Course

This mini-course of four lectures is an introduction, review, and critique of two approaches to deriving the Einstein equation from hypotheses about horizon entropy. 

It will be based on two papers: 

• "Thermodynamics of Spacetime: The Einstein Equation of State" arxiv.org/abs/gr-qc/9504004
• "Entanglement Equilibrium and the Einstein Equation" arxiv.org/abs/1505.04753

We may also discuss ideas in "Gravitation and vacuum entanglement entropy" arxiv.org/abs/1204.6349

Zoom Link: https://pitp.zoom.us/j/96212372067?pwd=dWVaUFFFc3c5NTlVTDFHOGhCV2pXdz09 

The main objective of this course is to discuss some advanced topics in gravitational physics and its applications to high energy physics. Necessary mathematical tools will be introduced on the way. These mathematical tools will include a review of differential geometry (tensors, forms, Lie derivative), vielbeins and Cartan’s formalism, hypersurfaces, Gauss-Codazzi formalism, and variational principles (Einstein-Hilbert action & Gibbons-Hawking term). Several topics in black hole physics including the Kerr solution, black hole astrophysics, higher-dimensional black holes, black hole thermodynamics, Euclidean action, and Hawking radiation will be covered. Additional advanced topics will include domain walls, brane world scenarios, Kaluza-Klein theory and KK black holes, Gregory-Laflamme instability, and gravitational instantons

This course will cover the basics of Quantum Foundations under three main headings. Part I – Novel effects in Quantum Theory. A number of interesting quantum effects will be considered. (a) Interferometers: Mach-Zehnder interferometer, Elitzur-Vaidman bomb tester, (b) The quantum-Zeno effect. (c) The no cloning theorem. (d) Quantum optics (single mode). Hong-Ou-Mandel dip. Part II Conceptual and interpretational issues. (a) Axioms for quantum theory for pure states. (b) Von-Neumann measurement model. * (c) The measurement (or reality) problem. (d) EPR Einstein’s 1927 remarks, the Einstein-Podolsky-Rosen argument. (e) Bell’s theorem, nonlocality without inequalities. The Tirolson bound. (f) The Kochen-Specker theorem and related work by Spekkens (g) On the reality of the wavefunction: Epistemic versus ontic interpretations of the wavefunction and the Pusey-Barrett-Rudolph theorem proving the reality of the wave function. (h) Gleason’s theorem. (i) Interpretations. The landscape of interpretations of quantum theory (the Harrigen Spekkens classification). The de Broglie-Bohm interpretation, the many worlds interpretation, wave-function collapse models, the Copenhagen interpretation, and QBism. Part III Structural issues. (a) Reformulating quantum theory: I will look at some reformulations of quantum theory and consider the light they throw on the structure of quantum theory. These may include time symmetric quantum theory and weak measurements (Aharonov et al), quantum Bayesian networks, and the operator tensor formalism. (b) Generalised probability theories: These are more general frameworks for probabilistic theories which admit classical and quantum as special cases. (c) Reasonable principles for quantum theory: I will review some of the recent work on reconstructing quantum theory from simple principles. (d) Indefinite causal structure and indefinite causal order. Finally I will conclude by looking at (i) the close link between quantum foundations and quantum information and (ii) possible future directions in quantum gravity motivated by ideas from quantum foundations.

The course begins by discussing several topics in equilibrium statistical physics including phase transitions and the renormalization group. The second part of the course covers non-equilibrium statistical physics including kinetics of aggregation, spin dynamics, population dynamics, and complex networks.

The course has three parts. In the first part of the course, the path integral formulation of non-relativistic quantum mechanics and the functional integral formulation of quantum field theory are developed. The second part of the course covers renormalization and the renormalization group. Finally, non-abelian gauge theories are quantized using functional integral techniques.

This course uses quantum electrodynamics (QED) as a vehicle for covering several more advanced topics within quantum field theory, and so is aimed at graduate students that already have had an introductory course on quantum field theory. Among the topics hoped to be covered are: gauge invariance for massless spin-1 particles from special relativity and quantum mechanics; Ward identities; photon scattering and loops; UV and IR divergences and why they are handled differently; effective theories and the renormalization group; anomalies.

The course starts by looking for a quantum theory that is compatible with special relativity, without assuming fields are fundamental. Nevertheless fields turn out to be a very good, maybe inevitable mathematical tool for formulating and studying such a relativistic quantum theory. The second part of the course introduces the Dirac theory and canonically quantizes it. It also quantizes the Maxwell field theory. The Feynman diagram technique for perturbation theory is developed and applied to the scattering of relativistic fermions and photons. Renormalization of quantum electrodynamics is done to one-loop order.

Prerequisite: PSI Quantum Theory course or equivalently Graduate level Quantum Mechanics and QFT of scalar theory

This is a theoretical physics course that aims to review the basics of theoretical mechanics, special relativity and classical field theory, with the emphasis on geometrical notions and relativistic formalism.