Related papers: Semiclassical Expansions, the Strong Quantum Limit…
We perform a Feynman diagram calculation of the two-loop scattering amplitude for gravitationally interacting massive particles in the classical limit. Conveniently, we are able to sidestep the most taxing diagrams by exploiting the…
The classical mechanics of a finite number of degrees of freedom requires a symplectic structure on phase space C, but it is independent of any complex structure. On the contrary, the quantum theory is intimately linked with the choice of a…
These lectures are an introduction to formal semiclassical quantization of classical field theory. First we develop the Hamiltonian formalism for classical field theories on space time with boundary. It does not have to be a cylinder as in…
We consider the quantum kinetic-theory description for interacting massive spin-half fermions using the Wigner function formalism. We derive a general kinetic theory description assuming that the spin effects appear at the classical and…
As it is known, neither classical logical conjunction "and" nor classical logical alternative "either...or" can replace "+" representing a linear superposition of two quantum states. Therefore, to provide a logical account of the quantum…
It is shown that spatially flat, isotropic cosmologies derived from the Brans--Dicke gravity action exhibit a scale factor duality invariance. This classical duality is then associated with a hidden $N=2$ supersymmetry at the quantum level…
We study how the singular behaviour of classical systems at bifurcations is reflected by their quantum counterpart. The semiclassical contributions of individual periodic orbits to trace formulae of Gutzwiller type are known to diverge when…
We discuss the duality theorem, which provides a relation between loop integrals and phase space integrals. We rederive the duality relation for the one-loop case and extend it to two and higher-order loops. We explicitly show its…
It is well known that the action functional can be used to define classical, quantum, closed, and open dynamics in a generalization of the variational principle and in the path integral formalism in classical and quantum dynamics,…
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…
Experimentally, certain degrees of freedom may appear classical because their quantum fluctuations are smaller than the experimental error associated with measuring them. An approximation to a fully quantum theory is described in which the…
We derive a semiclassical quantization for a spin, study it for not too small a spin quantum number (S>5), and compute the 2S+1 eigenvalues of a Hamiltonian exhibiting resonant tunnelling as the magnetic field parallel to the anisotropy…
By introducing a doublet of electromagnetic four dimensional vector potentials, we set up a manifestly Lorentz covariant and SO(2) duality invariant classical field theory of electric and magnetic charges. In our formulation one does not…
This study analyzes the geometrical relationship between a classical string and its semi-classical quantum model. From an arbitrary $(2+1)-$dimensional geometry, a specific ansatz for a classical string is used to generate a semi-classical…
We use a local scale invariance of a classical Hamiltonian and describe how to construct six different formulations of quantum mechanics in spaces with two time-like dimensions. All these six formulations have the same classical limit…
Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…
The theory described by the sum of the Einstein-Hilbert action and the action of conformal scalar field possesses the duality symmetry which includes some special conformal transformation of the metric, and also inversion of scalar field…
Wave-particle duality, a fundamental principle of quantum mechanics, encapsulates the complementary relationship between the wave and particle behaviors of quantum systems. In this paper, we treat quantum coherence and classical…
Semi-classical approaches approximate fully quantum descriptions with partially classical ones. Here we use a toy model to highlight the failings of the standard mean-field semi-classical approach, and show how including environmental…
We prove a duality theorem for quantum groupoid (weak Hopf algebra) actions that extends the well-known result for usual Hopf algebras.