We formulate the second quantization of a charged scalar field in homogeneous, time-dependent electromagnetic fields, in which the Hamiltonian is an infinite system of decoupled, time-dependent oscillators for electric fields, but it is another infin
ite system of coupled, time-dependent oscillators for magnetic fields. We then employ the quantum invariant method to find various quantum states for the charged field. For time-dependent electric fields, a pair of quantum invariant operators for each oscillator with the given momentum plays the role of the time-dependent annihilation and the creation operators, constructs the exact quantum states, and gives the vacuum persistence amplitude as well as the pair-production rate. We also find the quantum invariants for the coupled oscillators for the charged field in time-dependent magnetic fields and advance a perturbation method when the magnetic fields change adiabatically. Finally, the quantum state and the pair production are discussed when a time-dependent electric field is present in parallel to the magnetic field.
We perform the first study for the bound states of colored scalar particles $phi$ (scalar quarks) in terms of mass generation with quenched SU(3)$_c$ lattice QCD. We investigate the bound states of $phi$, $phi^daggerphi$ and $phiphiphi$ (scalar-quark
hadrons), as well as the bound states of $phi$ and quarks $psi$, i.e., $phi^daggerpsi$, $psipsiphi$ and $phiphipsi$ (chimera hadrons). All these new-type hadrons including $phi$ have a large mass of several GeV due to large quantum corrections by gluons, even for zero bare scalar-quark mass $m_phi=0$ at $a^{-1}sim 1{rm GeV}$. We find a similar $m_psi$-dependence between $phi^daggerpsi$ and $phiphipsi$, which indicates their similar structure due to the large mass of $phi$. From this study, we conjecture that all colored particles generally acquire a large effective mass due to dressed gluons.
We find a strong evidence for the survival of $J/Psi$ and $eta_c$ as spatially-localized $cbar c$ (quasi-)bound states above the QCD critical temperature $T_c$, by investigating the boundary-condition dependence of their energies and spectral functio
ns. In a finite-volume box, there arises a boundary-condition dependence for spatially spread states, while no such dependence appears for spatially compact states. In lattice QCD, we find almost {it no} spatial boundary-condition dependence for the energy of the $cbar c$ system in $J/Psi$ and $eta_c$ channels for $Tsimeq(1.11-2.07)T_c$. We also investigate the spectral function of charmonia above $T_c$ in lattice QCD using the maximum entropy method (MEM) in terms of the boundary-condition dependence. There is {it no} spatial boundary-condition dependence for the low-lying peaks corresponding to $J/Psi$ and $eta_c$ around 3GeV at $1.62T_c$. These facts indicate the survival of $J/Psi$ and $eta_c$ as compact $cbar c$ (quasi-)bound states for $T_c < T < 2T_c$.
