Related papers: Vertical Integration from the Large Hilbert Space
A complete treatment of the (2,2) NSR string in flat (2+2) dimensional space-time is given, from the formal path integral over N=2 super Riemann surfaces to the computational recipe for amplitudes at any loop or gauge instanton number. We…
We discuss the possibility of introducing a multi-resolution in a Hilbert space which is not necessarily a space of functions. We investigate which of the classical properties can be translated to this more general framework and the way in…
We develop the BRST-BV approach to construct the general off-shell Lorentz covariant cubic, quartic, $e$-tic interaction vertices for irreducible higher spin fields on $d$-dimensional Minkowski space. We consider two different cases for…
Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…
The transition amplitudes for the free spinless and spinning relativistic particles are obtained by applying an operator method developed long ago by Dirac and Schwinger to the BFV form of the BRST theory for constrained systems.
We first analyze the anti-BRST and double BRST structures of a certain higher derivative theory that has been known to possess BRST symmetry associated with its higher derivative structure. We discuss the invariance of this theory under…
In this work, we investigate a theory of stochastic integration for operator-valued processes with respect to semimartingales taking values in the dual of a nuclear space. Our construction of this particular stochastic integral relies on…
The aim of this lecture is to present in a comprehensible way what the BRST quantization means and how the "classical" master equation, action and BRST transformations have to be prolonged towards the same "quantum" items. The presentation…
We propose a variable metric forward-backward splitting algorithm and prove its convergence in real Hilbert spaces. We then use this framework to derive primal-dual splitting algorithms for solving various classes of monotone inclusions in…
The one-sided and full Hilbert transforms are evaluated exactly by means of the method of finite-part integration [E.A. Galapon, \textit{Proc. Roy. Soc. A} \textbf{473}, 20160567 (2017)]. In general, the result consists of two terms -- the…
The Batalin-Vilkovisky (BV) formalism is a powerful generalization of the BRST approach of gauge theories and allows to treat more general field theories. We will see how, starting from the case of a finite dimensional configuration space,…
Functional analysis, especially the theory of Hilbert spaces and of operators on these, form an important area in mathematics. We formalized the Isabelle/HOL library Complex_Bounded_Operators containing a large amount of theorems about…
We present an alternative construction of the infinite dimensional It\^{o} integral with respect to a Hilbert space valued L\'{e}vy process. This approach is based on the well-known theory of real-valued stochastic integration, and the…
We discuss the extended BRST and anti-BRST symmetry (including shift symmetry) in the Batalin-Vilkovisky (BV) formulation for two and three form gauge theories. Further we develop the superspace formulation for the BV actions for these…
BRST-methods provide elegant and powerful tools for the construction and analysis of constrained systems, including models of particles, strings and fields. These lectures provide an elementary introduction to the ideas, illustrated with…
This paper is a sequel to [6]. In that paper we transferred the discussions in [1] and [13] concerning almost invariant half-spaces for operators on complex Banach spaces to the context of operators on Hilbert space, and we gave easier…
We present a geometric interpretation of the integration-by-parts formula on an arbitrary vector bundle. As an application we give a new geometric formulation of higher-order variational calculus.
Usually, the dynamics of linear time-invariant systems described by an integral operator of convolution type, which is defined in the Hilbert space of Lebesgue square integrable functions on the whole line. Such a description leads to…
Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a…
This paper proposes a novel multiscale estimator for the integrated volatility of an Ito process, in the presence of market microstructure noise (observation error). The multiscale structure of the observed process is represented…