Related papers: Projective Limits of State Spaces I. Classical For…

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…

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…

Instead of formulating the states of a Quantum Field Theory (QFT) as density matrices over a single large Hilbert space, it has been proposed by Kijowski [Kijowski, 1977] to construct them as consistent families of partial density matrices,…

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…

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…

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 [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…

Interesting non-linear functions on the phase spaces of classical field theories can never be quantized immediately because the basic fields of the theory become operator valued distributions. Therefore, one is usually forced to find a…

Matrix configurations coming from matrix models comprise many important aspects of modern physics. They represent special quantum spaces and are thus strongly related to noncommutative geometry. In order to establish a semiclassical limit…

The quantization rules recently proposed by M. Navarro (and independently I.V. Kanatchikov) for a finite-dimensional formulation of quantum field theory are applied to the Klein-Gordon and the Dirac fields to obtain the quantum equations of…

Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the…

The aim of this work is to firstly demonstrate the efficacy of the recently proposed Orlicz space formalism for Quantum theory \cite{ML}, and secondly to show how noncommutative differential structures may naturally be incorporated into…

The recent controversy of applicability of quantum formalism to brain dynamics has been critically analysed. The prerequisites for any type of quantum formalism or quantum field theory is to investigate whether the anatomical structure of…

We propose a geometric setting of the axiomatic mathematical formalism of quantum theory. Guided by the idea that understanding the mathematical structures of these axioms is of similar importance as was historically the process of…

Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an…

We discuss the issues with tentative generalisations of the process matrix formalism from finite-dimensional mechanical systems all the way to quantum field theory. We present a detailed overview of possible open problems that arise when…

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…

Quantum Field Theory (QFT) makes predictions by combining assumptions about (1) quantum dynamics, typically a Schrodinger or Liouville equation; (2) quantum measurement, usually via a collapse formalism. Here I define a "classical density…

This thesis is devoted to the first-quantized approach to quantum field theory, commonly known as the 'Worldline Formalism'. It collects most of the works completed by the author during the PhD, illustrating the versatility and efficiency…

Classical mechanics has a natural mathematical setting in symplectic geometry and it may be asked if the same is true for quantum mechanics. More precisely, is it possible to capture certain quantum idiosyncrasies within the symplectic…