Related papers: What is an anomaly?
We study properties of a scalar quantum field theory on the two-dimensional noncommutative plane with $E_q(2)$ quantum symmetry. We start from the consideration of a firstly quantized quantum particle on the noncommutative plane. Then we…
The ontology emerging from quantum field theory and the results following from Bell's theorems allowed the development of an intuitive picture of the microscopic world described by quantum mechanics, that is, we can say that we understand…
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 construct a quantum theory of free fermion field based on the generalized uncertainty principle using supersymmetry as a guiding principle. A supersymmetric field theory with a real scalar field and a Majorana fermion field is given…
I discuss the general principles underlying quantum field theory, and attempt to identify its most profound consequences. The deepest of these consequences result from the infinite number of degrees of freedom invoked to implement locality.…
This is an introductory chapter of the book in progress on quantum foundations and incompleteness of quantum mechanics. Quantum mechanics is represented as statistical mechanics of classical fields.
This paper proposes a general framework for nonperturbatively defining continuum quantum field theories. Unlike most such frameworks, the one offered here is finitary: continuum theories are defined by reducing large but finite quantum…
Anomaly, a generic feature of relativistic quantum field theory, is shown to be present in non-relativistic classical ideal fluid. A new result is the presence of anomalous terms in current algebra, an obvious analogue of Schwinger terms…
We comment on the present status, the concepts and their limitations, and the successes and open problems of the various approaches to a relativistic quantum theory of elementary particles, with a hindsight to questions concerning quantum…
For classical field theories with probabilistic initial conditions the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial…
We explore the implications of restricting the framework of quantum theory and quantum computation to finite fields. The simplest proposed theory is defined over arbitrary finite fields and loses the notion of unitaries. This makes such…
Despite its name, Quantum Field Theory (QFT) has been built to describe interactions between localizable particles. For this reason the actual formalism of QFT is partly based on a suitable generalization of the one already used for systems…
Quantum field theory (QFT) based on the principles of special relativity (SR) and it is in fact the \emph{kinematic theory of fields}. The root assumption is that there is "relativistic description" of \emph{any} isolated quantum system in…
The definitions of classical and quantum singularities in general relativity are reviewed. The occurence of quantum mechanical singularities in certain spherically symmetric and cylindrically symmetric (including infinite line…
A class of quantum field theories invariant with respect to the action of an odd vector field Q on a source supermanifold $\Sigma$ is considered. We suppose that Q satisfies the conditions under which an integral of any Q-invariant function…
This article gives an elementary account of the recently proposed theory of spontaneous quantum gravity. It is argued that a viable quantum theory of gravity should be falsifiable, and hence it should dynamically explain the observed…
Quantum backflow refers to the counterintuitive fact that the probability can flow in the direction opposite to the momentum of a quantum particle. This phenomenon has been seen to be small and fragile for one-dimensional systems, in which…
Many novel quantum phenomena emerge in non-equilibrium relativistic quantum matter under extreme conditions such as strong magnetic fields and rotations. The quantum kinetic theory based on Wigner functions in quantum field theory provides…
A formal symmetry between generalized coordinates and momenta is postulated to formulate classical and quantum theories of a particle coupled to an Abelian gauge field. It is shown that the symmetry (a) requires the field to have dynamic…
Quantum Relativity is supposed to be a new theory, which locally is a deformation of Special Relativity, and globally it is a background independent theory including the main ideas of General Relativity, with hindsight from Quantum Theory.…