How to Describe the Space-time Structure with Nets of C*-algebras
نویسنده
چکیده
The major subject of algebraic quantum eld theory is the study of nets of local C*-algebras, i.e. maps O 7 ! A(O) assigning to each open, relatively compact region O of space-time (M; g) a C*-algebra A(O), whose self-adjoint elements describe local observables measurable in the region O. A question discussed recently in a number of papers is how much information about the geometric structure of the underlying space-time (M; g) is encoded in the algebraic structure of the net O 7 ! A(O). Following these ideas it will be demonstrated in this paper how space-time related concepts like causality and observers can be described in a purely algebraic way, i.e. using only the local algebras A(O). These results are then used to show how the space-time (M; g) can be reconstructed from the set L loc := fA(O) j O M open; O compactg of local algebras.
منابع مشابه
Primitive Ideal Space of Ultragraph $C^*$-algebras
In this paper, we describe the primitive ideal space of the $C^*$-algebra $C^*(mathcal G)$ associated to the ultragraph $mathcal{G}$. We investigate the structure of the closed ideals of the quotient ultragraph $ C^* $-algebra $C^*left(mathcal G/(H,S)right)$ which contain no nonzero set projections and then we characterize all non gauge-invariant primitive ideals. Our results generalize the ...
متن کاملArens Regularity and Weak Amenability of Certain Matrix Algebras
Motivated by an Arens regularity problem, we introduce the concepts of matrix Banach space and matrix Banach algebra. The notion of matrix normed space in the sense of Ruan is a special case of our matrix normed system. A matrix Banach algebra is a matrix Banach space with a completely contractive multiplication. We study the structure of matrix Banach spaces and matrix Banach algebras. Then we...
متن کاملNonexpansive mappings on complex C*-algebras and their fixed points
A normed space $mathfrak{X}$ is said to have the fixed point property, if for each nonexpansive mapping $T : E longrightarrow E $ on a nonempty bounded closed convex subset $ E $ of $ mathfrak{X} $ has a fixed point. In this paper, we first show that if $ X $ is a locally compact Hausdorff space then the following are equivalent: (i) $X$ is infinite set, (ii) $C_0(X)$ is infinite dimensional, (...
متن کاملOn the maximal ideal space of extended polynomial and rational uniform algebras
Let K and X be compact plane sets such that K X. Let P(K)be the uniform closure of polynomials on K. Let R(K) be the closure of rationalfunctions K with poles o K. Dene P(X;K) and R(X;K) to be the uniformalgebras of functions in C(X) whose restriction to K belongs to P(K) and R(K),respectively. Let CZ(X;K) be the Banach algebra of functions f in C(X) suchthat fjK = 0. In this paper, we show th...
متن کاملApproximate $n-$ideal amenability of module extension Banach algebras
Let $mathcal{A}$ be a Banach algebra and $X$ be a Banach $mathcal{A}-$bimodule. We study the notion of approximate $n-$ideal amenability for module extension Banach algebras $mathcal{A}oplus X$. First, we describe the structure of ideals of this kind of algebras and we present the necessary and sufficient conditions for a module extension Banach algebra to be approximately n-ideally amenable.
متن کامل