INTERFACE BETWEEN QUANTUM THEORY AND GRAVITY
I gave a set of 10 x 1.5 hour lectures on this topic recently. A summary of the lectures and the links to pdf of slides and YouTube videos are given below.
A detailed review article, complementing and expanding on these lectures is now avialable in the arxiv:1909.02015. For pdf
click here.
The videos of the lectures are now avilable in YouTube at
this link.
Lectures 1 to 3: (QFT Basics)
I start with the three points of contact/conflict between GR and QT, viz. the thermal nature of the horizons, smallness of the cosmological constant and the role of Planck length as a zero-point-length. I then introduce the path integral approach to QT and describe how GR actually helps you to understand the Lagrangian in classical mechanics! Next I describe how to compute the relativistic propagator from the path integral for a "single" particle (involving a square root action). This relativistic propagator for a "single" particle naturally renders itself to an alternative description, thereby allowing us to discover quantum fields. The lectures conclude describing the properties of vacuum fluctuations (which will become thermal fluctuations to an accelerated observer) and a brief description of the Casimir effect (and the question of whether Casimir energy gravitates).
Lectures 4 to 8: (The Hot Spacetime)
These five lectures provide a comprehensive description of the thermality of horizons from different perspectives.
They start with an operational definition of coordinate systems and derive the "natural" coordinates for uniform velocity observer (aka Lorentz transformation!) and for the uniformly accelerated observer. I then provide the intuitive connection between exponential redshift and Planckian power spectrum (which is a running theme throughout). Since the (locally) inertial propagator contains ALL the features of QFT, one should be able to obtain the thermality of Rindler horizon by just studying it and I show that this can indeed be done, rather easily. Next, other standard derivations of horizon thermality (based on vacuum functional, path integral approach etc) are described and compared with one another. I then discuss the derivation of Hawking radiation from a BH and several subtleties as regards entropy of BHs. The last part discusses response of detectors in D-dimensions (and some cautionary comments).
Lecture 9 (Cosmological constant)
This lecture discusses several aspects of the cosmological constant -- many of which are not adequately appreciated in the literature -- and concludes emphasising the single most important (but usually ignored!) clue about the nature of gravity, which the cosmological constant provides.
Lecture 10 (Microstructure of Spacetime)
The last lecture puts together the lessons we learn from the three clues regarding the nature of QG provided by
(1) the thermality of local Rindler horizons, (2) the cosmological constant and (3) the Planck length. I show how these lead to the conclusions that: (a) gravitational field equations have the same status as the equations of fluid mechanics and (b) cosmological evolution should not be viewed as a special solution to the gravitational field equation. The alternative approach, suggested by the three clues mentioned earlier, provides better insight into classical gravity, offers a different perspective on cosmic evolution and predicts the numerical value of the cosmological constant.