International Journal of Modern Physics B

Are there quark stars in nature? We review the question in the light of modern astrophysical observations. Quark stars have properties which are very similar to those of neutron stars. For example they are now known to have the same kind of cooling properties. Their masses may also be similar. On the other hand, gamma ray bursts (GRB), the brightest phenomenon observable at present in the sky, could possibly be conversion of normal or neutron matter on the surface of a quark star.

The best observational evidence for the existence of quark stars seems to be some compact objects, the X-Ray burst source 4U 1820-30, the X-ray pulsar Her X-1, the star 4U 1728-34 and SAX J-1808.4-3658, this last one being the stablest and fastest rotating hard X-ray pulsar known to date. The mass of at least these four objects is high and their radius is low, placing them close to the black hole line, in the mass–radius (M–R) plot.

Unlike the extremal Reissner–Nordström black hole in ordinary spacetime, the one in anti-de Sitter spacetime is a minimum of action and has zero entropy if (functional integral) quantization is carried out after extremalization. However, if extremalization is carried out after quantization, then the entropy is a quarter of the area as in the usual case. This is because the functional integral is dominated by non-extremal configurations of lower action. However, some special non-extremal black holes have higher action and may decay into extremal configurations.

An attempt is also made to see if the anti-de Sitter version can be described by a microscopic model consisting of a one-dimensional gas of massless particles as in the usual case. Such a description is possible only in the limit of vanishing cosmological constant.

We briefly review developments in string theory which explain the information puzzle that arises in the applications of quantum mechanics to black holes.

This article gives a review of the topic of regularising chiral gauge theories and is aimed at a general audience. It begins by clarifying the meaning of chirality and goes on to discussing chiral projections in field theory, parity violation and the distinction between vector and chiral field theories. It then discusses the standard model of electroweak interactions from the perspective of chirality. It also reviews at length the phenomenon of anomalies in quantum field theories including the intuitive understanding of anomalies based on the Dirac sea picture as given by Nielsen and Ninomiya. It then raises the issue of a non-perturbative and constructive definition of the standard model as well as the importance of such formulations. The second Nielsen–Ninomiya theorem about the impossibility of regularising chiral gauge theories under some general assumptions is also discussed. After a brief review of lattice regularisation of field theories, it discusses the issue of fermions on the lattice with special emphasis on the problem of species doubling. The implications of these problems to introducing chiral fermions on the lattice as well as the interpretations of anomalies within the lattice formulations and the lattice Dirac sea picture are then discussed. Finally the difficulties of formulating the standard model on the lattice are illustrated through detailed discussions of the Wilson–Yukawa method, the domain wall fermions method and the recently popular Ginsparg–Wilson method.

In quantum field theory radiative corrections can be finite but undetermined.

We give a pedagogical account of coupled cluster methods, of Hamiltonian lattice gauge theory and of the application of coupled cluster methods to the study of Hamiltonian lattice gauge theory.

There are many different models of the nucleon, the basic building block of most of the matter in the universe. We discuss the origin of the spin in different models and look for definitive experimental signals that support the view.

Evidence in support of a nonzero neutrino mass, through the phenomenon of oscillations, is steadily becoming more compelling. A pedagogic introduction to vacuum neutrino oscillations and resonant flavour conversion is presented in this paper, prefaced by a thumbnail sketch of the relevant properties of the neutrino as embodied in the Standard Model of particle physics. The recent results from solar and atmospheric neutrinos are summarised and their combined implications on neutrino properties are outlined. Some attempts to incorporate a nonzero neutrino mass in extensions of the Standard Model are briefly discussed.

After a general introduction, we discuss the motivation for supersymmetry in the light of the present status of the Standard Model of particle interactions. We then outline the MSSM which is the minimal supersymmetric extension of the latter model and focus on corresponding accelerator signals. The question of R-parity violation is raised and some collider-specific phenomenology discussed. Four salient points are made in the conclusion.

We present a simple proof of quantum contextuality for a spinless particle with a one-dimensional configuration space. We then discuss how the maximally realistic deterministic quantum mechanics recently constructed by this author and V. Singh can be applied to different contexts.

