#Physics Reading List: From Zero to Research Literature

Audience: Pure math undergraduate with no prior physics. Mathematical rigor preferred over hand-waving. End goal: read research literature in dark matter, string theory, and theoretical physics.

Long-term spine: Landau & Lifshitz, Course of Theoretical Physics (10 volumes). Once you have the foundations from Phase 1, L&L becomes the primary vehicle for deepening your physics understanding. The individual volumes are noted at the appropriate points below.

#Phase 0: Orientation and Motivation

Before grinding through textbooks, build intuition for what physics is actually about and where the field stands.

• Feynman, The Character of Physical Law -- Short, readable, gives you a sense of how physicists think. Not a textbook. Read in a weekend.
• Sean Carroll, The Biggest Ideas in the Universe (3 volumes) -- Carroll is a working cosmologist who refuses to dumb things down. Volume 1 (Space, Time, and Motion) covers classical mechanics through GR with real equations. Volume 2 (Quanta and Fields) does the same for QM and QFT. These are conceptual companions, not replacements for textbooks.
• Susskind & Hrabovsky, The Theoretical Minimum: What You Need to Know to Start Doing Physics -- Covers classical mechanics at minimum viable depth. Designed for exactly your situation. Pairs with Susskind's Stanford lecture series (free on YouTube).

#Phase 1: Foundations

These are the core undergraduate physics subjects. You need all of them before touching QFT or GR properly.

#1.1 Classical Mechanics

This is where you learn Lagrangian and Hamiltonian mechanics, which are the language of all subsequent physics.

• Taylor, Classical Mechanics -- Standard undergraduate text. Clear, well-structured, good problems. Covers Newton, Lagrange, Hamilton, oscillations, central forces, rigid bodies. Start here.
• Kleppner & Kolenkow, An Introduction to Mechanics -- More rigorous Newtonian mechanics. Good if Taylor feels too slow at the start.
• Landau & Lifshitz, Mechanics (Course of Theoretical Physics, Vol. 1) -- Terse, elegant, starts from the principle of least action. A math student will appreciate the style. Use as a second pass after Taylor.
• Goldstein, Poole & Safko, Classical Mechanics (3rd ed.) -- Graduate-level. Comprehensive treatment of Lagrangian/Hamiltonian mechanics, canonical transformations, Hamilton-Jacobi theory. You will want this before doing QFT.
• Arnold, Mathematical Methods of Classical Mechanics -- The differential-geometric treatment. Symplectic manifolds, Lie groups. As a math student you may find this the most satisfying treatment, but read it after Taylor or Goldstein so you have physical intuition to attach the formalism to.

Online:

• MIT OCW 8.01 (Newtonian, skip if comfortable) and 8.223 (Classical Mechanics II -- Lagrangian/Hamiltonian).
• Susskind, Theoretical Minimum Lecture 1-10 (Classical Mechanics), Stanford on YouTube.

#1.2 Electromagnetism

• Griffiths, Introduction to Electrodynamics (4th ed.) -- The universal standard. Covers electrostatics, magnetostatics, electrodynamics, Maxwell's equations, electromagnetic waves, special relativity. Do the problems.
• Purcell & Morin, Electricity and Magnetism (3rd ed.) -- More physical intuition. Good complement to Griffiths.
• Landau & Lifshitz, The Classical Theory of Fields (Course of Theoretical Physics, Vol. 2) -- Covers special relativity AND electrodynamics in a unified treatment. Also introduces general relativity. Read after Griffiths. This is where L&L starts paying dividends -- the relativistic formulation of electrodynamics here is more elegant than what you will find elsewhere.
• Jackson, Classical Electrodynamics (3rd ed.) -- Graduate-level. Notorious for difficulty. Use as reference for radiation theory, multipole expansions, relativistic electrodynamics.

Online:

• MIT OCW 8.02 (basic E&M), 8.07 (Electromagnetism II, pairs with Griffiths).
• Feynman Lectures on Physics, Volume II (free at feynmanlectures.caltech.edu).

