International Journal of Modern Physics A

These pedagogical notes are dedicated to a derivation of the Unruh effect. There is a special emphasis on the transparency of the arguments and the exhibition of detailed calculations. We assume the reader has a basic knowledge of quantum mechanics and relativity. The notes can hopefully be used in a self-contained way by advanced undergraduate or beginning graduate students.

We study whether the approach of Deffayet et al. (DPSV) can be adopted for obtaining a derivative part of quadratic action for scalar perturbations in beyond Horndeski theories about homogeneous and isotropic backgrounds. We find that even though the method does remove the second and higher derivatives of metric perturbations from the linearized Galileon equation, in the same manner as in the general Horndeski theory, it gives incorrect result for the quadratic action. We analyze the reasons behind this property and suggest the way of modifying the approach, so that it gives valid results.

Superconducting cosmic strings (SCSs) have received revived interests recently. In this paper we treat closed SCSs as oriented knotted line defects, and concentrate on their topology by studying the Hopf topological invariant. This invariant is an Abelian Chern–Simons action, from which the HOMFLYPT knot polynomial can be constructed. It is shown that the two independent parameters of the polynomial correspond to the writhe and twist contributions, separately. This new method is topologically stronger than the traditional (self-)linking number method, which fails to detect essential topology of knots sometimes, shedding new light upon the study of physical intercommunications of superconducting cosmic strings as a complex system.

We derive the one-loop effective action for scalar, pseudoscalar, and electromagnetic fields coupled to a Dirac fermion in an extension of QED with Yukawa couplings. Using the Schwinger proper-time formalism and zeta-function regularization, we calculate the full nonperturbative effective action to one loop in the constant background field approximation. Our result is nonperturbative in the external fields, and goes beyond existing results in the literature which treat only the first nontrivial order involving the pseudoscalar. The result has an even and odd part, which are related to the modulus and phase of the fermion functional determinant. The even contribution to the effective action involves the modulus of the effective Yukawa couplings and is invariant under global chiral transformations while the odd contribution is proportional to the angle between the scalar and pseudoscalar couplings. In different limits the effective action reduces either to the Euler–Heisenberg effective action or the Coleman–Weinberg potential. We also comment on the relationship between the odd part of the effective action and the chiral anomaly in QED.

In this paper, a charged half-spin particle depicted by the Dirac equation in the presence of a uniform magnetic field and a mixed potential are analyzed in the rotating cosmic string space–time. In order to facilitate this study, we assume that the symmetrical center of the potential is on the string and the magnetic field is parallel to the string. Based on the functional analysis method, we obtain the energy eigenvalues for different physical situations. It shows that the energy levels of the system depend explicitly on the angular deficit $\alpha$ and the rotational parameter $a$ which characterize the global structure of the metric in the space–time of the rotating cosmic string.

Christodoulou and Rovelli have shown that the interior volume of a Schwarzschild black hole grows linearly with time. The entropy of a scalar field in this interior volume of a Schwarzschild black hole has been calculated and shown to increase linearly with the advanced time too. In this paper, considering Hawking radiation from a d-dimensional charged black hole, we investigate the proportional relation between the entropy of the scalar field in the interior volume and the Bekenstein–Hawking entropy using the method of our previous work. We also derive this proportionality relation using Hamiltonian analysis and find a consistent result. We then investigate the proportionality coefficient with respect to d and find that it gradually decreases as the dimension of space–time increases.

Some features of noncommutativity are investigated in this work. A noncommutative (NC) versions for the 2D harmonic oscillator and scalar field theory are obtained via the Noncommutative Mapping and fourfold discussion are presented: first, the Lagrangian of the damped harmonic oscillator (DHO), which was an original explanation for the dissipative process presenting in the atomic nuclei collision, is reobtained through noncommutativity. Here, we show that the NC parameter plays the role of the viscous damping coefficient; second, the NC harmonic oscillator is mapped into the bosonic string theory in the light cone frame, which appears as a bosonic string theory attached to a D3-brane; third, we discuss the connection between DHO and bosonic string attached to a D3-brane; fourth, the NC scalar field is indicating into 2D-NC harmonic oscillator.