Janos Polonyi

It is well known that a minimal distance emerges in quantum field theories owing to the need to regularize the UV divergences. The macroscopical limit at large minimal distance, and weak spatial resolution, is investigated for a self-interacting scalar quantum field theory with the help of the renormalization group. The lowering of the cutoff always opens the dynamics, hence the renormalization group has to be implemented for open quantum field theories. A strongly coupled nonrelativistic scaling regime is found, supporting a second-order phase transition between weakly and strongly open theories. The weakly (strongly) open bare theories develop into strongly (weakly) open dynamics during the renormalization group flow. The two known conditions of the classical limit, the strong decoherence and the suppression of the quantum fluctuations, are confirmed for closed bare theories at distances beyond a nonrelativistic correlation length.

The renormalization group method, more specifically the Wegner-Houghton equation, is used to find first order phase transitions in a simple scalar field theory with a polynomial potential. An improved definition of the running parameters allows us to explore the renormalization group flow down to the IR endpoint and to locate phase transitions. Beyond the expected first order transition further radiative correction generated first and second order transitions are found. The phase diagram is reviewed by a Monte-Carlo simulation of the lattice regulated version of the theory but the serious slow down of the convergence prevents us from obtaining conclusive results from the simulation. Published by the American Physical Society 2024

We discuss the problem of the quantization and dynamic evolution of a scalar free field in the interior of a Schwarzschild black hole. A unitary approach to the dynamics of the quantized field is proposed: a time-dependent Hamiltonian governing the Heisenberg equations is derived. It is found that the system is represented by a set of harmonic oscillators coupled via terms corresponding to the creation and annihilation of pairs of particles and that the symmetry properties of the spacetime, homogeneity and isotropy are obeyed by the coupling terms in the Hamiltonian. It is shown that Heisenberg equations for annihilation and creation operators are transformed into ordinary differential equations for appropriate Bogolyubov coefficients. Such a formulation leads to a general question concerning the possibility of gravitationally driven instability, that is however excluded in this case.

This is a nice and easily readable essay about the evergreen subject of the statistical time arrow. My remarks and suggestions are the following: - The homogeneous probability distribution in a continuous space is not an indication of equilibrium or...

The master equation for the reduced density matrix of a charged particle interacting with a translation invariant weakly coupled environment is considered. The electric current is renormalized by the system-environment interaction, leading to a direct signature of the environment in the bremsstrahlung. The general solution is given in the absence of the external electromagnetic field, and the spread and the decoherence of a wave packet are followed. The increased complexity and importance of the boundary conditions for the density matrix are pointed out.

The functional renormalization group flow of a scalar field theory with quartic couplings and a sharp spatial momentum cutoff is presented in four-dimensional Minkowski space-time for the bare action by retaining the entanglement of the IR and the UV particle modes. It is argued that the open interaction channels have to be taken into account in quantum field theory defined by the help of a cutoff, and a non-perturbative UV-IR entanglement is found in closed or almost closed models.

It is shown that the mixed states of a closed dynamics supports a reduplicated symmetry, which is reduced back to the subgroup of the original symmetry group when the dynamics is open. The elementary components of the open dynamics are defined as operators of the Liouville space in the irreducible representations of the symmetry of the open system. These are tensor operators in the case of rotational symmetry. The case of translation symmetry is discussed in more detail for harmonic systems.

Classical physics is approached from quantum mechanics in the macroscopic limit. The technical device to achieve this goal is the quantum version of the central limit theorem, derived for an observable at a given time and for the time-dependent expectation value of the coordinate. The emergence of the classical trajectory can be followed for the average of an observable over a large set of independent microscopical systems, and the deterministic classical laws can be recovered in all practical purposes, owing to the largeness of Avogadro’s number. This result refers to the observed system without considering the measuring apparatus. The emergence of a classical trajectory is followed qualitatively in Wilson’s cloud chamber.

The null energy condition is considered the most fundamental of the energy conditions, on which several key results, such as the singularity theorems, are based. The Casimir effect is one of the rare equilibrium mechanisms by which it is breached without invoking modified gravity or nonminimal couplings to exotic matter. In this work we propose an independent dynamical mechanism by which it is violated, with the only ingredients being standard (but nonperturbative) quantum field theory and a minimally coupled scalar field in a double-well potential. As for the Casimir effect, we explain why the averaged null energy condition is not violated by this mechanism. Nevertheless, the transient behavior could have profound impacts in early universe cosmology.