#1.3 Thermodynamics and Statistical Mechanics

• Schroeder, An Introduction to Thermal Physics -- Excellent first text. Covers thermodynamics, statistical mechanics, quantum statistics.
• Landau & Lifshitz, Statistical Physics, Part 1 (Course of Theoretical Physics, Vol. 5) -- Terse and elegant. Read after Schroeder. The L&L treatment of phase transitions and the Gibbs distribution is particularly good.
• Reif, Fundamentals of Statistical and Thermal Physics -- More rigorous, denser. Good second treatment.
• Pathria & Beale, Statistical Mechanics (3rd ed.) -- Graduate-level. Comprehensive.

Online:

• MIT OCW 8.044 (Statistical Physics I).
• Susskind, Theoretical Minimum lectures on Statistical Mechanics.

#1.4 Special Relativity

• Taylor & Wheeler, Spacetime Physics (2nd ed.) -- The classic introduction. Focuses on invariants and spacetime diagrams.
• Griffiths, Introduction to Electrodynamics, Chapter 12 -- SR from the E&M perspective. Shows how electric and magnetic fields transform.
• L&L Vol. 2 (The Classical Theory of Fields) covers SR thoroughly in its first half.

#Phase 2: Intermediate / Upper Undergraduate

#2.1 Quantum Mechanics

• Griffiths, Introduction to Quantum Mechanics (3rd ed.) -- Standard first course. Wave function, Schrodinger equation, hydrogen atom, angular momentum, perturbation theory, scattering.
• Shankar, Principles of Quantum Mechanics (2nd ed.) -- More mathematical. Starts with linear algebra review, then develops QM from the Dirac formalism. Better suited to someone who thinks in terms of vector spaces and operators.
• Landau & Lifshitz, Quantum Mechanics: Non-Relativistic Theory (Course of Theoretical Physics, Vol. 3) -- The L&L treatment is characteristically concise and powerful. The chapters on angular momentum, perturbation theory, and scattering are superb. Read after Griffiths or Shankar.
• Sakurai & Napolitano, Modern Quantum Mechanics (3rd ed.) -- Graduate-level. Starts from Stern-Gerlach and builds up. Emphasis on Dirac notation, symmetries, angular momentum theory. Essential reading.
• Weinberg, Lectures on Quantum Mechanics (2nd ed.) -- Weinberg's perspective is always worth having.

Problem books:

• Irodov, Problems in General Physics -- Famous for difficult problems spanning all of undergraduate physics.
• Zettili, Quantum Mechanics: Concepts and Applications -- Many worked examples.

Online:

• MIT OCW 8.04/8.05/8.06 (Quantum Physics I/II/III). Allan Adams's 8.04 lectures are particularly good.
• Susskind, Theoretical Minimum lectures on Quantum Mechanics.
• Feynman Lectures, Volume III.

#2.2 Continuum Mechanics and Fluid Dynamics (L&L Track)

• Landau & Lifshitz, Fluid Mechanics (Course of Theoretical Physics, Vol. 6) -- If you are following the L&L series, this comes after statistical physics. Not strictly necessary for your string theory / dark matter goals, but completes your understanding of classical physics and the L&L approach.
• Landau & Lifshitz, Theory of Elasticity (Course of Theoretical Physics, Vol. 7) -- Similarly, optional for your main path but part of the complete L&L education.

#2.3 Mathematical Methods (as needed)

• Arfken, Weber & Harris, Mathematical Methods for Physicists -- Reference for special functions, Green's functions, complex analysis applications, tensor analysis.
• Nakahara, Geometry, Topology and Physics -- For differential geometry, fiber bundles, characteristic classes as used in gauge theory and string theory.
• Frankel, The Geometry of Physics -- Similar to Nakahara but with a different emphasis.

