Related papers: The Uncertainty Principle and Classical Amplitudes
Uncertainty relations are usually formulated as trade-off relations between two or more observables. Here we show that the uncertainty of a single observable already has a nontrivial lower bound originating from the noncommutativity between…
The classical eikonal is defined to be the generator of all scattering observables in a scattering problem in classical mechanics. It was originally introduced as the log of the quantum S-matrix in the classical limit. But its classical…
The fidelity amplitude is a quantity of paramount importance in echo type experiments. We use semiclassical theory to study the average fidelity amplitude for quantum chaotic systems under external perturbation. We explain analytically two…
A striking feature of our fundamentally indeterministic quantum universe is its quasiclassical realm -- the wide range of time place and scale in which the deterministic laws of classical physics hold. Our quasiclassical realmis an emergent…
By averaging over an ensemble of field configurations, a classical field theory can display many of the characteristics of quantum field theory, including Lorentz invariance, a loop expansion, and renormalization effects. There is…
Heisenberg's uncertainty principle is often cited as an example of a "purely quantum" relation with no analogue in the classical limit where $\hbar \to 0$. However, this formulation of the classical limit is problematic for many reasons,…
Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constrains on the accuracy of two noncommuting observables.…
The classical and quantum evolution of a generic probability distribution is analyzed. To that end, a formalism based on the decomposition of the distribution in terms of its statistical moments is used, which makes explicit the differences…
We study the process, within classical general relativity, in which an incident gravitational plane wave, of weak amplitude and long wavelength, scatters off a massive spinning compact object, such as a black hole or neutron star. The…
I discuss a formalism for computing quantum scattering amplitudes using a semiclassical expansion of a functional integral representation for the S-matrix. The classical background for the expansion is determined by solving the equations of…
We study the gravitational scattering of massive particles with and without spin in the effective theory of gravity at one loop level. Our focus is on long distance effects arising from nonanalytic components of the scattering amplitude and…
We study the behavior of a nonlinear semiclassical system using Shannon entropy and two approaches to statistical complexity. These systems involve the interaction between classical variables (representing the environment) and quantum ones.…
Asymptotic behavior of the scattering amplitude for two scalar particles by scalar, vector and tensor exchanges at high energy and fixed momentum transfers is reconsidered in quantum field theory. In the framework of the quasi-potential…
We introduce a formalism for describing four-dimensional scattering amplitudes for particles of any mass and spin. This naturally extends the familiar spinor-helicity formalism for massless particles to one where these variables carry an…
We show how to compute classical wave observables using quantum scattering amplitudes. We discuss observables both with incoming and with outgoing waves. The required classical limits are naturally described by coherent states of massless…
Accelerated charges emit both electromagnetic and gravitational radiation. Classically, it was found that the electromagnetic energy spectrum radiated by an electron in a monochromatic plane wave is proportional to the corresponding…
The uncertainty principle is considered to be one of the most striking features in quantum mechanics. In the textbook literature, uncertainty relations usually refer to the preparation uncertainty which imposes a limitation on the spread of…
A classical random walker starting on a node of a finite graph will always reach any other node since the search is ergodic, namely it is fully exploring space, hence the arrival probability is unity. For quantum walks, destructive…
We study classical radiation fields at next-to-leading order using the methods of scattering amplitudes. The fields of interest to us are sourced when two massive, point-like objects scatter inelastically, and can be computed from one-loop…
The uncertainty principle, originally formulated by Heisenberg, dramatically illustrates the difference between classical and quantum mechanics. The principle bounds the uncertainties about the outcomes of two incompatible measurements,…