09/01/2007-Quantum mechanics systems; Arbitrary systems;
Ladder of states; Operators that differ by a phase and its
properties: relationship between vacum states, squeezed states,
Bogolubov transformation coefficients,
Harmonic Oscillator example, 2 particle states, 2 mode squeezed
state; Density matrix; Reduced density matrix:
[1]; [2];
[3]; [4];
[All].
11/01/2007- Reduced density matrix; Thermal state from 2 particle
squeezed state; Scalar field theory in flat spacetime; Lagrangean and
Hamiltonian formalism; Fourier modes of Klein-Gordon field; SHO energy;
Lorentz frame (INdependence of vacuum state); Accelerated frames
(DEpendence on coordinate system of vacuum state)
[1]; [2];
[3]; [4];
[All].
16/01/2007- ADM formalism; Definitions: current & inner product
btw two scalar fields (solutions of KG EOM); Integration of a quantum
field (satisfying KG eqn) over a classical solution; Definition of
creation/annihilation operators in terms of this integral (operator
in the classical field); Positive norm solutions of wave eqn;
Hamiltonian diagonalization (matrix notation); # of particles.
[1]; [2];
[3];
[All].
18/01/2007- Hamiltonian diagonalization (cont.); Application
to Cosmology; Vacuum state evolution (into infinite # of particles);
Adiabatic definition of a particle; What is a particle?; Homework 1.
[1]; [2];
[3]; [4];
[All].
23/01/2007- Quantization of flat spacetime; Rindler coordinates;
Solution of KG eqn in the Rindler coordinates; Complex analysis of the
solution (Analiticity).
[1]; [2];
[3]; [4];
[All].
25/01/2007- Classical modes for the solution of wave eqn;
Normalization of the Rindler modes; Temperature definition;
Minkowski vacuum as thermal state when expressed in terms of the
Rindler modes.
[1]; [2];
[3]; [4];
[All].
30/01/2007- What do we mean by a particle?; Harmonic Oscillator
detector; Accelerated detectors; Minkowski vacuum as a thermal
state:
[1]; [2];
[3]; [4];
[All].
01/02/2007- Lowest order excitation terms of simple particle
detectors; Two-point function; Decay probability; Experiments?:
[1]; [2];
[3]; [4];
[All].
06/02/2007- What happens when a detector detects an thermal
particle?; Rindler observer; Conditional statements in QM
(Non-local); Energy conditinal on detection; HW2:
[1]; [2];
[3]; [4];
[5];
[All].
08/02/2007- Eternal Black Holes:
[1]; [2];
[3]; [4];
[All].
13/02/2007- Einstein-Rosen bridge; Quantum fields on this
background; Angular momentum barrier; Albedo (grey body factors);
[1]; [2];
[3]; [4];
[All].
15/02/2007- Black Holes formed by collapse; Shell implosion;
Squeezed wavepackets; Transplanckian problem; Black hole entropy
is real, but what is it?:
[1]; [2];
[3]; [4];
[All].
15/02/2007-27/02/2007: READING WEEK
27/02/2007- Energy-Momentum tensor for BH radiation; Normal
order; Point splitting (generalization of normal order);
Hadarmard form; Conservation and 0 trace issue; 2d massless
scalar field point splitting procedure; HW2 correction:
[1]; [2];
[3]; [4];
[5]; [6];
[All].