Related papers: Spaces of Quantum Field Theories
We show that many well-known quantum field theories emerge as representations of a single $^\ast$-algebra. These include free quantum field theories in flat and curved space-times, lattice quantum field theories, Wightman quantum field…
In this chapter I discuss the impact of concepts of Quantum Field Theory in modern Condensed Physics. Although the interplay between these two areas is certainly not new, the impact and mutual cross-fertilization has certainly grown…
Quantum fields are shown to provide an example of infinite-dimensional quantum groups. A dictionary is established between quantum field and quantum group concepts: the expectation value over the vacuum is the counit, Wick's theorem is the…
It is described how quantum field theory went from a theory for calculating the properties of stationary states, in the mold of quantum mechanics, to the scattering-focused theory we know today. This development is located as originating in…
We review the status of (scalar) quantum field theory on curved spacetimes using a novel formulation in terms of non linear functionals over the smooth configuration fields. In particular, this entails also a new foundation of locally…
By studying the geometric properties of correlation functions on the theory space, we are naturally led to a connection for the infinite dimensional vector bundle of composite fields over the theory space. We show how the short distance…
In modern quantum information theory one deals with an idealized situation when the spacetime dependence of quantum phenomena is neglected. However the transmission and processing of (quantum) information is a physical process in spacetime.…
Since the quantum field theory treats a system of particles, there must be a distribution which is associated with the system of particles. It means that a meaningful quantity is adjoined in the system of particles. It seems that these…
We examine quantum field theory in spacetimes that are time nonorientable but have no other causal pathology. These are Lorentzian universes-from-nothing, spacetimes with a single spacelike boundary that nevertheless have a smooth…
In the present paper we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution…
We discuss quantum theory of fields \phi defined on (d+1)-dimensional manifold {\cal M} with a boundary {\cal B}. The free action W_{0}(\phi) which is a bilinear form in \phi defines the Gaussian measure with a covariance (Green function)…
I briefly review several important formal theory developments in quantum field theory and string theory that were reported at ICHEP conferences in past decades, and explain how they underlie a new research area referred to as physical or…
In this article a non--technical survey is given of the present status of Axiomatic Quantum Field Theory and interesting future directions of this approach are outlined. The topics covered are the universal structure of the local algebras…
In spacetime physics, we frequently need to consider a set of all spaces (`universes') as a whole. In particular, the concept of `closeness' between spaces is essential. However, there has been no established mathematical theory so far…
Symmetries are a central concept in our understanding of physics. In quantum theories, a quantum reference frame (QRF) can be used to distinguish between observables related by a symmetry. The framework of operational QRFs provides a means…
Group field theories are particular quantum field theories defined on D copies of a group which reproduce spin foam amplitudes on a space-time of dimension D. In these lecture notes, we present the general construction of group field…
Without a complete theory of quantum gravity, the question of how quantum fields and quantum particles behave in a superposition of spacetimes seems beyond the reach of theoretical and experimental investigations. Here we use an extension…
At present, our notion of space is a classical concept. Taking the point of view that quantum theory is more fundamental than classical physics, and that space should be given a purely quantum definition, we revisit the notion of Euclidean…
Quantum field theory at finite temperature and density can be used for describing the physics of relativistic plasmas. Such systems are frequently encountered in astrophysical situations, such as the early Universe, Supernova explosions,…
The notion of a coherent space is a nonlinear version of the notion of a complex Euclidean space: The vector space axioms are dropped while the notion of inner product is kept. Coherent spaces provide a setting for the study of geometry in…