Related papers: Application of symbol-operator technique for effec…
The paper suggests a method of extrapolation of notion of one-sided semi-infinite sequences representing traces of two-sided band-limited sequences; this features ensure uniqueness of this extrapolation and possibility to use this for…
We present a new method to propagate $p$-adic precision in computations, which also applies to other ultrametric fields. We illustrate it with many examples and give a toy application to the stable computation of the SOMOS 4 sequence.
We study the performance of the perturbative bias expansion when combined with the multi-tracer technique, and their impact on the extraction of cosmological parameters. We consider two populations of tracers of large-scale structure and…
Analysis of execution traces plays a fundamental role in many program analysis approaches, such as runtime verification, testing, monitoring, and specification mining. Execution traces are frequently parametric, i.e., they contain events…
Using the technique of labeled operators, compact explicit expressions are given for all traced heat kernel coefficients containing zero, two, four and six covariant derivatives, and for diagonal coefficients with zero, two and four…
In previous work, we gave a local formula for the index of Heisenberg elliptic operators on contact manifolds. We constructed a cocycle in periodic cyclic cohomology which, when paired with the Connes-Chern character of the principal…
We re express the fermion's probability amplitude as a trace over spinor indices, which formulation surprisingly does not exist in literature. This formulation puts the probabilty amplitude and the the probabilty(squared amplitude) of a…
We calculate the beta-functions for an open string sigma-model in the presence of a U(1) background. Passing to N=2 boundary superspace, in which the background is fully characterized by a scalar potential, significantly facilitates the…
The higher derivative expansion of the one-loop effective action for an external scalar potential is calculated to order O(T**7), using the string-inspired Bern-Kosower method in the first quantized path integral formulation. Comparisons…
Efficiency of intrinsic operator techniques (using only products and ranks of tensor operators) is first evidenced by condensed proofs of already known $\bigtriangledown$-triangle sum rules of su(2)/su$_q$(2). {\em A new compact}…
In this paper we obtain explicit formulas for the traces of Hecke operators on spaces of cusp forms in certain instances related to arithmetic triangle groups. These expressions are in terms of hypergeometric character sums over finite…
Suzuki-Trotter decompositions of exponential operators like $\exp(Ht)$ are required in almost every branch of numerical physics. Often the exponent under consideration has to be split into more than two operators, for instance as local…
An algorithm for numerically computing the exponential of a matrix is presented. We have derived a polynomial expansion of $e^x$ by computing it as an initial value problem using a symbolic programming language. This algorithm is shown to…
We prove a formula for a characteristic polynomial of an operator expressed as a polynomial of rank 1 operators. The formula uses a discrete analog of path integration and implies a generalization of the Forman-Kenyon's formula [4,6] for a…
This paper considers computational methods that split a vector field into three components in the case when both the vector field and the split components might be unbounded. We first employ classical Taylor expansion which, after some…
We establish higher order trace formulas for pairs of contractions along a multiplicative path generated by a self-adjoint operator in a Schatten-von Neumann ideal, removing earlier stringent restrictions on the kernel and defect operator…
A first order trace formula is obtained for a regular differential operator perturbed by a finite signed measure multiplication operator.
We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses different forms of integral operators that generalizes the…
We develop a general gauge invariant construction of the one-loop effective action for supersymmetric gauge field theories formulated in ${\cal N}=1/2$ superspace. Using manifestly covariant techniques (the background superfield method and…
A supersymmetric theory in two-dimensions has enough data to define a noncommutative space thus making it possible to use all the tools of noncommutative geometry. In particular, we apply this to the N=1 supersymmetric non-linear sigma…