Related papers: Generating function method and its applications to…
We present three explicit formulas for the number of electronic configurations in an atom, i.e. the number of ways to distribute $Q$ electrons in $N$ subshells of respective degeneracies $g_1$, $g_2$, ..., $g_N$. The new expressions are…
It is shown that any function $G(q_{i}, p_{i}, t)$, defined on the extended phase space, defines a one-parameter group of canonical transformations which act on any function $f(q_{i}, t)$, in such a way that if $G$ is a constant of motion…
We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include condensed matter systems with quenched disorder (e.g. spin glass) or cosmological systems in…
When one tries to take into account the non-trivial vacuum structure of Quantum Field Theory, the standard functional-integral tools such as generating functionals or transitional amplitudes, are often quite inadequate for such purposes.…
Two methods of constructing 2D Toda $\tau$-functions that are generating functions for certain geometrical invariants of a combinatorial nature are related. The first involves generation of paths in the Cayley graph of the symmetric group…
General analytical solutions of the Quantum Hamilton Jacobi Equation for conservative one-dimensional or reducible motion are presented and discussed. The quantum Hamilton's characteristic function and its derivative, i.e. the quantum…
We consider the determination of the number $c_k(\alpha)$ of ordered factorisations of an arbitrary permutation on n symbols, with cycle distribution $\alpha$, into k-cycles such that the factorisations have minimal length and such that the…
We determine the generating function of the harmonic oscillator by a new method. Using this generating function we derive the eigenfunctions of the moment p. We find that the normalization of these eigenfunctions is a real and not complex…
A formula is derived that provides generating functions for any multi-j-symbol, such as the 3-j-symbol, the 6-j-symbol, the 9-j-symbol, etc. The result is completely determined by geometrical objects (loops and curves) in the graph of the…
We present the path integral representation of the generating function for classical exclusive particle systems. By introducing hard-core bosonic creation and annihilation operators and appropriate commutation relations, we construct the…
We investigate two methods of constructing a solution of the Schr\"{o}dinger equation from the canonical transformation in classical mechanics. One method shows that we can formulate the solution of the Schr\"{o}dinger equation from linear…
We construct new integral representations for transformations of the ordinary generating function for a sequence, $\langle f_n \rangle$, into the form of a generating function that enumerates the corresponding "square series" generating…
We provide a generating functional for the gravitational field, associated to the relaxation of the primary constraints as extended to the quantum sector. This requirement of the theory, relies on the assumption that a suitable time…
Within the framework of the theory of irreducible tensor operators, using well-known general analytical results for double sums ($\sum_{jm}$) of products of two $3j$-Wigner symbols, analytical expressions for single sums ($\sum_m$) for the…
In this work we show how to complete some Hamilton-Jacobi solutions of linear, nonconservative classical oscillatory systems which appeared in the literature and we extend these complete solutions to the quantum mechanical case. In…
Recoupling coefficients (3nj symbols) are unitary transformations between binary coupled eigenstates of N=(n+1) mutually commuting SU(2) angular momentum operators. They have been used in a variety of applications in spectroscopy, quantum…
The Hilbert spaces of matrix quantum mechanical systems with $N \times N$ matrix degrees of freedom $ X $ have been analysed recently in terms of $S_N$ symmetric group elements $U$ acting as $X \rightarrow U X U^T $. Solvable models have…
We introduce a novel, systematic method for the complete symbolic reduction of multi-loop Feynman integrals, leveraging the power of generating functions. The differential equations governing these generating functions naturally yield…
Let $P$ be a generalized laplacian on $R^{2n+1}$. It is known that $P$ is the generating functional of semigroups of measures $\mu_{t}$ on the Heisenberg group $H^{n}$ and $\nu_{t}$ on the Abelian group $R^{2n+1}$. Under some smoothness and…
By using the generating function formula for the product of two q-Hermite polynomials q-deformation of the Feynman Green function for the harmonic oscillator is obtained.