Related papers: Scale invariance and constants of motion
If scale invariance is exact, unparticles are unlikely to be probed in colliders since there are stringent constraints from astrophysics and cosmology. However these constraints are inapplicable if scale invariance is broken at a scale mu…
A covariant scalar-tensor-vector gravity theory is developed which allows the gravitational constant $G$, a vector field coupling $\omega$ and the vector field mass $\mu$ to vary with space and time. The equations of motion for a test…
With the present trend in experimental particle physics of probing yet shorter distances and with the requirement on the theoretical side of renormalizability, conformal invariance becomes an attractive symmetry for particle interactions.…
This paper begins with a dynamical model that was obtained by applying a machine learning technique (FJet) to time-series data; this dynamical model is then analyzed with Lie symmetry techniques to obtain constants of motion. This analysis…
Pattern formation in systems with a conserved quantity is considered by studying the appropriate amplitude equations. The conservation law leads to a large-scale neutral mode that must be included in the asymptotic analysis for pattern…
The motion of a radiating point particle can be represented by a series of geodesics whose "constants" of motion evolve slowly with time. The evolution of these constants of motion can be determined directly from the self-force equations of…
The physics of many closed, conservative systems can be described by both classical and quantum theories. The dynamics according to classical theory is symplectic and admits linear instabilities which would initially seem at odds with a…
Using our mathematical framework developed in \cite{cresson-pierret_scale} called \emph{scale dynamics}, we propose in this paper a new way of interpreting the problem of adding or modifying potentials in mechanics and specifically in…
The mobility of an overdamped particle, in a periodic potential tilted by a constant external field and moving in a medium with periodic friction coefficient is examined. When the potential and the friction coefficient have the same…
The local phase-invariance of the momentum-space Schr\"odinger equation for free-particle has been used to construct quantum kinematics that describes a motion of the particle in external U(1) background gauge field. The gauge structure…
Quantum scale invariant regularization is a variant of dimensional regularization where the renormalization scale is treated as a dynamical field. But, rather than be regarded as a novel regularization method on par with dimensional…
This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in…
We generalize the scale invariant gravity by allowing a negative kinetic energy term for the classical scalar field. This gives birth to a new scalar-tensor theory of gravity, in which the scalar field is in fact an auxiliary field. For a…
We show that observational limits on the possible time variation of constants of Nature are significantly affected by allowing for both space and time variation. Bekenstein's generalisation of Maxwell's equations to allow for cosmological…
It will be argued here that the cosmological constant problem exists because of the way the vacuum is defined in quantum field theory. It has been known for some time that for QFT to be gauge invariant certain terms--such as part of the…
Within the so-called scaled quantum theory, the standard bouncing ball problem is analyzed under the presence of a gravitational field and harmonic potential. In this framework, the quantum-classical transition of the density matrix is…
We show that a theory with conformal invariance, which is explicitly broken by small terms, provides a solution to the fine tuning problem of the cosmological constant. In the absence of the symmetry breaking terms, the cosmological…
It is argued that the dynamics of an isolated system, due to the concrete procedure by which it is separated from the environment, has a non-Hamiltonian contribution. By a unified quantum field theoretical treatment of typical subdynamics,…
This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in…
In double field theory, the equation of motion for a point particle in the background field is considered. We find that the motion is described by a geodesic flow in the doubled geometry. Inspired by the analysis on the particle motion, we…