Exact solutions of (deformed) Jackiw–Teitelboim gravity

It is well known that Jackiw–Teitelboim (JT) gravity posses the simplest theory on 2-dimensional gravity. The model has been fruitfully studied in recent years. In the present work, we investigate exact solutions for both JT and deformed JT gravity recently proposed in the literature. We revisit exact Euclidean solutions for Jackiw-Teitelboim gravity using all the non-zero components of the dilatonic equations of motion using proper integral transformation over Euclidean time coordinate. More precisely, we study exact solutions for hyperbolic coverage, cusp geometry and another compact sector of the AdS$$_2$$ 2 spacetime manifold.

Perturbative quantum field theory (QFT): Algebraic methods

This chapter discusses systematically the algebraic properties of perturbation theory in the example of a local, relativistic scalar quantum field theory (QFT). Although only scalar fields are considered, many results can be easily generalized to relativistic fermions. The Euclidean formulation of QFT, based on the density matrix at thermal equilibrium, is studied, mainly in the simpler zero-temperature limit, where all d coordinates, Euclidean time and space, can be treated symmetrically. The discussion is based on field integrals, which define a functional measure. The corresponding expectation values of product of fields called correlation functions are analytic continuations to imaginary (Euclidean) time of the vacuum expectation values of time-ordered products of field operators. They have also an interpretation as correlation functions in some models of classical statistical physics, in continuum formulations or, at equal time, of finite temperature QFT. The field integral, corresponding to an action to which a term linear in the field coupled to an external source J has been added, defines a generating functional Z(J) of field correlation functions. The functional W(J) = ln Z(J) is the generating functional of connected correlation functions, to which contribute only connected Feynman diagrams. In a local field theory connected correlation functions, as a consequence of locality, have cluster properties. The Legendre transform Γ(φ) [N1]of W(J) is the generating functional of vertex functions. To vertex functions contribute only one-line irreducible Feynman diagrams, also called one-particle irreducible (1PI).

Geometric description of Schrödinger equation in Finsler and Funk geometry

For a system of [Formula: see text] non-relativistic spinless bosons, we show by using a set of suitable matching conditions that the quantum equations in the pilot-wave limit can be translated into a geometric language for a Finslerian manifold. We further link these equations to Euclidean time-like relative Funk geometry and show that the two different metrics in both of these geometric frameworks lead to the same coupling.

Calm Multi-Baryon Operators

There are many outstanding problems in nuclear physics which require input and guidance from lattice QCD calculations of few baryons systems. However, these calculations suffer from an exponentially bad signal-to-noise problem which has prevented a controlled extrapolation to the physical point. The variational method has been applied very successfully to two-meson systems, allowing for the extraction of the two-meson states very early in Euclidean time through the use of improved single hadron operators. The sheer numerical cost of using the same techniques in two-baryon systems has so far been prohibitive. We present an alternate strategy which offers some of the same advantages as the variational method while being significantly less numerically expensive. We first use the Matrix Prony method to form an optimal linear combination of single baryon interpolating fields generated from the same source and different sink interpolating fields. Very early in Euclidean time this optimal linear combination is numerically free of excited state contamination, so we coin it a calm baryon. This calm baryon operator is then used in the construction of the two-baryon correlation functions.To test this method, we perform calculations on the WM/JLab iso-clover gauge configurations at the SU(3) flavor symmetric point with mπ~ 800 MeV — the same configurations we have previously used for the calculation of two-nucleon correlation functions. We observe the calm baryon significantly removes the excited state contamination from the two-nucleon correlation function to as early a time as the single-nucleon is improved, provided non-local (displaced nucleon) sources are used. For the local two-nucleon correlation function (where both nucleons are created from the same space-time location) there is still improvement, but there is significant excited state contamination in the region the single calm baryon displays no excited state contamination.

SPECTROSCOPY AND THERMODYNAMICS OF MSW BLACK HOLE

We study the thermodynamics and spectroscopy of a (2+1)-dimensional black hole proposed by Mandal et al.1 [Mod. Phys. Lett. A6, 1685 (1991)]. We put the background spacetime in Kruskal like co-ordinate and find period with respect to Euclidean time. Different thermodynamic quantities like entropy, specific heat, temperature etc. are obtained. The adiabatic invariant for the black hole is found and quantized using Bohr–Sommerfeld quantization rule. The study shows that the area spectrum of MSW black hole is equally spaced and the value of spacing is found to be ℏ.

THERMODYNAMICS AND SPECTROSCOPY OF SCHWARZSCHILD BLACK HOLE SURROUNDED BY QUINTESSENCE

The thermodynamic and spectroscopic behavior of Schwarzschild black hole surrounded by quintessence are studied. We have derived the thermodynamic quantities and studied their behavior for different values of quintessence parameter. We put the background spacetime into the Kruskal-like coordinate to find the period with respect to Euclidean time. Also assuming that the adiabatic invariant obeys Bohr–Sommerfeld quantization rule, detailed study of area spectrum and entropy spectrum have been done for special cases of the quintessence state parameter. We find that the spectra are equally spaced.

AREA SPECTRUM OF BTZ BLACK HOLES FROM THE PERIODICITY IN EUCLIDEAN TIME

In this paper, we analyze the area spectrum of BTZ three-dimensional black holes by considering an outgoing wave and relating its period of motion with the period of the gravitational system with respect to Euclidean time. The area spectra obtained for the rotating and non-rotating black holes are equally spaced and it is important to note that in this paper, we do not need to use the small angular momentum assumption which is necessary in the quasinormal mode approach for rotating black holes. The results suggest that the periodicity of the black hole gravitational system may be the origin of area quantization.