Semi-classical analysis of the string theory cigar

We study the semi-classical limit of the reflection coefficient for the SL(2, ℝ)k/U(1) CFT. For large k, the CFT describes a string in a Euclidean black hole of 2-dimensional dilaton-gravity, whose target space is a cigar with an asymptotically linear dilaton. This sigma-model description is weakly coupled in the large k limit, and we investigate the saddle-point expansion of the functional integral that computes the reflection coefficient. As in the semi-classical limit of Liouville CFT studied in [1], we find that one must complexify the functional integral and sum over complex saddles to reproduce the limit of the exact reflection coefficient. Unlike Liouville, the SL(2, ℝ)k/U(1) CFT admits bound states that manifest as poles of the reflection coefficient. To reproduce them in the semi-classical limit, we find that one must sum over configurations that hit the black hole singularity, but nevertheless contribute to the saddle-point expansion with finite action.

The classical limit of Schrödinger operators in the framework of Berezin quantization and spontaneous symmetry breaking as an emergent phenomenon

The algebraic properties of a strict deformation quantization are analyzed on the classical phase space [Formula: see text]. The corresponding quantization maps enable us to take the limit for [Formula: see text] of a suitable sequence of algebraic vector states induced by [Formula: see text]-dependent eigenvectors of several quantum models, in which the sequence converges to a probability measure on [Formula: see text], defining a classical algebraic state. The observables are here represented in terms of a Berezin quantization map which associates classical observables (functions on the phase space) to quantum observables (elements of [Formula: see text] algebras) parametrized by [Formula: see text]. The existence of this classical limit is in particular proved for ground states of a wide class of Schrödinger operators, where the classical limiting state is obtained in terms of a Haar integral. The support of the classical state (a probability measure on the phase space) is included in certain orbits in [Formula: see text] depending on the symmetry of the potential. In addition, since this [Formula: see text]-algebraic approach allows for both quantum and classical theories, it is highly suitable to study the theoretical concept of spontaneous symmetry breaking (SSB) as an emergent phenomenon when passing from the quantum realm to the classical world by switching off [Formula: see text]. To this end, a detailed mathematical description is outlined and it is shown how this algebraic approach sheds new light on spontaneous symmetry breaking in several physical models.

Relativistic Maxwell Theory and Einstein Field Equation derived from Variational Principle

In this article, I'll be reviewing relativistic mechanisms using the calculus of variation in the classical limit. The variational principle is considered to be one of the most important mechanisms to build a theory. Newton's second law of motion is a consequence of Euler-Lagrange equations which gives the least (or stationary) trajectory of a particle between any two arbitrary points. I'll the use action principle by deriving the relativistic Maxwell's field equation, geodesic equation, and Einstein's field equation.

Radiated momentum in the post-Minkowskian worldline approach via reverse unitarity

We compute the four-momentum radiated during the scattering of two spinless bodies, at leading order in the Newton’s contant G and at all orders in the velocities, using the Effective Field Theory worldline approach. Following [1], we derive the conserved stress-energy tensor linearly coupled to gravity generated by localized sources, at leading and next-to-leading order in G, and from that the classical probability amplitude of graviton emission. The total emitted momentum is obtained by phase-space integration of the graviton momentum weighted by the modulo squared of the radiation amplitude. We recast this as a two-loop integral that we solve using techniques borrowed from particle physics, such as reverse unitarity, reduction to master integrals by integration-by-parts identities and canonical differential equations. The emitted momentum agrees with recent results obtained by other methods. Our approach provides an alternative way of directly computing radiated observables in the post-Minkowskian expansion without going through the classical limit of scattering amplitudes.

On an exponential representation of the gravitational S-matrix

An exponential representation of the S-matrix provides a natural framework for understanding the semi-classical limit of scattering amplitudes. While sharing some similarities with the eikonal formalism it differs from it in details. Computationally, rules are simple because pieces that must be subtracted are given by combinations of unitarity cuts. Analyzing classical gravitational scattering to third Post-Minkowskian order in both maximal supergravity and Einstein gravity we find agreement with other approaches, including the contributions from radiation reaction terms. The kinematical relation for the two-body problem in isotropic coordinates follows immediately from this procedure, again with the inclusion of radiation reaction pieces up to third Post-Minkowskian order.

Extracting Einstein from the loop-level double-copy

The naive double-copy of (multi) loop amplitudes involving massive matter coupled to gauge theories will generically produce amplitudes in a gravitational theory that contains additional contributions from propagating antisymmetric tensor and dilaton states even at tree-level. We present a graph-based approach that combines the method of maximal cuts with double-copy construction to offer a systematic framework to isolate the pure Einstein-Hilbert gravitational contributions through loop level. Indeed this allows for a bootstrap of pure-gravitational results from the double-copy of massive scalar-QCD. We apply this to construct the novel result of the D-dimensional one-loop five-point QFT integrand relevant in the classical limit to generating observables associated with the radiative effects of massive black-hole scattering via pure Einstein-Hilbert gravity.

Two-Dimensional Pauli Equation in Noncommutative Phase-Space

We study the Pauli equation in a two-dimensional noncommutative phase-space by considering a constant magnetic field perpendicular to the plane. The noncommutative problem is related to the equivalent commutative one through a set of two-dimensional Bopp-shift transformations. The energy spectrum and the wave function of the two-dimensional noncommutative Pauli equation are found, where the problem in question has been mapped to the Landau problem. In the classical limit, we have derived the noncommutative semiclassical partition function for one- and N- particle systems. The thermodynamic properties such as the Helmholtz free energy, mean energy, specific heat and entropy in noncommutative and commutative phasespaces are determined. The impact of the phase-space noncommutativity on the Pauli system is successfully examined.