Quantum energy inequalities and local covariance II: Categorical formulation

We formulate Quantum Energy Inequalities (QEIs) in the framework of locally covariant quantum field theory developed by Brunetti, Fredenhagen and Verch, which is based on notions taken from category theory. This leads to a new viewpoint on the QEIs, and also to the identification of a new structural property of locally covariant quantum field theory, which we call Local Physical Equivalence. Covariant formulations of the numerical range and spectrum of locally covariant fields are given and investigated, and a new algebra of fields is identified, in which fields are treated independently of their realisation on particular spacetimes and manifestly covariant versions of the functional calculus may be formulated.Comment: 27 pages, LaTeX. Further discussion added. Version to appear in General Relativity and Gravitatio

General Covariance in Algebraic Quantum Field Theory

In this review we report on how the problem of general covariance is treated within the algebraic approach to quantum field theory by use of concepts from category theory. Some new results on net cohomology and superselection structure attained in this framework are included.Comment: 61 pages, 3 figures, LaTe

Family Genericity

Type abstraction in object-oriented languages embody two techniques, each with its own strenghts and weaknesses. The first technique is extension, yielding abstraction mechanisms with good support for gradual specification.The prime example is inheritance. The second technique is functional abstraction, yielding more precise knowledge about the outcome. The prime example is type parameterized classes. This paper argues that these techniques should beclearly separated to work optimally, and also that current languages fail to do this.We have applied this design philosophy to a language based on an extension mechanism, namely virtual classes. As a result, some elements based on functional abstraction have been introduced, but they are simple and only used for things where they excel; conversely, the virtual classes have become more flexible, because their role is now more well-defined.We designate the result as family genericity. The presented language design has been implemented