#Phase 3: Advanced / Graduate

#3.1 General Relativity

• Carroll, Spacetime and Geometry: An Introduction to General Relativity -- The best first GR textbook for someone headed toward research. Clear, modern, good treatment of differential geometry followed by Einstein's equations, Schwarzschild solution, cosmology.
• Landau & Lifshitz, The Classical Theory of Fields (Vol. 2), second half -- The GR treatment in L&L is compact and powerful. The derivation of the Einstein field equations from the action principle is classic L&L. Read this alongside or after Carroll.
• Wald, General Relativity -- The mathematically rigorous treatment. Precise about manifold structure, causal structure, singularity theorems.
• Misner, Thorne & Wheeler, Gravitation -- Encyclopedic, 1200+ pages, two parallel tracks. A reference more than a textbook.

Online:

• Carroll's GR lecture notes (gr-qc/9712019 on arXiv) -- free, condensed version of his textbook.
• Susskind, Theoretical Minimum lectures on General Relativity.
• MIT OCW 8.962 (General Relativity).

#3.2 Particle Physics and the Standard Model

• Griffiths, Introduction to Elementary Particles (2nd ed.) -- Accessible overview. Covers quarks, leptons, Feynman diagrams, gauge symmetries, Higgs mechanism.
• Halzen & Martin, Quarks and Leptons -- More quantitative. Good bridge to QFT.

#3.3 Quantum Field Theory

This is the framework underlying the Standard Model, and QFT competence is a prerequisite for string theory.

• Peskin & Schroeder, An Introduction to Quantum Field Theory -- The standard graduate text. Covers canonical quantization, Feynman diagrams, QED, renormalization, non-Abelian gauge theories, the Standard Model.
• Schwartz, Quantum Field Theory and the Standard Model -- More modern than Peskin & Schroeder, sometimes clearer.
• Landau & Lifshitz, Quantum Electrodynamics (Course of Theoretical Physics, Vol. 4) -- The L&L treatment of QED. Characteristically concise. The treatment of radiative corrections and renormalization is elegant. Read alongside or after Peskin & Schroeder for a different perspective.
• Srednicki, Quantum Field Theory -- Available free on Srednicki's website. Organized differently (spin-0, then spin-1/2, then spin-1).
• Weinberg, The Quantum Theory of Fields (3 volumes) -- The definitive treatment. Volume 1 (Foundations), Volume 2 (Modern Applications), Volume 3 (Supersymmetry). Not a first text but essential reference. Weinberg derives everything from symmetry principles.
• Zee, Quantum Field Theory in a Nutshell -- Focuses on physical intuition and the big picture.
• Duncan, The Conceptual Framework of Quantum Field Theory -- Focuses on foundational and conceptual issues. Good for a mathematician.

Online:

• MIT OCW 8.323 (Relativistic Quantum Field Theory I/II/III).
• Tong, Quantum Field Theory lecture notes (DAMTP Cambridge, free).
• Susskind, Theoretical Minimum lectures on Particle Physics and QFT.

#3.4 Remaining L&L Volumes

• Landau & Lifshitz, Statistical Physics, Part 2 (Course of Theoretical Physics, Vol. 9) -- Covers condensed matter theory: superfluidity, superconductivity, Fermi liquid theory, phase transitions. Read after QFT basics are in place.
• Landau & Lifshitz, Physical Kinetics (Course of Theoretical Physics, Vol. 10) -- Transport phenomena, kinetic equations, plasma physics. The final volume. Read as interest dictates.

Note: L&L Vol. 8 (Electrodynamics of Continuous Media) covers electromagnetic properties of matter -- dielectrics, magnetic media, superconductors, electromagnetic waves in media. Read when relevant to your interests.

#3.5 Cosmology

• Ryden, Introduction to Cosmology -- Accessible undergraduate-level introduction.
• Dodelson & Schmidt, Modern Cosmology (2nd ed.) -- The standard graduate text. Covers the hot Big Bang, inflation, CMB anisotropies, large-scale structure, dark matter, dark energy. This is where you learn to read cosmology papers.
• Weinberg, Cosmology -- Weinberg's treatment. Thorough and rigorous.
• Kolb & Turner, The Early Universe -- Classic text on early universe physics: baryogenesis, nucleosynthesis, relic abundances (directly relevant to dark matter).
• Mukhanov, Physical Foundations of Cosmology -- Strong on inflation and perturbation theory.

