Related papers: Higher Time Derivative Theories From Integrable Mo…
We introduce a `proper time' formalism to study the instability of the vacuum in a uniform external electric field due to particle production. This formalism allows us to reduce a quantum field theoretical problem to a quantum-mechanical…
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,…
A quantum-mechanical Hamiltonian with a gravitational potential is derived in the framework of local times. This Hamiltonian is the one used by E. H. Lieb (Bull. Amer. Math. Soc. 22(1990), 1-49) in his explanation of stability and…
Attempts to quantize general relativity encounter an odd problem. The Hamiltonian that normally generates time evolution vanishes in the case of general relativity as a result of diffeomorphism invariance. The theory seems to be saying that…
Modifications of Einstein's theory of gravitation have been extensively considered in the past years, in connection to both cosmology and quantum gravity. Higher-curvature and higher-derivative gravity theories constitute the main examples…
We propose a solution to the problem of time for systems with a single global Hamiltonian constraint. Our solution stems from the observation that, for these theories, conventional gauge theory methods fail to capture the full classical…
State-of-the-art quantum simulators permit local temporal control of interactions and midcircuit readout. These capabilities open the way towards the exploration of intriguing nonequilibrium phenomena. We illustrate this with a kinetically…
Black-hole perturbation theory is a useful tool to investigate issues in astrophysics, high-energy physics, and fundamental problems in gravity. It is often complementary to fully-fledged nonlinear evolutions and instrumental to interpret…
There are theories which implement the idea that the constants of nature may be "time dependent." These introduce new fields representing "evolving constants," in addition to physical fields. We argue that dynamical matter coupling…
Completely integrable finite dimensional Hamiltonian systems are well understood thanks to the work of Liouville and Arnold. On the other hand, the Lax Pair formulation of the KdV equation marks the beginning of the extension of the…
We develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution. Indeed, the covariance condition can be…
When an isolated quantum system is driven out of equilibrium, expectation values of general observables start oscillating in time. This article reviews the general theory of such temporal fluctuations. We first survey some results on the…
Quantum timeless approaches solve the problem of time by recovering the usual unitary evolution of quantum theory relative to a clock in a stationary quantum Universe. For some Hamiltonians of the Universe, such as those including an…
Field equations in four order derivatives with respect to time and space coordinates based on modified classic relativistic energy of the fractal theory of time and space are received. It is shown appearing of new spin characteristics and…
Complex systems are sometimes subject to non Gaussian alpha stable Levy fluctuations. A new method is devised to estimate this uncertain parameter and other system parameters, using observations on either mean exit time or escape…
This paper explores a mathematical technique for deriving dynamical invariants (i.e. constants of motion) in time-dependent gravitational potentials. The method relies on the construction of a canonical transformation that removes the…
The "problem of time" in canonical quantum gravity refers to the difficulties involved in defining a Hilbert space structure on states -- and local observables on this Hilbert space -- for a theory in which the spacetime metric is treated…
Based on an extended space-time symmetry a new attempt to search for links between general relativity and quantum mechanics is proposed. A simplified cylindrical model of gravitational geometrical dynamics leads to a microscopic geodesic…
We consider two simple models of higher-derivative and nonlocal quantu systems.It is shown that, contrary to some claims found in literature, they can be made unitary.
A temporally varying discretization often features in discrete gravitational systems and appears in lattice field theory models subject to a coarse graining or refining dynamics. To better understand such discretization changing dynamics in…