On convergence of the Schwinger — DeWitt expansion
نویسنده
چکیده
The Schwinger — DeWitt expansion for the evolution operator kernel of the Schrödinger equation is studied for convergence. It is established that divergence of this expansion which is usually implied for all continuous potentials, excluding ones of the form V (q) = aq2 + bq + c, really takes place only if the coupling constant g is treated as independent variable. But the expansion may be convergent for some kinds of the potentials and for some discrete values of the charge, if the latter is considered as fixed parameter. Class of such potentials is interesting because inside of it the property of discreteness of the charge in the nature is reproduced in the theory in natural way.
منابع مشابه
Convergence of the Schwinger — DeWitt expansion for some potentials
It is studied time dependence of the evolution operator kernel for the Schrödinger equation with a help of the Schwinger — DeWitt expansion. For many of potentials this expansion is divergent. But there were established nontrivial potentials for which the Schwinger — DeWitt expansion is convergent. These are, e.g., V = g/x, V = −g/ cosh x, V = g/ sinh x, V = g/ sin x. For all of them the expans...
متن کاملExamples of potentials with convergent Schwinger — DeWitt expansion
Convergence of the Schwinger — DeWitt expansion for the evolution operator kernel for special class of potentials is studied. It is shown, that this expansion, which is in general case asymptotic, converges for the potentials considered (widely used, in particular, in one-dimensional many-body problems), and besides, convergence takes place only for definite discrete values of the coupling cons...
متن کاملMethod for calculating the imaginary part of the Hadamard elementary function G „1... in static, spherically symmetric spacetimes
Whenever real particle production occurs in quantum field theory, the imaginary part of the Hadamard elementary function G (1) is non-vanishing. A method is presented whereby the imaginary part of G (1) may be calculated for a charged scalar field in a static spherically symmetric spacetime with arbitrary curvature coupling and a classical electromagnetic field A. The calculations are performed...
متن کاملO ct 1 99 5 hep - th / 9509005 Off - Diagonal Elements of the DeWitt Expansion from the Quantum Mechanical Path Integral
The DeWitt expansion of the matrix element M xy = x| exp −[ 1 2 (p − A) 2 + V ]t |y, (p = −i∂) in powers of t can be made in a number of ways. For x = y (the case of interest when doing one-loop calculations) numerous approaches have been employed to determine this expansion to very high order; when x = y (relevant for doing calculations beyond one-loop) there appear to be but two examples of p...
متن کاملOn the Evolution Operator Kernel for the Coulomb and Coulomb–like Potentials
With a help of the Schwinger — DeWitt expansion analytical properties of the evolution operator kernel for the Schrödinger equation in time variable t are studied for the Coulomb and Coulomb-like (which behaves themselves as 1/|~q| when |~q| → 0) potentials. It turned out to be that the Schwinger — DeWitt expansion for them is divergent. So, the kernels for these potentials have additional (bey...
متن کامل