Related papers: Vacuum Expectation Values of the Quantum Fields
A framework for quantum field theory coupled to three-dimensional quantum gravity is proposed. The coupling with quantum gravity regulates the Feynman diagrams. One recovers the usual Feynman amplitudes in the limit as the cosmological…
We present an axiomatization of non-relativistic Quantum Mechanics for a system with an arbitrary number of components. The interpretation of our system of axioms is realistic and objective. The EPR paradox and its relation with realism is…
This extended write-up of a talk gives an introductory survey of mathematical problems of the quantization of gauge systems. Using the Schwinger model as an exactly tractable but nontrivial example which exhibits general features of gauge…
Infinite statistics in which all representations of the symmetric group can occur is known as a special case of quon theory. However, the validity of relativistic quon theories is still in doubt. In this paper we prove that there exists a…
We show that the principles of a ''complete physical theory'' and the conclusions of the standard quantum mechanics do not irreconcilably contradict each other as is commonly believed. In the algebraic approach, we formulate axioms that…
A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner…
We study several examples from quantum control theory in the framework of Wigner functions and measures for infinite dimensional open quantum systems. An axiomatic definition of coherent quantum feedback is proposed within this setting.
The existence of inequivalent representations in quantum field theory with {\it finitely} many degrees of freedom is shown. Their properties are exemplified and analysed for concrete and simple models. In particular the relations to…
Basing on the theory of Feynman's influence functional and its hierarchical equations of motion, we develop a linear response theory for quantum open systems. Our theory provides an effective way to calculate dynamical observables of a…
Quantum diffusion, as developed in the 1990s, could explain how a system, subject to measurement, goes into an eigenstate of the measured observable. Here it is shown that quantum diffusion theory can be interpreted as a result within…
The quantum field theories (QFT) constructed in [1,2] include phenomenology of interest. The constructions approximate: scattering by $1/r$ and Yukawa potentials in non-relativistic approximations; and the first contributing order of the…
We give a pedagogical introduction to quantum anomalies, how they are calculated using various methods, and why they are important in condensed matter theory. We discuss axial, chiral, and gravitational anomalies as well as global…
The notion of the quantum angle is introduced. The quantum angle turns out to be a metric on the set of physical states of a quantum system. Its kinematics and dynamics is studied. The certainty principle for quantum systems is formulated…
Relativistic quantum transport theory has begun to play an important role in the space-time description of matter under extreme conditions of high energy density in out-of-equilibrium situations. The following introductory lectures on some…
Quantum field theory is constructed upon the assumption of stabilities of the vacuum and of the one-particle state. For finite temperature, the one-particle state becomes unstable because of thermal fluctuations, whereas the thermal vacuum…
The vacuum correlations of the gravitational field are highly non-trivial to be defined and computed, as soon as their arguments and indices do not belong to a background but become dynamical quantities. Their knowledge is essential however…
We give a tutorial exposition of the analogue of the filtering equation for quantum systems focusing on the quantum probabilistic framework and developing the ideas from the classical theory. Quantum covariances and conditional expectations…
The primary ingredients of reality are the universal quantum fields, which fluctuate persistently, spontaneously, and randomly. The general perception of the scientific community is that these quantum fluctuations are due to the uncertainty…
We give a mathematical definition of quantum field theory on a manifold, and definition of quantization of a classical field theory given by a variational principle.
We consider the quantum Hall effect in terms of an effective field theory formulation of the edge states, providing a natural common framework for the fractional and integral effects.