arXiv subjects
Publications and source records attributed to Janos Polonyi.
A non-Grassmanian path integral representation is given for the solution of the Klein-Gordon and the Dirac equations. The trajectories of the path integral are rendered differentiable by the relativistic corrections. The nonrelativistic limit is briefly discussed from the point of view of the renormalization group.
The renormalization group is applied to the phi4 model in the symmetry broken phase in order to identify different scaling regimes. The new scaling laws reflect nonuniversal behavior at the phase transition. The extension of the analysis to finite temperature is briefly outlined. It is mentioned that the coupling constants can be found in the mixed phase by taking into account the saddle points of the blocking procedure.
It is shown that in the Effective Standard Model new phenomena can arise due to the presence of small instanton configurations. The chief result is that under certain conditions new hidden coupling constants could exist in the model. In the Electroweak sector that might result in the possibility of observing B+L violating processes due to a highly non perturbative contribution to the holy grail function. The same phenomenon might occur in the QCD sector of the theory and could be observed in the DIS experiments at HERA.
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.
Certain effective vertices may generate a non-homogeneous, periodic vacuum structure. The excitations above such a vacuum are studied in the framework of the $ϕ^4$ and gauge models. The formation of the non-homogeneous vacuum is accompanied by the dynamical breakdown of the space-time inversion symmetry. Chiral transformation is introduced for bosons in close analogy with lattice fermions.
The effects of instantons close to the cut-off is studied in four dimensional SU(2) gauge theory with higher order derivative terms in the action. It is found in the framework of the dilute instanton gas approximation that the convergence of the topological observables requires non-universal beta function.
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 energy effective models.
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 are non-vanishing in the ultraviolet regime. We find an indication for the existence of relevant operators at the infrared fixed point, contrary to common expectations. This result makes the sufficiency of using only renormalizable coupling constants in parametrizing the long distance phenomena questionable.
The running coupling constants are introduced in Quantum Mechanics and their evolution is described by the help of the renormalization group equation.
It is pointed out that the universality might seriously be violated by models with several fixed points.
Blocking transformation is performed in quantum field theory at finite temperature. It is found that the manner temperature deforms the renormalized trajectories can be used to understand better the role played by the quantum fluctuations. In particular, it is conjectured that domain formation and mass parameter generation can be observed in theories without spontaneous symmetry breaking.
It is shown that the inhomogeneous saddle points of scale invariant theories make the semiclassical expansion sensitive on the choice of non-renormalizable operators. In particular, the instanton fugacity and the beta function of the two dimensional non-linear sigma model depends on apparently non-renormalizable operators. This represents a non-perturbative breakdown of that concept of universality which is based on low dimensional operators.