We consider scalar field theories in dimensions lower than four in the context of the Wegner-Houghton renormalization group equations (WHRG). The renormalized trajectory makes a non-perturbative interpolation between the ultraviolet and the infrared scaling regimes. Strong indication is found that in two dimensions and below the models with polynomial… (More)
A c-number path integral representation is constructed for the solution of the Dirac equation. The integration is over the real trajectories in the continuous three-space and other two canonical pairs of compact variables controlling the spin and the chirality flips. The path integral representation of the quantum amplitudes  has become an essential… (More)
Renormalization group flow equations for scalar λΦ 4 are generated using three classes of smooth smearing functions. Numerical results for the critical exponent ν in three dimensions are calculated by means of a truncated series expansion of the blocked potential. We demonstrate how the convergence of ν as a function of the order of truncation can be… (More)
The running coupling constants are introduced in Quantum Mechanics and their evolution is described by the help of the renormalization group equation. The harmonic oscillator and the propagation on curved spaces are presented as examples. The hamiltonian and the lagrangian scaling relations are obtained. These evolution equations are used to construct low… (More)
Some features of the high temperature gluonic matter, such as the breakdown of the fundamental group symmetry by the kinetic energy, the screening of test quarks by some unusual gluon states and the explanation of the absence of isolated quarks in the vacuum without the help of infinities are presented in this talk. Special attention is paid to separate the… (More)
It is argued that universality is severely limited for models with multiple fixed points. As a demonstration the renormalization group equations are presented for the potential and the wave function renormalization constants in the O(N) scalar field theory. Our equations are superior compared with the usual approach which retains only the contributions that… (More)
The haaron gas description is reviewed for the QCD vacuum. The role of non-renormalizable operators is emphasised in the mechanism which generates the string tension. Additional examples are mentioned where certain non-renormalizable operators of the bare lagrangian turn out to be important at finite energy scale.
The authors ligated the nervus lienalis of the cat, and observed the subsequent accumulation of mitochondria in nonmyelinated axons in close vicinity proximal and distal to the ligature. In enlarged axons they found groups of mostly homogen population of mitochondria with specific morphologic signs. Concerning the mitochondrial ultrastructure authors… (More)
It is pointed out that models with condensates have nontrivial renormal-ization group flow on the tree level. The infinitesimal form of the tree level renormalization group equation is obtained and solved numerically for the φ 4 model in the symmetry broken phase. We find an attractive infrared fixed
SU(2) gauge theory with competing interactions is shown to possess a rich phase structure with anti-ferromagnetic vacua. It is argued that the phase boundaries persist in the weak coupling limit suggesting the existence of different renormalized continuum theories for QCD.