Modern Physics Letters A

Quantized Yang–Mills fields lie at the heart of our understanding of the strong nuclear force. To understand the theory at low energies, we must work in the strong coupling regime. The primary technique for this is the lattice. While basically an ultraviolet regulator, the lattice avoids the use of a perturbative expansion. I discuss the historical circumstances that drove us to this approach, which has had immense success, convincingly demonstrating quark confinement and obtaining crucial properties of the strong interactions from first principles.

Anisotropic dark energy model with dynamic pressure anisotropies along different spatial directions is constructed at the backdrop of a spatially homogeneous diagonal Bianchi type V (BV) spacetime in the framework of General Relativity. A time varying deceleration parameter generating a hybrid scale factor is considered to simulate a cosmic transition from early deceleration to late time acceleration. We found that the pressure anisotropies along the y- and z-axes evolve dynamically and continue along with the cosmic expansion without being subsided even at late times. The anisotropic pressure along the x-axis becomes equal to the mean fluid pressure. At a late phase of cosmic evolution, the model enters into a phantom region. From a statefinder diagnosis, it is found that the model overlaps with $\Lambda \mathrm{\text{CDM}}$ at late phase of cosmic time.

By use of the Jacobi determinant, we verify that, for a thermodynamic system which satisfies the first law of thermodynamics, if only there is second-order phase transition in the system, the Prigogine–Defay ratio is the constant 1. This conclusion is universal and independent of the concrete forms of the thermodynamic functions and also apply to black holes.

We calculate the Green’s functions for a scalar field theory with quartic interactions for which the fields are multiplied with a generic translation invariant star product. Our analysis involves both non-commutative products, for which there is the canonical commutation relation among coordinates, and nonlocal commutative products. We give explicit expressions for the one-loop corrections to the two- and four-point functions. We find that the phenomenon of ultraviolet/infrared mixing is always a consequence of the presence of non-commuting variables. The commutative part of the product does not have the mixing.

As a solution to the well-known problem that the shock wave potentially responsible for the explosion of a supernova actually tends to stall, we propose a new energy source arising from our model for dark matter. Our earlier model proposed that dark matter should consist of cm-large white dwarf-like objects kept together by a skin separating two different sorts of vacua. These dark matter balls or pearls will collect in the middle of any star throughout its lifetime. At some stage during the development of a supernova, the balls will begin to take in neutrons and then other surrounding material. By passing into a ball nucleons fall through a potential of order 10 MeV, causing a severe production of heat — of order 10 foe for a solar mass of material eaten by the balls. The temperature in the iron core will thereby be raised, splitting up the iron into smaller nuclei. This provides a mechanism for reviving the shock wave when it arrives and making the supernova explosion really occur. The onset of the heating due to the dark matter balls would at first stop the collapse of the supernova progenitor. This opens up the possibility of there being two collapses giving two neutrino outbursts, as apparently seen in the supernova SN1987A — one in Mont Blanc and one 4 h 43 min later in both IMB and Kamiokande.

We present an ideal system of interacting fermions where the solutions of the many-body Schrödinger equation can be obtained without making approximations. These exact solutions are used to test the validity of two many-body effective approaches, the Hartree–Fock and the random phase approximation theories. The description of the ground state done by the effective theories improves with increasing number of particles.

An application of the quantum N-portrait to the Universe is discussed, wherein the spacetime geometry is understood as a Bose–Einstein condensate of N soft gravitons. If near or at the critical point of a quantum phase transition, indications are found that the vacuum energy is partly suppressed by 1/N, as being due to quanta not in the condensate state. Time evolution decreases this suppression, which might have implications for cosmic expansion.