Related papers: Projective Limits of State Spaces: Quantum Field T…

Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler…

Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski [Kijowski 1977] to represent quantum states as projective families of density matrices over a collection of…

In this series of papers, we investigate the projective framework initiated by Jerzy Kijowski and Andrzej Oko{\l}\'ow, which describes the states of a quantum theory as projective families of density matrices. After discussing the formalism…

Some skeptical arguments on the physical reality of quantum states are given. First, I argue that the algebraic formalism of quantum field theory in curved spacetime (algebraic QFTCS, AQFTCS) leads to such a skepticism. Of course we have…

In this series of papers, we investigate the projective framework initiated by Jerzy Kijowski and Andrzej Oko{\l}\'ow, which describes the states of a quantum (field) theory as projective families of density matrices. The present first…

It is well-known that there exist infinitely-many inequivalent representations of the canonical (anti)-commutation relations of Quantum Field Theory (QFT). A way out, suggested by Algebraic QFT, is to instead define the quantum theory as…

We present a method of constructing a space of quantum states for a field theory: given phase space of a theory, we define a family of physical systems each possessing a finite number of degrees of freedom, next we define a space of quantum…

We present a rigorous quantization scheme that yields a quantum field theory in general boundary form starting from a linear field theory. Following a geometric quantization approach in the K\"ahler case, state spaces arise as spaces of…

The holographic principle and the thermodynamics of de Sitter space suggest that the total number of fundamental degrees of freedom associated with any finite-volume region of space may be finite. The naive picture of a short distance…

In this article we propose a `second quantization' scheme especially suitable to deal with non-trivial, highly symmetric phase spaces, implemented within a more general Group Approach to Quantization, which recovers the standard Quantum…

The present paper is the companion of [1] in which we proposed a scheme that tries to derive the Quantum Field Theory (QFT) on Curved Spacetimes (CST) limit from background independent Quantum General Relativity (QGR). The constructions of…

We argue in a model-independent way that the Hilbert space of quantum gravity is locally finite-dimensional. In other words, the density operator describing the state corresponding to a small region of space, when such a notion makes sense,…

The density matrix formalism which is widely used in the theory of measurements, quantum computing, quantum description of chemical and biological systems always imply the averaging over the states of the environment. In practice this is…

In [arXiv:1411.3592] an extension of the Ashtekar-Lewandowski (AL) state space of Loop Quantum Gravity was set up with the help a projective formalism introduced by Kijowski [Kijowski 1977; see also: arXiv:1304.6330, arXiv:1411.3590]. The…

We extend the framework of general boundary quantum field theory (GBQFT) to achieve a fully local description of realistic quantum field theories. This requires the quantization of non-K\"ahler polarizations which occur generically on…

We propose a new non-perturbative method for studying UV complete unitary quantum field theories (QFTs) with a mass gap in general number of spacetime dimensions. The method relies on unitarity formulated as positive semi-definiteness of…

In this series of papers, we investigate the projective framework initiated by Jerzy Kijowski and Andrzej Oko{\l}\'ow, which describes the states of a quantum theory as projective families of density matrices. A strategy to implement the…

This work proposes a reconstruction of the quantum field theory (QFT) scattering framework: the path integral governs an interaction kernel region, while the Hilbert space encodes asymptotic free boundary conditions. We critically reexamine…

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…

In the standard construction of Quantum Field Theory, a vacuum state is required. The vacuum is a vector in a separable, infinite-dimensional Hilbert space often referred to as Fock space. By definition the vacuum wavestate depends on…