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I am currently struggling to understand what directions theoretical physics takes after one has studied special and general relativity and a standard course in quantum mechanics.

Assuming one comes from mathematics background (ie no background reading in mathematics needed) and that one has studied:

  • Classical Mechanics
  • Hamiltonian and Lagrangian Mechanics
  • Electromagnetism
  • Special Relativity
  • Quantum Mechanics
  • General Relativity
  • Statistical Physics and Thermodynamics

What are the directions of theoretical physics post this point. So potentially in what order would you learn:

  • Quantum Field Theory
  • String Theory(s)
  • Standard Model
  • Supersymmetry
  • Loop Quantum Gravity/ Quantum Gravity
  • M-Theory
Gold
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Trajan
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  • Possible duplicate of Book recommendations – knzhou Jan 26 '18 at 17:16
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    This is way too broad. (Of course QFT comes first though.) – knzhou Jan 26 '18 at 17:17
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    The link doesnt show any order, its just a list – Trajan Jan 26 '18 at 17:18
  • Also there isnt a conclusive answer to this anywhere on the internet. Nowhere answers the direction of nonexperimentally verified theoretical physics – Trajan Jan 26 '18 at 17:19
  • Uh, that's because there isn't one direction. There are tons of subfields of "theoretical physics". This question will probably be closed as primarily opinion-based unless you specify what you want to know. – knzhou Jan 26 '18 at 17:20
  • Thats almost an answer in itself – Trajan Jan 26 '18 at 17:29
  • Permian should first ask himself whether he truly loves mathematical abstraction, or whether he'd prefer a nexus to the tangible. The Standard Model is experimentally verifiable, but it offers plenty of theoretical questions for him to ponder. It has too damn many adjustable parameters. Is the Higgs field the only way to impart mass? Why are neutrinos so light? How are quarks confined? – Bert Barrois Jan 26 '18 at 17:34
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    If you are talking of graduate courses I would take in a semester quantum field theory and the foundations of the standard model, usually in what is a particle physics course. You cannot be a high energy physicist if you are not grounded in the basic data, because the complexity of theories is such that one has to keep grounding oneself on what the final objective is: a theory of everything that would be predictive and be validated by data. – anna v Jan 26 '18 at 17:38
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    With regard to your list, QFT does indeed come first as it is a prerequisite to all the other topics in that list. Of course @knzhou already said this but your subsequent comment on order of the list suggested that you might have misunderstood. – K7PEH Jan 26 '18 at 17:39
  • @annav thanks, its frustrating how there is no clear directions past undergrad level – Trajan Jan 26 '18 at 18:18
  • @K7PEH What about the other topics? – Trajan Jan 26 '18 at 18:18
  • I just dont see how the topics above fit together in a high level explanation – Trajan Jan 26 '18 at 18:43
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    @Permian -- I am not sure why you are asking about the topics and how they fit together. However, let me take a stab at that particular question. QFT is the mathematical method of the standard model theories: QED, Electro-weak, QCD. You need to know QFT in order to study those subjects. And, String Theory is the Field theory of string vibrations and this includes M-Theory. And, I know little about Loop Quantum Gravity but I believe it follows a curved space time QFT approach. – K7PEH Jan 26 '18 at 19:54
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    By the time you have mastered at a graduate level QFT and particle physics, you should know what area of research draws your interest. There will be a professor whose current research is attractive . Loop quantum gravity is non standard, proposes a different path. Supersymmetry and string M theories are another path, followed by most theoreticians. First supersymmetry then string M theories, which are the most popular quantum gravities too. There is also the field of lattice QCD calculations, and even maybe the amplituhedron! – anna v Jan 27 '18 at 05:02
  • @annav thats exactly the sort of explanation i was looking for – Trajan Jan 27 '18 at 08:47
  • @K7PEH Ill have look at what these QED, Electro-weak, QCD are later but thanks – Trajan Jan 27 '18 at 08:50
  • I guarantee this question gets 1000s of views eventually. Its very hard to find the answer online... – Trajan Jan 30 '18 at 21:09

1 Answers1

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1) Quantum Field Theory --> Quantum mechanics + special relativity, fields as fundamental entities, particles as excitations of fields.

2) Standard Model --> The Quantum Field Theory describing (good part of) our universe, but no gravitation

3) Supersymmetry --> Possible extension of Standard Model, still no gravity.

4) Supergravity --> Extension of Standard Model, with gravity. Low energy limit of string theory.

5) Quantum Gravity --> gravity and quantum relevant at the same time. It's worth having a look at the Hamiltonian formalism and first attempts to quantize gravity.

5a) String Theory(s), M-Theory --> Viable quantum gravity theory (M-theory is usually introduced after String theory, for pedagogical and practical reasons)

5b) Loop Quantum Gravity --> Viable quantum gravity theory

5a and 5b can be taken in any order.

Rexcirus
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