. On the other hand radiative corrections have to be taken into…
Classical vortex solutions in $(1+2)$-dimensional multi-Higgs systems are studied. In particular the existence of such a solution requires equal characteristic lengths and a specific relation between the ratio of the two Higgs vacuum…
We consider first-passage percolation with positive, stationary-ergodic weights on the square lattice $\mathbb{Z}^d$. Let $T(x)$ be the first-passage time from the origin to a point $x$ in $\mathbb{Z}^d$. The convergence of the scaled…
The idea of wave mechanics leads naturally to assume the well-known relation $E=\hbar \omega $ in the specific form $H=\hbar W$, where $H$ is the classical Hamiltonian of a particle and $W$ is the dispersion relation of the sought-for wave…
We analyze the Higgs sector of the Standard Model in the light of recently found exact solutions of its dynamical equation. We work in a conformal regime with zero mass term. It is seen that, provided self-interaction coupling is finite,…
We make a change of variable in the standard model Higgs field by a fermion operator and show that the latter is responsible for the electroweak vacuum. By computing the vacuum expectation value of this fermion operator in the path integral…
A system of two charged particles in a harmonic trap with additional magnetic field is considered. The problem is reduced to a single-particle one in relative coordinates. The ground- and lowest excited-state energies and wave functions are…
Quantum mechanics rests on the assumption that time is a classical variable. As such, classical time is assumed to be measurable with infinite accuracy. However, all real clocks are subject to quantum fluctuations, which leads to the…
The so-called metastability bound asserts that an unnaturally small Higgs mass is a necessary condition for electroweak vacuum metastability, offering a new approach towards solving the hierarchy problem. So far, this result relies on the…
We model a single-electron ion (hydrogenic atom) as a static, spherically symmetric electrovacuum spacetime in which the nucleus is treated as a timelike line-singularity and the electron is treated as a test particle following Dirac's…
We investigate the Higgs potential beyond the Planck scale in the superstring theory, under the assumption that the supersymmetry is broken at the string scale. We identify the Higgs field as a massless state of the string, which is…
We consider the energy levels of a hydrogen-like atom in the framework of $\theta $-modified, due to space noncommutativity, Dirac equation with Coulomb field. It is shown that on the noncommutative (NC) space the degeneracy of the levels…
We investigate a field theoretical approach to the Jordan-Brans- Dicke (JBD) theory extended with a particular potential term on a cosmological background by starting with the motivation that the Higgs field and the scale factor of the…
A new class of solutions to the electroweak hierarchy problem is presented that does not require either weak scale dynamics or anthropics. Dynamical evolution during the early universe drives the Higgs mass to a value much smaller than the…
The dynamical quantum effects arising due to the boundary presence with two types of boundary conditions (BC) satisfied by scalar fields are studied. It is shown that while the Neumann BC lead to the usual scalar field mass generation, the…
We discuss the vacuum energy density term resulting from the spontaneous breakdown of the electroweak gauge symmetry, in the Higgs Mechanism. We alternatively expand the scalar field at one of the degenerate states that lie outside the…
We find the electric field of a point charge in `truncated hyperbolic motion', in which the charge moves at a constant velocity followed by motion with a constant acceleration in its instantaneous rest frame. The same Lienard-Wiechert…