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I outline why the renormalisation group is needed to analyse the scale dependence and hence determine the power counting for effective theories of strongly interacting systems. I summarise the results of several such analyses for two- and…
A perturbative formulation of algebraic field theory is presented, both for the classical and for the quantum case, and it is shown that the relation between them may be understood in terms of deformation quantization.
In the framework of the recently proposed asymptotically finite gauge models the cosmological constant is essentially weakened by quantum effects. The next (and more general) claim is that the coupling between quantum fields may suppress…
We classify the unitary, renormalizable, Lorentz violating quantum field theories of interacting scalars and fermions, obtained improving the behavior of Feynman diagrams by means of higher space derivatives. Higher time derivatives are not…
There is a large class of classical null-fronted metrics in which a free scalar field has an infinite number of conservation laws. In particular, if the scalar field is quantized, the number of particles is conserved. However, with more…
The topic of quantum reference frames (QRFs) has attracted a great deal of attention in the recent literature. Potentially, the correct description of such frames is important for both the technological applications of quantum mechanics and…
Because the subject of relativistic quantum field theory (QFT) contains all of non-relativistic quantum mechanics, we expect quantum field computation to contain (non-relativistic) quantum computation. Although we do not yet have a quantum…
We review the application of the loop representation to gauge theories and general relativity. The emphasis lies on exhibiting the loop calculus techniques, and their application to the canonical quantization. We discuss the role that knot…
Detecting nonclassical properties that do not allow classical interpretation of photoelectric counting events is one of the crucial themes in quantum optics. Observation of individual nonclassical effects for a single-mode field, however,…
Concerning renormalisation group theory applied to phase transitions, we examine the value of positive numerical and analytical evidence, the divergent short-wavelength behaviour of classical free fields and the absence of UV-divergences in…
It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation…
A new representation for canonical gravity and supergravity is presented, which combines advantages of Ashtekar's and the Wheeler~DeWitt representation: it has a nice geometric structure and the singular metric problem is absent. A formal…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from…
Ever since the appearance of renormalization theory there have been several differently motivated attempts at non-localized (in the sense of not generated by point-like fields) relativistic particle theories, the most recent one being at…
We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically…
In this work we develop a re-formulation of quantum field theory through the more general weighted Lorentz invariant measures that the definition of quantum fields allows; this approach provides finite answers for the long-live problems of…
Quantum-mechanical concepts can be formulated in constructive finite terms without loss of their empirical content if we replace a general unitary group by a unitary representation of a finite group. Any linear representation of a finite…
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…
The modern quantum theory is based on the assumption that quantum states are represented by elements of a complex Hilbert space. It is expected that in future quantum theory the number field will be not postulated but derived from more…
This article shows that one can consistently incorporate nonunitary representations of at least one group into the ``ordinary'' nonrelativistic quantum mechanics. This group turns out to be Lorentz group thus giving us an alternative…