Series of iterated quantum stochastic integrals
نویسندگان
چکیده
We consider series of iterated non-commutative stochastic integrals of scalar operators on the boson Fock space. We give a sufficient condition for these series to converge and to define a reasonable operator. An application of this criterion gives a condition for the convergence of some formal series of generalized integrator processes such as considered in [CEH]. .
منابع مشابه
Greedy decomposition integrals
In this contribution we define a new class of non-linear integrals based on decomposition integrals. These integrals are motivated by greediness of many real-life situations. Another view on this new class of integrals is that it is a generalization of both the Shilkret and PAN integrals. Moreover, it can be seen as an iterated Shilkret integral. Also, an example in time-series analysis is prov...
متن کاملForward and backward adapted quantum stochastic calculus and double product integrals
We show that iterated stochastic integrals can be described equivalently either by the conventional forward adapted, or by backward adapted quantum stochastic calculus. By using this equivalence we establish two properties of triangular (causal) and rectangular double quantum stochastic product integrals, namely a necessary and su¢ cient condition for their unitarity, and the coboundary relatio...
متن کاملFrom algebraic to analytic double product integrals
The algebraic theory of double product integrals and particularly its role in the quantisation of Lie bialgebras is described. When the underlying associative algebra is that of the Itô differentials of quantum stochastic calculus such product integrals are formally represented as operators which are infinite sums of iterated integrals in Fock space. In this paper we describe some of the analyt...
متن کاملIterated Integrals in Quantum Field Theory
These notes are based on a series of lectures given to a mixed audience of mathematics and physics students at Villa de Leyva in Colombia. The first half is an introduction to iterated integrals and polylogarithms, with emphasis on the case P\{0, 1,∞}. The second half gives an overview of some recent results connecting them with Feynman diagrams in perturbative quantum field theory.
متن کاملAlgebraic theory of causal double products
Corresponding to each ”rectangular” double product [5] in the form of a formal power series R[h] with coefficients in the tensor product T (L) ⊗ T (L) with itself of the Itô Hopf algebra, we construct ”triangular” elements T [h] of T (L) satisfying ∆T [h] = T [h](1)R[h]T{h](2). In Fock space representations of T (L) by iterated quantum stochastic integrals when L is the algebra of Itô different...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017