For general boundary conditions, we show that the energy H of a classical Heisenberg ferromagnetic spin system on a curved surface satisfies the inequality H≥|Γ|. Here Γ is a certain geometric phase or anholonomy associated with the spin vector field. This is a generalization of the well known Bogomol'nyi inequality H≥4πQ (Q=integer). For a wide variety of curved surfaces, seeking solutions with certain symmetries, we find that the variational equation δH=0 can be reduced to a sine-Gordon equation with a geometry-dependent parameter. Soliton lattice solutions of this equation are analyzed. It is shown that both H and Γ develop two branches each, all of which merge at the one-soliton limit. This branching is interpreted as a topological transition of the spin textures that occurs at the one-soliton point.

Classical Heisenberg spins in the continuum limit (i.e. the nonlinear σ-model) are studied on an elastic cylinder section with homogeneous boundary conditions. The latter may serve as a physical realization of magnetically coated microtubules and cylindrical membranes. The corresponding rigid cylinder model exhibits topological soliton configurations with geometrical frustration due to the finite length of the cylinder section. Assuming small and smooth deformations allows to find shapes of the elastic support by relaxing the rigidity constraint: an inhomogeneous Lamé equation arises. Finally, this leads to a novel geometric effect: a global shrinking of the cylinder section with swellings.

We obtain the exact ground state of N-particles in one dimension both on a line and on a circle in case the N particles are interacting via nearest and next-to-nearest neighbour interactions. Further, we establish a mapping between these N-body problems and short range Dyson models introduced recently to model intermediate spectral statistics. Using this mapping we compute one and two point functions of a related many-body theory in the thermodynamic limit and show the absence of long range order. Generalization of the model on the line to higher dimensions as well as to other root systems is also considered. Finally, we also consider a variant of the above model in two dimensions in which all the states exhibit novel correlations.

The nature of the transition from the quantum tunneling regime to the thermal hopping regime has importance in the study of condensed matter physics and cosmological phase transitions. It may also be of significance in collapse from quantum state to a classical state due to measurement (or loss of coherence due to some other process). We study this transition analytically in scalar field theory with a fourth order term. We obtain analytic bounce solutions which correctly give the action in thin and thick wall limits of the potential. We find that the transition is of the second order for the case of thick wall while it seems to be of first order for the case of thin wall.

We sharpen the RVB mechanism of superconductivity proposed by Anderson in 1987 and explain the spin gap phenomenon as well as superconductivity in a single CuO₂ layer. We state our mechanism in the form a theorem, and heuristic proof, in which the neutral spinon pairing in the spin gap phase frustrates the single electron kinetic energy leading to a new "singular" Landau parameter, which is a finite "tomographic" BCS interaction in an underlying tomographic Luttinger liquid.

To understand the origin of high temperature superconductivity model based on the close proximity of the Fermi level to a quasi-two-dimensional Van Hove Singularity (VHS) in the density of states has been suggested. Here we present our study of the dependence of the zero temperature gap to the critical temperature for s- and d-wave superconductors on the Fermi level shift (δ) from the VHS within the BCS theory. Exact numerical calculations for the s and d gap ratios are carried out and approximate analytic expressions for the ratio are given. We find that the maximum gap ratio occurs at δ=0, and it decreases symmetrically with increasing δ.

Within the hard-core boson model and the 1/S spin wave approximation, we have constructed the linear response theory for disordered boson system. Our numerical results shows that the instability of the superfluidity occurs when the paramagnetic part cancels out the diamagnetic part with a critical finite amout of disorder.

We give a brief introduction to Luttinger liquids and to the phenomena of electronic transport or conductance in quantum wires. We explain why the subject of transport in Luttinger liquids is relevant and fascinating and review some important results on tunneling through barriers in a one-dimensional quantum wire and the phenomena of persistent currents in mesoscopic rings. We give a brief description of our own work on transport through doubly-crossed Luttinger liquids and transport in the Schulz–Shastry exactly solvable Luttinger-like model.

With a view to making this article accessible to researchers in diverse fields such as nuclear physics, particle physics, formal field theory and condensed matter physics, we begin by first giving a brief introduction. In Sec. 1, we explain the words such as "Luttinger liquid" and "transport" in the title. We also motivate the study of this subject by showing that field is very important at the current time from the applications point of view and describe why it is theoretically fascinating. We then give a quick review of some of the important results in the field in Sec. 2, before we go on to describe some work that we have recently done and are doing in this field in Sec. 3. Finally, in Sec. 4, we conclude by re-emphasizing the importance of this area and drawing attention towards future possibilities.