Related papers: Osterwalder-Schrader axioms - Wightman Axioms
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…
Motivated by the recent rapid development of complexity theory applied to quantum mechanical processes we present the complete derivation of Nielsen's complexity of unitaries belonging to the representations of oscillator group. Our…
Group representations play a central role in theoretical physics. In particular, in quantum mechanics unitary --- or, in general, projective unitary --- representations implement the action of an abstract symmetry group on physical states…
This paper is concerned with a structural analysis of euclidean field theories on the euclidean sphere. In the first section we give proposal for axioms for a euclidean field theory on a sphere in terms of C*-algebras. Then, in the second…
The description of space-time in a quantum theoretical framework must be considered as a fundamental problem in physics. Most attempts start with an already given classical space-time - then the quantization is done. In contrast to this the…
Based on the concept of curved spacetime in Einsteinian General Relativity, the field theories and their quantum theories in the curved octonion spaces etc are discussed. The research results discover the close relationships of the curved…
The challenges posed by the development of field theories, both classical and quantum, force us to question their most basic and foundational ideas like the role and origin of space-time, the meaning of physical states, etc. Among them the…
Algebraic quantum field theory, or AQFT for short, is a rigorous analysis of the structure of relativistic quantum mechanics. It is formulated in terms of a net of operator algebras indexed by regions of a Lorentzian manifold. In several…
We explore a field theoretical approach to quantum computing and control. This book consists of three parts. The basics of systems theory and field theory are reviewed in Part I. In Part II, a gauge theory is reinterpreted from a systems…
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 principles of the theory of quantum groups are reviewed from the point of view of the possibility of their use for deformations of symmetries in physical models. The R-matrix approach to the theory of quantum groups is discussed in…
We discuss a general model for effective quantum field theories (QFTs), which for example comprises quantum chromodynamics and quantum electrodynamics. We assume in the model a perturbative expansion of the Lagrangian with respect to a…
A nonlinear Wightman field is taken to be a nonlinear map from a linear space of test functions to a linear space of Hilbert space operators, with inessential modifications to other axioms only to the extent dictated by the introduction of…
de Sitter symmetry on quantum level implies that operators describing a given system satisfy commutation relations of the de Sitter algebra. This approach gives a new perspective on fundamental notions of quantum theory. We discuss…
Quantum mechanics postulates the existence of states determined by a particle position at a single time. This very concept, in conjunction with superposition, induces much of the quantum-mechanical structure. In particular, it implies the…
We discuss new approaches to fundamental problems of mathematics and mathematical physics such as mathematical foundation of quantum field theory, the Riemann hypothesis, and construction of noncommutative algebraic geometry.
Quantization of the system comprising gravitational, fermionic and electromagnetic fields is developed in the loop representation. As a result we obtain a natural unified quantum theory. Gravitational field is treated in the framework of…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…
Several complications arise in quantum field theory because of the infinite many degrees of freedom. However, the distinction between one-particle and many-particle effects -- mainly induced by the vacuum -- is not clear up to now. A field…
In this dissertation the question of the unification of quantum theory and general relativity is treated. Based on the conceptual structure of these theories and under incorporation of certain ideas from classical philosophy there are…