Research

 

 

I am currently (2008) researching the unification of quantum theory and gravitation.  I am concerned with particle creation via quantum fields in various spacetimes, and how ‘quantum field theory in curved spacetime’ can be used to understand and create a new appoach for a theory of quantum gravity.  Particularly, I am studing the creation of particles via:

 

(1) a flat spacetime that undergoes an intermediate expansion,

(2) a flat spacetime that has an imposed boundary condition that represents an accelerating mirror,

(3) a curved spacetime around a black hole,

(4) a curved spacetime from a collapsing star. 

 

This work is being done in close collaboration with Charles Evans (UNC) and Paul Anderson (WFU).  I am also trying to understanding why an accelerated observer through the Minkowski zero-temperature vacuum detects a thermal bath of particles with a finite temperature proportional to the acceleration.  Known as the Unruh effect, this along with Hawking radiation stands as two of the most important predictions in theoretical physics in the last 25 years.  These effects are clues to understanding the unification of quantum field theory, general relativity and thermodynamics. 

 

These questions are of interest: 

1: How can general relativity and quantum theory be combined?

2: How can the foundations of quantum mechanics be understood?

3: How are the various particles and forces unified in a theory that explains them all as manifestations of single, fundamental entity?

4: How are the values of the free constants in the standard model chosen?

5: How do the constants of cosmology get chosen? (What is dark energy?)

 

Gravity, Cosmology and High Energy Physics Program at Carolina

 

String Theory Seminar at Carolina

 

String Theory Seminar at Duke 

 

Quantum Relativity Group at Georgia Tech

 

Various attempts at quantum gravity:

 

String theory

Loop quantum gravity

Dynamical triangulations

Hartle’s quantum spacetime

Hawking’s Euclidean geometry

Quantum Regge calculus

Sorkin’s casual sets

t’Hoofts deterministic approach

Finkelstein’s quantum relativity.

Noncommunitive geometry

Penrose’s twister theory

 

 

 

Write-Ups, work, projects, presentations, problems, etc:

Cylindrical Spacetime:

·        Cylindrical2D.pdf

·        Cylindrical2D.tex

 

Cosmic Particle Creation:

·        Expansion.pdf

·        Expansion.tex

 

Particle Creation via Collapse:

·        Starcollapse.pdf

·        Starcollapse.tex

 

Curved Space Quantization:

·        Curved.pdf

·        Curved.tex

 

Detailed Bogolubov Transformation for Moving Mirror:

·        Accelerating_Mirror2D.pdf

·        Accelerating_Mirror2D.tex

 

Casimir Effect:

·        Casimir.pdf

·        Casimir.tex

 

Unruh Effect:

·        Unruh.pdf

·        Unruh.tex

 

Units, Renormalization, Vacuum Divergence and the Harmonic Potential:

·        renorm.pdf

·        renorm.tex

 

Acceleration radiation power point presentation:

·        Unruh.ppt

 

Maxwell equations from geometric algebra:

·        electro.pdf

·        electro.tex

 

Lepton pair production:

·        QED.tex

·        QED.pdf

 

Davies’ moving mirrors and thermalization:

·        Moving_Mirrors.pdf

·        Moving_Mirrors.tex

 

Ever heard of a red black hole?

 

Summary of a hydrogen fuel cell experimental project:

·        040601_Sapphire.pdf

·        040601_Sapphire_Items.pdf

 

Essay on the black hole singularity:

 

Essay on unifying physics:

 

Some derivations of E = mc^2:

 

References for black hole thermodynamics:

 

An introduction to geometric algebra power point presentation:

 

Notes on the Zitterbewegung (“trembling motion”):

 

Lab reports:

 

Analysis of sci-fi book, Mars:

 

Feynman’s integral :

 

A brief summary of Goldstein’s survey of elementary principles:

 

Reading notes of Carroll’s quantum field theory in curved spacetime:

 

Short summary and reference notes on Carroll’s SR and flat spacetime:

 

Solutions

My solutions for selected textbook problems.  (some are wrong, most are right)  Please use these as guides.  I’m not responsible for your grade or your inability to learn physics if you cheat. 

GR Friedman equation and energy conservation, Oppenheimer-Volkoff equation (stellar hydrostatic equilibrium)

 

Field Theory 263, Jack Ng Homework 1:

 

Jackson Problems: 1.1, 1.4, 1.5, 1.6, 1.10, 1.12, 1.13

 

Jackson Problems: 2.2, 2.5, 2.7, 2.11

 

Sakurai Ch. 4: Problems 4.1, 4.2, 4.3, 4.4, 4.8, 4.10, 4.12

 

Sakurai Ch. 5: Problems 5.1, 5.3, 5.4, 5.7, 5.8, 5.9, 5.11

 

Sakurai Ch. 5: Problems 5.13, 5.14, 5.17, 5.20, 5.21

 

Sakurai Ch. 6: All the problems. (You’ll only need one package(youngtab) to download to get it to compile.  Click start => miktex => miketex package manager.)

Goldstein Ch.1: Derivations:

 

Goldstein Ch.1: Exercises:

 

Goldstein Problems 1.1, 1.2, 1.6, 1.8, 1.14, 1.20

 

Goldstein Problems 1.21, 2.7, 2.12

 

Goldstein Problems 2.13, 2.14

 

Goldstein Problems 2.18, 2.21, 3.13, 3.14, 3.20

 

Goldstein Problems 3.7a, 3.31, 3.32

 

Goldstein Problems 4.1, 4.2, 4.10, 4.14, 4.15

 

Goldstein Problems 4.22, 5.15, 5.21, 5.23, Foucault Pendulum

 

Goldstein Problems 5.4, 5.6, 5.7, 5.26

 

Goldstein Problems 8.19, 8.24, 8.25

 

Goldstein Problems 9.2, 9.6, 9.16, 9.31

 

Goldstein Problems 10.7b, 10.17, 10.26

 

Goldstein Problems 10.13, 10.27, Cylinder

 

 

 

Physics is just the refinement of everyday thinking. – A. Einstein