#Phase 4: Research Frontier

#4.1 String Theory / M-Theory

• Zwiebach, A First Course in String Theory (2nd ed.) -- The place to start. Designed for advanced undergrads/beginning grads. Covers bosonic strings, superstrings, D-branes. Excellent problems.
• Polchinski, String Theory (2 volumes) -- The standard graduate text. Volume 1 covers bosonic strings, Volume 2 covers superstrings. Requires solid QFT.
• Becker, Becker & Schwarz, String Theory and M-Theory -- More modern, covers M-theory, dualities, flux compactifications.
• Green, Schwarz & Witten, Superstring Theory (2 volumes) -- The original comprehensive text. Historical importance.

Online:

• Tong, String Theory lecture notes (DAMTP Cambridge, free).
• MIT OCW 8.821 (String Theory and Holographic Duality).

#4.2 Dark Matter: Entry Points into the Literature

Once you have GR, particle physics, and cosmology, you can start reading dark matter literature directly.

• Bertone, Hooper & Silk, "Particle Dark Matter: Evidence, Candidates and Constraints" (Physics Reports 405, 2005) -- The standard review. arXiv: hep-ph/0404175.
• Jungman, Kamionkowski & Griest, "Supersymmetric Dark Matter" (Physics Reports 267, 1996) -- Classic review of SUSY dark matter candidates.
• Feng, "Dark Matter Candidates from Particle Physics and Methods of Detection" (ARAA 48, 2010) -- More concise and modern overview.
• Planck Collaboration results papers -- The CMB measurements that constrain dark matter density and cosmological parameters.
• Particle Data Group reviews -- The PDG "Dark Matter" review (updated annually at pdg.lbl.gov).

#4.3 String Theory: Entry Points into the Literature

• Aharony, Gubser, Maldacena, Ooguri & Oz, "Large N Field Theories, String Theory and Gravity" (Physics Reports 323, 2000) -- The standard review of AdS/CFT.
• Tong, "String Theory" (2009) -- Lecture notes that double as a readable review.

#The Landau & Lifshitz Roadmap

For reference, the complete Course of Theoretical Physics and where each volume fits:

The L&L series is not designed to be read cold. Each volume assumes you have seen the material before in a more pedagogical text. The value of L&L is the unified perspective, the elegance of derivation, and the depth of physical insight compressed into minimal space. Read the introductory text first, then L&L for the definitive treatment.

#Recommended Progression

Year 1: Build the foundation.

1. Susskind, Theoretical Minimum (book) alongside Taylor, Classical Mechanics. Then L&L Vol. 1.
2. Griffiths, Introduction to Electrodynamics. Then L&L Vol. 2 (first half: SR and E&M).
3. Schroeder, Thermal Physics. Then L&L Vol. 5.
4. Taylor & Wheeler, Spacetime Physics for SR.

Year 2: Quantum mechanics and GR. 5. Shankar or Griffiths QM, then Sakurai. Then L&L Vol. 3. 6. Carroll, Spacetime and Geometry for GR. Then L&L Vol. 2 (second half: GR). 7. Griffiths, Introduction to Elementary Particles.

Year 3: QFT, cosmology, and specialization. 8. Peskin & Schroeder (or Schwartz) for QFT. L&L Vol. 4 alongside. 9. Dodelson & Schmidt, Modern Cosmology. 10. Zwiebach, A First Course in String Theory. 11. Start reading review articles in your area of interest.

#Free Online Resources Summary

#A Note on Problem-Solving

Reading physics is not learning physics. You must do problems. For each subject:

1. Work through the textbook problems (at minimum the odd-numbered ones).
2. For classical mechanics and E&M, supplement with Irodov for challenge problems.
3. For quantum mechanics, Zettili has extensive worked examples.
4. For QFT, the Peskin & Schroeder problems are essential.

Physics is learned with pencil and paper. A math student already knows this from proofs and problem sets. The same discipline applies here.