Related papers: Gauss-Manin equations for propagators in the case …
Starting from the Mellin-Barnes integral representation of a Feynman integral depending on set of kinematic variables $z_i$, we derive a system of partial differential equations w.r.t.\ new variables $x_j$, which parameterize the…
We compute the Gauss-Manin differential equation for any period of a polynomial in \ $\C[x_{0},\dots, x_{n}]$ \ with \ $(n+2)$ \ monomials. We give two general factorizations theorem in the algebra \ $\C< z, (\frac{\partial}{\partial…
Massive and massless vector particles, in the framework of generalized Weinberg-Tucker-Hammer equations, are considered in the Petiau-Duffin-Kemmer formalism. We obtain solutions of equations in the form of matrix-dyads. The Lagrangian is…
We consider the Schrodinger equation with a generalized uncertainty principle for a free particle. We then transform the problem into a second ordinary differential equation and thereby obtain the corresponding propagator. The result of…
The general lines of the derivation and the main properties of the master equations for the master amplitudes associated to a given Feynman graph are recalled. Some results for the 2-loop self-mass graph with 4 propagators are then…
We consider second order differential operators with coefficients which are Gaussian random fields. When the covariance becomes singular at short distances then the propagators of the Schr\"odinger equation as well as of the wave equation…
In this work we solve exactly a class of three-body propagators for the most general quadratic interactions in the coordinates, for arbitrary masses and couplings. This is done both for the constant as the time-dependent couplings and…
Gauge theories with and without matter are formulated in the derivative expansion. Amplitudues are derived as a power series in the energy scales; there are simplifications as compared with the usual loop expansion. The incorporation and…
The generalized Maxwell equations are considered which include an additional gradient term. Such equations describe massless particles possessing spins one and zero. We find and investigate the matrix formulation of the first order of…
The Einstein equations for static gravitational field depend on energy density and pressure. So one may expect that solutions should depend on two parameters: mass and its analogue originated from pressure. Yet the Schwarzschild solution…
Propagators of unstable particles are considered in the spectral representation which naturally follows from the concept of continuous mass. The spectral functions are found with the help of the most general formal and physical assumptions.…
The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper estimates for the integral representation of the moment…
We give formulae for first and second derivatives of generalized eigenvalues/eigenvectors of symmetric matrices and generalized singular values/singular vectors of rectangular matrices when the matrices are linear or nonlinear functions of…
This expository note gives a digest version of Hormander's propagation of singularities theorem for the wave equation.
Efficient computation methods are devised for the perturbative solution of Schwinger--Dyson equations for propagators. We show how a simple computation allows to obtain the dominant contribution in the sum of many parts of previous…
The consequence of dynamical mass generation on the singularity structure of propagators is discussed. First the phenomena of dynamical mass generation is discussed in the framework of Euclidean gap equations, then a possible Minkowski…
These short notes present to the reader (students, in particular) a concise approach to the derivation of the propagator of Hamiltonians with position-dependent kinetic energy. The formalism is applied to the von Roos Hamiltonian with…
By using geometric methods and superenergy tensors, we find new simple criteria for the causal propagation of physical fields in spacetimes of any dimension. The method can be applied easily to many different theories and to arbitrary…
A method is presented to compute approximate solutions for eigenequations in quantum mechanics with an arbitrary kinetic part. In some cases, the approximate eigenvalues can be analytically determined and they can be lower or upper bounds.…
The propagators of unstable particles are considered in the framework of the convolution representation. Spectral function was found for a special case when the propagator of scalar unstable particle has Breight-Wigner form. The expressions…