Related papers: Generating function method and its applications to…
The quantum mechanical version of the four kinds of classical canonical transformations is investigated by using non-hermitian operator techniques. To help understand the usefulness of this appoach the eigenvalue problem of a harmonic…
Strongly coupled gravitational systems describe Einstein gravity and matter in the limit that Newton's constant G is assumed to be very large. The nonlinear evolution of these systems may be solved analytically in the classical and…
We demonstrate a systematic method for solving the Hamilton-Jacobi equation for general relativity with the inclusion of matter fields. The generating functional is expanded in a series of spatial gradients. Each term is manifestly…
We present an overview of the role of generating functions in quantum mechanical contexts, mainly in the modern theory of polarization and in the study of quantum phase transitions. Generating functions enable the derivation of moments and…
Using the Wigner-Vlasov formalism, an exact 3D solution of the Schr\"odinger equation for a scalar particle in an electromagnetic field is constructed. Electric and magnetic fields are non-uniform. According to the exact expression for the…
A time dependent variational principle is used to dequantize a second order quadrupole boson Hamiltonian. The classical equations for the generalized coordinate and the constraint for angular momentum are quantized and then analytically…
In this work it is shown that there are symmetries beyond the Euclidean group $E\left(3\right)$ in 3-body problem, and by extension in many-body problem, with inverse squared distance inter particle force. The symmetries in 3-body problem…
The spatial gradient expansion of the generating functional was recently developed by Parry, Salopek, and Stewart to solve the Hamiltonian constraint in Einstein-Hamilton-Jacobi theory for gravitationally interacting dust and scalar fields.…
We analyze the asymptotics of the Wigner $3j$-symbol as a matrix element connecting eigenfunctions of a pair of integrable systems, obtained by lifting the problem of the addition of angular momenta into the space of Schwinger's…
We compute the generating function for the characters of the irreducible representations of SU(n) whose associated Young diagrams have only two rows with the same number of boxes. The result is a rational determinantal expression in which…
Gaussian unitary transformations are generated by quadratic Hamiltonians, i.e., Hamiltonians containing quadratic terms in creations and annihilation operators, and are heavily used in many areas of quantum physics, ranging from quantum…
Deriving a comprehensive set of reduction rules for Feynman integrals has been a longstanding challenge. In this paper, we present a proposed solution to this problem utilizing generating functions of Feynman integrals. By establishing and…
In this review, we compare different descriptions of photon-number statistics in harmonic generation processes within quantum, classical and semiclassical approaches. First, we study the exact quantum evolution of the harmonic generation by…
Different generators of a deformed oscillator algebra give rise to one-parameter families of $q$-exponential functions and $q$-Hermite polynomials related by generating functions. Connections of the Stieltjes and Hamburger classical moment…
A generating function for the Wigner's $D$-matrix elements of $SU(3)$ is derived. From this an explicit expression for the individual matrix elements is obtained in a closed form.
We develop a generating-function formulation for the symbolic reduction of multi-loop Feynman integrals. In this framework, integration-by-parts identities are rewritten as differential equations for sector-wise generating functions, so the…
Classical mechanics admits multiple equivalent formulations, from Newton's equations to the variational Lagrange-Hamilton framework and the scalar Hamilton-Jacobi (HJ) theory. In the HJ formulation, classical ensembles evolve through the…
The nonlinear oscillator model allows a basic understanding of all nonlinear processes and can be adopted to analyse optical vibrational modes and electronic transition in molecules and crystals, in order to derive general properties of…
Uhlenbeck proved that a set of simple elements generates the group of rational loops in GL(n,C) that satisfy the U(n)-reality condition. For an arbitrary complex reductive group, a choice of representation defines a notion of rationality…
We represent the generators of the SU(N) algebra as bilinear combinations of Fermi operators with imaginary chemical potential. The distribution function, consisting of a minimal set of discrete imaginary chemical potentials, is found for…