Renormalized spectrum of quasiparticle in limited number of states, strongly interacting with two-mode polarization phonons at T=0 K

Within unitary transformed Hamiltonian of Fröhlich type, using the Green's functions method, exact renormalized energy spectrum of quasiparticle strongly interacting with two-mode polarization phonons is obtained at T=0 K in a model of the system with limited number of its initial states. Exact analytical expressions for the average number of phonons in ground state and in all satellite states of the system are presented. Their dependences on a magnitude of interaction between quasiparticle and both phonon modes are analyzed.

Running vacuum in quantum field theory in curved spacetime: renormalizing $$\rho _{vac}$$ without $$\sim m^4$$ terms

The $$\Lambda $$Λ-term in Einstein’s equations is a fundamental building block of the ‘concordance’ $$\Lambda $$ΛCDM model of cosmology. Even though the model is not free of fundamental problems, they have not been circumvented by any alternative dark energy proposal either. Here we stick to the $$\Lambda $$Λ-term, but we contend that it can be a ‘running quantity’ in quantum field theory (QFT) in curved space time. A plethora of phenomenological works have shown that this option can be highly competitive with the $$\Lambda $$ΛCDM with a rigid cosmological term. The, so-called, ‘running vacuum models’ (RVM’s) are characterized by the vacuum energy density, $$\rho _{vac}$$ρvac, being a series of (even) powers of the Hubble parameter and its time derivatives. Such theoretical form has been motivated by general renormalization group arguments, which look plausible. Here we dwell further upon the origin of the RVM structure within QFT in FLRW spacetime. We compute the renormalized energy-momentum tensor with the help of the adiabatic regularization procedure and find that it leads essentially to the RVM form. This means that $$\rho _{vac}(H)$$ρvac(H) evolves as a constant term plus dynamical components $${{\mathcal {O}}}(H^2)$$O(H2) and $$\mathcal{O}(H^4)$$O(H4), the latter being relevant for the early universe only. However, the renormalized $$\rho _{vac}(H)$$ρvac(H) does not carry dangerous terms proportional to the quartic power of the masses ($$\sim m^4$$∼m4) of the fields, these terms being a well-known source of exceedingly large contributions. At present, $$\rho _{vac}(H)$$ρvac(H) is dominated by the additive constant term accompanied by a mild dynamical component $$\sim \nu H^2$$∼νH2 ($$|\nu |\ll 1$$|ν|≪1), which mimics quintessence.

CR-HARMONIC MAPS

We develop the notion of renormalized energy in Cauchy–Riemann (CR) geometry for maps from a strictly pseudoconvex pseudo-Hermitian manifold to a Riemannian manifold. This energy is a CR invariant functional whose critical points, which we call CR-harmonic maps, satisfy a CR covariant partial differential equation. The corresponding operator coincides on functions with the CR Paneitz operator.

Heteroclinic connections for nonlocal equations

We construct heteroclinic orbits for a strongly nonlocal integro-differential equation. Since the energy associated to the equation is infinite in such strongly nonlocal regime, the proof, based on variational methods, relies on a renormalized energy functional, exploits a perturbation method of viscosity type, combined with an auxiliary penalization method, and develops a free boundary theory for a double obstacle problem of mixed local and nonlocal type. The description of the stationary positions for the atom dislocation function in a perturbed crystal, as given by the Peierls–Nabarro model, is a particular case of the result presented.

Aspects of the BTZ black hole interacting with fields

We show that there is no superradiance for the Dirac field in the rotating BTZ black hole if the field vanishes at infinity. Then we outline the calculation of the expression for the renormalized energy–momentum tensor, the effective action as well as the heat kernel for the Dirac field for the BTZ black hole. Finally, we point out how to construct the Hartle–Hawking–Israel state for the real scalar field in the non-rotating BTZ black hole in two and three dimensions.

Self-energy renormalization for inhomogeneous nonequilibrium systems and field expansion via complete set of time-dependent wavefunctions

The way to determine the renormalized energy of inhomogeneous systems of a quantum field under an external potential is established for both equilibrium and nonequilibrium scenarios based on thermo field dynamics. The key step is to find an extension of the on-shell concept valid in homogeneous case. In the nonequilibrium case, we expand the field operator by time-dependent wavefunctions that are solutions of the appropriately chosen differential equation, synchronizing with temporal change of thermal situation, and the quantum transport equation is derived from the renormalization procedure. Through numerical calculations of a triple-well model with a reservoir, we show that the number distribution and the time-dependent wavefunctions are relaxed consistently to the correct equilibrium forms at the long-term limit.

Energy-momentum tensor correlation function in Nf = 2 + 1 full QCD at finite temperature

We measure correlation functions of the nonperturbatively renormalized energy-momentum tensor in Nf = 2 + 1 full QCD at finite temperature by applying the gradient flow method both to the gauge and quark fields. Our main interest is to study the conservation law of the energy-momentum tensor and to test whether the linear response relation is properly realized for the entropy density. By using the linear response relation we calculate the specific heat from the correlation function. We adopt the nonperturba-tively improved Wilson fermion and Iwasaki gauge action at a fine lattice spacing = 0:07 fm. In this paper the temperature is limited to a single value T ≃ 232 MeV. The u, d quark mass is rather heavy with mπ=mρ ≃ 0:63 while the s quark mass is set to approximately its physical value.