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Two very different problems that can be studied by renormalization group methods are discussed with the aim of showing the conceptual unity that renormalization group has introduced in some areas of theoretical Physics. The two problems…
The procedures to overcome nonrenormalizability of \phi^4_n, n\ge5, quantum field theory models that were presented in a recent paper are extended to address nonrenormalizability of \phi^p_3, p=8,10,12,..., models. The principles involved…
In this paper, we develop a wave function renormalization scheme for models of non-relativistic quantum particles interacting with a quantized relativistic field, in the Hamiltonian formalism of quantum field theory. We construct the…
Most renormalizable quantum field theories can be rephrased in terms of Feynman diagrams that only contain dressed irreducible 2-, 3-, and 4-point vertices. These irreducible vertices in turn can be solved from equations that also only…
Traditional quantum field theory can lead to enormous zero-point energy, which markedly disagrees with experiment. Unfortunately, this situation is built into conventional canonical quantization procedures. For identical classical theories,…
The neutral massless scalar quantum field $\Phi$ in four-dimensional space-time is considered, which is subject to a simple bilinear self-interaction. Is is well-known from renormalization theory that adding a term of the form…
The problem of renormalization of the semiclassical one-loop equations used in the non-equilibrium field theory is considered. Recently, the renormalizability of such equations has been justified for some special cases of classical field…
Quantum field theory currently has a single standard mathematical characterization (the Standard Model), but no single accepted conceptual framework to interpret the mathematics. Many of these conceptualizations rely on intuitive concepts…
The state space and observables for the leading order of the large-N theory are constructed. The obtained model ("theory of infinite number of fields") is shown to obey Wightman-type axioms (including invariance under boost transformations)…
The main theme of the paper is the detailed discussion of the renormalization of the quantum field theory comprising two interacting scalar fields. The potential of the model is the fourth-order homogeneous polynomial of the fields,…
I suggest that the current situation in quantum field theory (QFT) provides some reason to question the universal validity of ontological reductionism. I argue that the renormalization group flow is reversible except at fixed points, which…
We obtain the exact non-perturbative solution of a scalar field theory defined on a space with noncommuting position and momentum coordinates. The model describes non-locally interacting charged particles in a background magnetic field. It…
Using continuous wavelet transform it is possible to construct a regularization procedure for scale-dependent quantum field theory models, which is complementary to functional renormalization group method in the sense that it sums up the…
In this thesis the two-particle-irreducible (2PI) formalism is investigated with several applications, particular emphasis on renormalizability. In the O(N) symmetric scalar quantum field theory formulated with auxiliary fields it is…
It is shown that the Sigma-Omega model which is widely used in the study of nuclear relativistic many-body problem can exactly be treated as an Abelian massive gauge field theory. The quantization of this theory can perfectly be performed…
We review realistic models that reproduce quantum theory in some limit and yield potentially new physics outside that limit. In particular, we consider deterministic hidden-variables theories (such as the pilot-wave model) and their…
The problem of an enormously large energy density of the quantum vacuum is discussed in connection with the concept of renormalization of physical parameters in quantum field theory. Using the method of dimensional regularization, it is…
Resonance and decay phenomena are ubiquitous in the quantum world. To understand them in their complexity it is useful to study solvable models in a wide sense, that is, systems which can be treated by analytical means. The present review…
We approach the study of non--integrable models of two--dimensional quantum field theory as perturbations of the integrable ones. By exploiting the knowledge of the exact $S$-matrix and Form Factors of the integrable field theories we…
A definition is given, in the framework of stochastic quantization, for the dynamics of a system composed of classical and quantum degrees of freedom mutually interacting. It is found that the theory breaks reflection positivity, and hence…