How is studying theory different? What do YOU need to do differently?

Different physicists need different tools in their lines of work, the two main groups in physics are theorists and experimentalists. It's fair to say that there are a lot more experimentalists than theorists (rightly so), so often the path for experimentalists is quite well laid in the structure of physics courses. Sometimes it's not so clear for theorists what they need to be doing to get to where they want to be. Asides from choosing theory options in your degree there are some general points of advice I'd like to give, hopefully they'll be useful! So here's some things I think you'll need to do differently to your experimental colleagues, regardless of your specific direction.

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More Maths!

This is not a stab at experimentalists, not some 'theorists are smarter than experimentalists' rubbish. Physicists need tools to solve problems and experimentalists need to use tools outside maths to solve the problems they look into. They use engineering, electronics and other skills which although related to maths don't necessarily require them to be actively solving maths problems constantly. For theorists, maths is their domain and their only real tool.

Theorists often need very specific mathematical tools relevant to their research, for example fluid mechanics researchers often need techniques from non-linear dynamics. But there are areas of maths that are practically ubiquitous throughout all physics, and crucial for both the experimentalist and theorist. Theorists must be particularly well versed in these, fluent in common mathematical language and having a good understanding of it. So here are three areas I think are key.

Calculus is an essential tool for almost all scientific fields, but theorists need serious calculus abilities. In particular geometric integrals involving volumes and surfaces of spheres and cylinders crop up a lot. Vector calculus is also an important arrow in your quiver, useful for topics like electromagnetism.

Differential equations crop up in physics all the time, solving them is a common necessity in problem solving. As a theorist you will almost certainly work with differential equations at some point in your career. You should be well versed in how to solve many types of differential equation problems analytically and potentially numerically (more on numerical methods later).

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Linear algebra is arguably the least fundamental of these three, but undoubtedly a key piece of your tool kit. Studying this leads to group theory which is essential for a number of fields. Understanding vectors and matrices along with the relevant techniques and manipulations is an important part of a theorists skill set.

Most importantly, if you want to do theory you better love maths! I've known plenty of experimentalists who view maths as a necessary evil but never a theorist who shared that view.

Programming:
Whilst there are areas of theory that don't use computers as a primary tool I'd be lying if I said they aren't crucial to most areas of theory. They can perform calculations that simply aren't worth your time, or calculations that are impractical for humans to carry out. Computers are key for a number of theoretical activities such as:

• Constructing simulations of many-particle systems
• Modelling fluid dynamics
• Finding numerical solutions to systems of differential equations
• Computing large matrix operations symbolically or numerically
• Kinematics calculations from track measurements in particle detectors

You can imagine how the above can be relevant to multiple fields. The main programming language used is C++, but Fortran is also used by some theorists. Symbolic manipulation languages like Mathematica are also used, with C++ extensions like Eigen often used by particle physicists.

Python is often the starting point for most physicists, it leads nicely into C++. All of this said don't feel pressure to take programming courses, I only have a compulsory 2nd year programming course under my belt and it hasn't caused any problems yet. I spoke to a UCL Particle Theory PhD about half a year ago (he'd done an MSci at Oxford), he said that plenty of PhD students teach themselves programming as and when they need such capabilities.

Quantum Mechanics:

Alongside your maths courses, quantum mechanics is a subject any prospective theorist should absorb thoroughly. It is the basis for almost all modern physics outside of relativity, so being quick with quantum is pretty much a pre-requisite for being a theorist except in a few areas (fluid mechanics comes to mind). Topics like quantum field theory (a graduate level topic) build on this foundation and are the primary tool of both particle physics and condensed matter physics (along with others).

Whilst knowledge of quantum mechanics is key for both experimentalists and theorists, theorists should be well versed in the mathematics of the theory, experimentalists often focus more on the physical phenomena that arises from quantum mechanics.

Statistical Mechanics:

This is an increasingly required area of expertise for theorists of all walks. Last academic year I spoke with a condensed matter theorist, Dr Andrew Ho, who told me that whilst previously areas like particle theory weren't expected to be well versed in statistical mechanics that has been changing. Within statistical mechanics is the most modern interpretation of thermodynamics, which is often used in calculations for various experiments.

Monte Carlo methods are increasingly prevalent in particle physics, as well as various data analysis techniques are also used for the large data sets that come out experiments like the LHC. Whilst data analysis can be a discipline of itself in physics, theorists can be heavily involved in statistics and data analysis. These are often contextualised in the setting of statistical mechanics.

So whilst this discipline may be seen as more relevant to experimental studies, it seems that statistical mechanics is increasingly relevant to many theorists.

Classical Mechanics:

And to a high level, we're not talking SUVAT style here! Specifically the topic of Lagrangian and Hamiltonian formalism is an essential requirement for most fields in theory. In depth knowledge of rotational mechanics is also likely to be useful. Experimentalists are often very familiar with calculations for specific mechanical systems they work with (though plenty of them are great with Lagrangian and Hamiltonian mechanics). As a theorist you need to be familiar with a high level of generalised classical mechanics. The primary reason for this is that Hamiltonian and Lagrangian formalism is the basis of field theory, a cornerstone tool for most theorists. If you have the option to take an undergraduate course in advanced mechanics you must absolutely take it!

Numerical Methods:

This is a slightly unspecific comment but it should suffice. There are plenty of problems in physics that can't be solved exactly, even with algebraic approximations. Systems of differential equations come to mind, some of them are only solvable numerically. There are algebraic alternatives to numerical methods like perturbation methods and asymptotics, but numerical methods are incredibly relevant to current research. You might find that none of these come up in your undergraduate course and that's absolutely fine. But if you have the opportunity to study them, consider if they are relevant to your current interests, I'd strongly suggest studying them if there is even a bit of relevance.

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So there's some points about what you might need to do differently in your studies to your experimental colleagues and some general advice about what you might find useful if you want to pursue theory. This list is not at all exhaustive, but I hope it highlights some important areas to focus on.