Related papers: Planck's Constant as a Dynamical Field & Path Inte…
We study the Brans-Dicke model in the presence of an axion. The dynamical equations are solved when the fields are space independent and the metric is spatially flat. It is found that at late time the scale factor undergoes decelerated…
We present further developments on the Lagrangian 1-form description for one-dimensional integrable systems in both discrete and continuous levels. A key feature of integrability in this context called a closure relation will be derived…
Using Dirac's approach to constrained dynamics, the Hamiltonian formulation of regular higher order Lagrangians is developed. The conventional description of such systems due to Ostrogradsky is recovered. However, unlike the latter, the…
The Planck constant $h$ is one of the most significant constants in quantum physics. Recently, the precision measurement of the numeral value of $h$ has been a hot issue due to its important role in establishment for both a new SI and a…
These short notes present to the reader (students, in particular) a concise approach to the derivation of the propagator of Hamiltonians with position-dependent kinetic energy. The formalism is applied to the von Roos Hamiltonian with…
The most general local Markovian stochastic model is investigated, for which it is known that the evolution equation is the Fokker-Planck equation. Special cases are investigated where uncorrelated initial states remain uncorrelated.…
The question whether the invariant speed c, Planck constant h/, and gravitational constant G can be or should be put equal to 1 is analyzed. The discussion is based on fundamental considerations concerning the notion of physical quantity.…
In the present article, we discuss a modification of classical electrodynamics in which ``ordinary'' point charges are absent. The modified equations contain additional terms describing the induced charges and currents. The densities of the…
We consider classically scale-invariant theories with non-minimally coupled scalar fields, where the Planck mass and the hierarchy of physical scales are dynamically generated. The classical theories possess a fixed point, where scale…
We apply the concept of dynamic propensity to a simple kinetically constrained model of glass formers, the two-vacancy assisted triangular lattice gas, or (2)-TLG. We find that the propensity field, defined in our case as the local…
In the present work, a consistent Lagrangian model that encapsulates fully kinetic ions and gyrokinetic electrons for solar wind electromagnetic turbulence is formulated. Using a consistent method, where both electrons and protons are…
Renormalized Hamiltonians for gluons are constructed using a perturbative boost-invariant renormalization group procedure for effective particles in light-front QCD, including terms up to third order. The effective gluons and their…
The novel proposal to invoke the split of the Ricci scalar into bulk and boundary terms in the gravitational action, opens up a new avenue of investigation into stellar dynamics. The Lagrangian contains functional forms of the bulk term…
We examine "dynamical similarities" in the Lagrangian framework. These are symmetries of an intrinsically determined physical system under which observables remain unaffected, but the extraneous information is changed. We establish three…
We investigate the presence of static solutions in generalized models described by a real scalar field in four-dimensional space-time. We study models in which the scalar field engenders higher-order derivatives and spontaneous symmetry…
Classically, the dynamics in a non-globally hyperbolic spacetime is ill posed. Previously, a prescription was given for defining dynamics in static spacetimes in terms of a second order operator acting on a Hilbert space defined on static…
We derive the general solution to the coupled Einstein and Dirac field equations in static and hyperplane-symmetric spacetime of arbitrary dimension including a cosmological constant of either sign. As a result, only a massful Dirac field…
A novel routine to investigate the scalar fields in a cosmological context is discussed in the framework of the Hamiltonian formalism. Starting from the Einstein-Hilbert action coupled to a Lagrangian density that contains two components -…
The dynamic hyperpolarizability of a particle bound by the one-dimensional $\delta$-function potential is obtained in closed form. On the first step, we analyze the singular structure of the non-linear response function as given by the…
Planck's constant was introduced as a fundamental scale in the early history of quantum mechanics. We find a modern approach where Planck's constant is absent: it is unobservable except as a constant of human convention. Despite long…