# Notebook

# My Notebook

Hello! This is my notebook. I am planning on writing a few sentences every few days about what I have been learning about. The hope is that in after some time I will be able to look back, and be amazed at all the different things I have learned.

This also should help guide those who come after me. You can see the path that I took to end up where I currently am.

### January 30th 2022

I read Chapter 39, Canonical Quantization of Spinor Fields II, in Mark Srednicki’s “Quantum Field Theory.” I also read Section 3.3, Holst Action and Barbero-Immirzi coupling constant in Carlo Rovelli and Francesca Vidotto’s “Covariant Loop Quantum Gravity: An elementary Introduction to Quantum Gravity and Spinfoam Theory.”

### January 29th 2022

I read Appendix F, Geodesic Congruences, Appendix G, Conformal Transformations, Appendix H, Conformal Diagrams, Appendix I, The Parallel Propagator, and Appendix J, Noncoordinate Bases of Sean Caroll’s “Spacetime and Geometry: An Introduction to General Relativity.” This means I have read this book cover to cover now.

### January 28th 2022

I read Appendix D, Hypersurfaces, and Appendix E, Stoke’s theorem of Sean Caroll’s “Spacetime and Geometry: An Introduction to General Relativity.”

### January 27th 2022

For QFT class we covered Chapter 41, LSZ reduction for spin-one-half particles, and Chapter 42, the free fermion propagator of Mark Srednicki’s “Quantum Field Theory.” In general relativity we discussed more things about Einstein-Cartan theory and differential geometry. Specifically we talked about the exterior derivative, extended the formalism to now have the covariant exterior derivative, then talked about the curvature of the connection, the torsion of co-frame fields, and ended with the Einstein-Cartan action.

### January 25th 2022

For QFT class today we covered Chapter 39, Canonical quantization of spinor fields II, and chapter 40 Parity, time reversal, and charge conjugation of Mark Srednicki’s “Quantum Field Theory”. In General relativity we started a discussion on Einstein-Cartan theory and exterior algebras. For reading I read Appendix A through Appendix C of Carrol’s “Spacetime and Geometry: An introduction to General Relativity.”

### January 22nd 2022

I read Chapter 9, Quantum Field Theory in Curved Spacetime, of Sean Caroll’s “Spacetime and Geometry: an Introduction to General Relativity.”

### January 19th 2022

I read Chapter 37, Canonical Quantization of Spinor Fields I, and Chapter 38, Spinor Technology, of Mark Srednicki’s “Quantum Field Theory.”

### January 18th 2022

I gave a presentation on Chapters 35/36 of Mark Srednicki’s “Quantum Field Theory.” In GR class we Hamiltonian formulation of GR. In doing so we talked about the Hamiltonian constraint and the diffeomorphisms constraints. From these constraints we showed there were only 2x2 actual degrees of freedom. We finished with a discussion on the Dirac Algebra of constraints.

### January 17th 2022

I have also read Srednicki’s “Quantum Field Theory” chapter 35, Manipulating Spinor indices, and chapter 36, Lagrangians for Spinor Fields. I have also made a presentation on those two chapters for the QFT course.

### January 16th 2022

I have read and taken notes for Weinberg’s “The Quantum Theory of Fields: Volume I” Sections 2.1 “Quantum Mechanics,” Section 2.2 “Symmetries,” Section 2.3 “Quantum Lorentz Transformations,” Section 2.4 “The Poincare Algebra,” and Section 2.5 “One-Particle States.” I enjoy the way this book presents a lot of QFT using a lot of the math other books stray away from.

### January 13th 2022

Second day of classes for the semester and we covered more of Chapter 2 of Weinbergs “The Quantum Theory of Fields: Volume I” as well as covered some conformal field theories. In general relativity we covered foliations, Cauchy surfaces, Gauss-Codazzi relations, ADM variables and decompositions.

### January 11th 2022

Today was the first day of classes for the day, and I am taking General Relativity II, and Quantum Field Theory II. Since it was the first day, it was mainly review, but in for QFT we explored representations of the Poincare group, and that discussion followed the second chapter of Steven Weinbergs “The Quantum Theory of Fields I.” In GR we discussed extrinsic curvature, such as Gauss' Theorema Egregium, and covered the prequisites to start ADM theory.

### January 10th 2022

I read and wrote notes for Chapter 34, Left- and Right-Handed Spinor Fields, of Mark Srednicki’s “Quantum Field Theory.”

### January 8th 2022

I read and wrote notes for Chapter 33, Representations of the Lorentz Group, of Mark Srednicki’s “Quantum Field Theory.”

### January 6th 2022

I wrote up my notes for the end of Chapter 3, Vector Fields and n-forms, of Chris J Isham’s “Modern Differential Geometry for Physicists.”

### January 4th 2022

I read the DeRham Cohomology part Chris J Isham’s “Modern Differential Geometry for Physicists” and discussed it with two colleagues. I also discussed group representations, and separating the idea of a representation of a group from the group itself.

### Pre Jan 4th 2022

At this point in my career I am in my second year of my PhD. Let me recound the different major things that would be different from someone else.

In undergrad I majored in physics and mathematics. The math courses that I took that are relevant to me today, are proof-based linear algebra, abstract algebra, two semesters of analysis, theory of complex variables. I also took two semesters of the graduate math methods for physicist course which focused on functional analysis such as the theory of distributions, Green’s functions, operators, and Hilbert spaces.

The only physics course in my undergrad that was non-standard was a course in general relativity. We went through Sean Caroll’s book “Spacetime and Geometry: An introduction to General Relativity.”

Once I was in graduate school, the electives I have so far taken were the first semester of general relativity as well as the first semester of quantum field theory. For general relativity we used Carroll’s book as the main text, but frequently deviated from it. We used tetrads frequently which do not appear in that text. For QFT we focused on the spin zero section of Mark Srednicki’s book “Quantum Field Theory.”