### For advanced undergraduate physics majors

- Black hole information paradox

To understand the article on gauge theory, you have to know quantum mechanics and what a vector potential is. Careful readers will find that the connection introduced in this article is precisely the electromagnetic potential 1-form explained in “Maxwell’s equations in differential forms.” Similarly, they will find that the notion of gauge transformations in both cases coincide. “Feynman path integral” shows how quantum mechanics can be as bizarre as it can be. Familiarity with Lagrangian, Hamiltonian and quantum mechanics is the prerequisite. Special relativity as taught in a freshman physics class, Einstein summation convention, Lagrangian mechanics are the only prerequisites to “Introduction to general relativity,” even though familiarity with Maxwell’s equations is required to understand section 5, which can be skipped for those who aren’t familiar, and the article “Feynman path integral” is needed to understand section 29 which deals the temperature of black hole. In this article, I tried to write only the essentials rather than being complete, to make it as easy as possible. I hope that this article may serve as a steppingstone to more advanced material. “Dirac string” shows that a possible existence of magnetic monopole necessarily implies the quantization of electric charge.

### Prerequisites for Loop Quantum Gravity (for advanced undergraduate physics majors)

Comments:

To understand loop quantum gravity, it is useful to cast the usual metric formalism of general relativity in the language of vierbein formalism. “A relatively short introduction to general relativity” listed in the “For physics major” section and “Differential forms, vector calculus and generalized Stoke’s theorem” listed in the “For science and engineering students” section are the only prerequisites to this article. Comments:

The only formal prerequisite for the first article is familiarity with angular momentum in quantum mechanics as explained in the section “Angular momentum in quantum mechanics." However, most of the content can be understood without this prerequisite as long as one is familiar with the concept of a matrix. The other articles should be read in the listed order. The second half of “Non-Abelian gauge theory” assumes familiarity with tensors as presented in the first six sections of “A relatively short introduction to general relativity.” The article “Wilson line and Wilson loop” is important since the “loop” in loop quantum gravity is the Wilson loop. Comments:

The prerequisites for the first article are “Maxwell’s equations in differential forms” and “Non-Abelian gauge theory.” “Vierbein formalism and Palatini action in general relativity” is also helpful. The first article shows that gauge invariance implies charge conservation. By reading the last article, you will see the similarity between non-Abelian gauge theory and the Palatini formulation of general relativity.

### Unification of Gravity and Electromagnetism in 5-dimensions (for advanced undergraduate physics majors)

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“Kaluza-Klein theory" explains a 5-dimensional theory, proposed in the early 20th century, which unifies gravity and electromagnetism in a natural manner. General relativity and the familiarity with Maxwell Lagrangian are the prerequisites.

### The Basic Cosmology, the second part

Comments:

These articles deal with the thermal history of our universe. “Statistical Mechanics,” “The Basic Cosmology, the first part,” and “Further statistical mechanics” are prerequisities. Physics undergraduates do not usually learn this material, but some astronomy undergraduates do.

### Loop Quantum Gravity (for physics graduate students)

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### Elasticity

Comments:

You don’t usually learn much about elasticity even though you may be a physics major. I never did either. It’s not because it treats highly advanced material, but because it is now regarded more as an engineering subject than a physics one. Nevertheless, I cover here the basics of elasticity as it is relevant in Verlinde’s emergent gravity. Verlinde found a good analogy of Verlinde gravity from elasticity.

### Verlinde’s emergent gravity (for advanced undergraduate physics majors)

- Verlinde’s derivation of Tully-Fisher relation

- Verlinde’s emergent gravity

- Covariant formulation of Verlinde gravity

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### The CMB anisotropy

Comments:

Unless you want to be a serious cosmologist, you won’t need to learn the material treated in this section.