Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFock space on $mathbb{C}^infty$ and Bose-Fock space
143
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this paper, we introduce the Fock space over $mathbb{C}^{infty}$ and obtain an isomorphism between the Fock space over $mathbb{C}^{infty}$ and Bose-Fock space. Based on this isomorphism, we obtain representations of some operators on the Bose-Fock space and answer a question in cite{coburn1985}. As a physical application, we study the Gibbs state.
rate research
Read More
We obtain sufficient conditions for a densely defined operator on the Fock space to be bounded or compact. Under the boundedness condition we then characterize the compactness of the operator in terms of its Berezin transform.
In this paper we develop a framework to extend the theory of generalized stochastic processes in the Hida white noise space to more general probability spaces which include the grey noise space. To obtain a Wiener-It^o expansion we recast it as a moment problem and calculate the moments explicitly. We further show the importance of a family of topological algebras called strong algebras in this context. Furthermore we show the applicability of our approach to the study of stochastic processes.
This article is devoted to studying the non-commutative Poisson boundary associated with $Big(Bbig(mathcal{F}(mathcal{H})big), P_{omega}Big)$ where $mathcal{H}$ is a separable Hilbert space (finite or infinite-dimensional), $dim mathcal{H} > 1$, with an orthonormal basis $mathcal{E}$, $Bbig(mathcal{F}(mathcal{H})big)$ is the algebra of bounded linear operators on the full Fock space $mathcal{F}(mathcal{H})$ defined over $mathcal{H}$, $omega = {omega_e : e in mathcal{E} }$ is a sequence of positive real numbers such that $sum_e omega_e = 1$ and $P_{omega}$ is the Markov operator on $Bbig(mathcal{F}(mathcal{H})big)$ defined by begin{align*} P_{omega}(x) = sum_{e in mathcal{E}} omega_e l_e^* x l_e, x in Bbig(mathcal{F}(mathcal{H})big), end{align*} where, for $e in mathcal{E}$, $l_e$ denotes the left creation operator associated with $e$. The non-commutative Poisson boundary associated with $Big(Bbig(mathcal{F}(mathcal{H})big), P_{omega}Big)$ turns out to be an injective factor of type $III$ for any choice of $omega$. Moreover, if $mathcal{H}$ is finite-dimensional, we completely classify the Poisson boundary in terms of its Connes $S$-invarinat and curiously they are type $III _{lambda }$ factors with $lambda$ belonging to a certain small class of algebraic numbers.
The localized equivariant homology of the quiver variety of type $A_{N-1}^{(1)}$ can be identified with the level one Fock space by assigning a normalized torus fixed point basis to certain symmetric functions, Jack($mathfrak{gl}_N$) symmetric functions introduced by Uglov. We show that this correspondence is compatible with actions of two algebras, the Yangian for $mathfrak{sl}_N$ and the affine Lie algebra $hat{mathfrak{sl}}_N$, on both sides. Consequently we obtain affine Yangian action on the Fock space.
We address the construction of smooth bundles of fermionic Fock spaces, a problem that appears frequently in fermionic gauge theories. Our main motivation is the spinor bundle on the free loop space of a string manifold, a structure anticipated by Killingback, with a construction outlined by Stolz-Teichner. We develop a general framework for constructing smooth Fock bundles, and obtain as an application a complete and well-founded construction of spinor bundles on loop space.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
