--- title: "Physics research routes: 42 courses from basics to open questions | Sandbox Physics" description: "42 physics research routes, each a bilingual course with Labs. Every route starts from one research question; suggested prerequisites link the routes." canonical_url: "https://sandboxphysics.com/learn/research-routes/" language: "en" page_type: "story" alternate_languages: zh-CN: "https://sandboxphysics.com/zh/learn/research-routes/" last_modified: "2026-11-03" --- Sandbox Physics · Research routes # Research routes Each route is a course that starts from one research question, works through the models and methods behind it, and ends at a reproduced result and the questions that are still open. Routes are independent courses. Where one route uses another, it is listed under “Read first”; you only need the chapters it relies on, not the whole route. The shared basics are in the textbook. [Open the textbook →](https://sandboxphysics.com/learn/) ## Suggested reading orders These orders link routes that build on each other. Start anywhere along an order if you already know the earlier topics. - ### Field theory 1. Measuring in relativity: clocks, light signals and four-momentum 2. Quantum field theory, renormalization and critical phenomena 3. Gauge theory and effective field theory 4. Collider physics: event reconstruction, jets and inference - ### Branches of field theory 1. Quantum field theory, renormalization and critical phenomena 2. Lattice gauge theory: Gauss’s law, confinement and string breaking 3. Scattering amplitudes: helicity, factorization and unitarity 4. Conformal field theory and the bootstrap 5. Holography and quantum gravity - ### Chemistry 1. Molecular electronic structure: correlation, DFT and bond breaking 2. Nonadiabatic dynamics: conical intersections and reaction branching 3. Nonlinear and two-dimensional spectroscopy - ### Chemistry through fluctuations 1. Stochastic thermodynamics: work, heat and hidden entropy 2. Free energy and rare events: enhanced sampling and kinetics 3. Electrochemistry and ion transport 4. Dynamic interfaces: capillary waves, dewetting and Marangoni flow - ### Living matter 1. Stochastic thermodynamics: work, heat and hidden entropy 2. Single-molecule biophysics: optical tweezers and molecular motors 3. Membranes and vesicles: bending, tethers and shapes - ### Quantum experiments 1. Time–frequency quantum optics: photon sources, modes and pulse gates 2. Cavity and waveguide QED: from one photon to several 3. Quantum optomechanics: cooling, measurement and back-action 4. Quantum many-body numerics: entanglement, MPS and DMRG ## All 42 routes ### High-energy physics and field theory - #### [Quantum field theory, renormalization and critical phenomena](https://sandboxphysics.com/learn/field-theory/) Why does averaging over fast, short-wavelength motion change the low-energy parameters, yet still leave stable predictions at long distances? Read first: Measuring in relativity: clocks, light signals and four-momentum - #### [Gauge theory and effective field theory](https://sandboxphysics.com/stories/gauge-effective-theory/) How can unresolved high-energy physics be packed into a few low-energy terms, and how do we know when that description fails? Read first: Quantum field theory, renormalization and critical phenomena - #### [Collider physics: event reconstruction, jets and inference](https://sandboxphysics.com/stories/collider-qcd/) How do physicists infer a short-range interaction from detector records, and tell jet physics apart from detector effects and chance? Read first: Gauge theory and effective field theory, Measuring in relativity: clocks, light signals and four-momentum - #### [Lattice gauge theory: Gauss’s law, confinement and string breaking](https://sandboxphysics.com/stories/lattice-gauge/) In a model that obeys Gauss’s law at every site, how does the electric flux between two charges grow, and how do new particles screen it? Read first: Quantum field theory, renormalization and critical phenomena, Gauge theory and effective field theory - #### [Scattering amplitudes: helicity, factorization and unitarity](https://sandboxphysics.com/stories/scattering-amplitudes/) Can symmetry, pole structure and consistency alone fix an interaction without listing every Feynman diagram? Read first: Quantum field theory, renormalization and critical phenomena, Measuring in relativity: clocks, light signals and four-momentum - #### [Heavy-ion collisions and quark–gluon matter](https://sandboxphysics.com/stories/qgp-hydrodynamics/) Why can matter that is still far from local equilibrium already flow like a fluid, and how do experiments measure its viscosity? Read first: Quantum field theory, renormalization and critical phenomena, Measuring in relativity: clocks, light signals and four-momentum - #### [Conformal field theory and the bootstrap](https://sandboxphysics.com/stories/conformal-bootstrap/) Without knowing the microscopic Hamiltonian, how far can consistency conditions alone pin down a critical system? Read first: Quantum field theory, renormalization and critical phenomena ### Nuclei, cosmology and spacetime - #### [Nuclear structure, reactions and nuclear astrophysics](https://sandboxphysics.com/stories/nuclear-bridge/) What part of the nucleus does each picture see: single particles in shells, collective deformation, or reaction data? No route to read first; the textbook basics are enough. - #### [Cosmological perturbations, acoustic peaks and inference](https://sandboxphysics.com/stories/cosmology/) How do correlations across the sky limit what the universe is made of, and why can different models predict nearly the same sky? Read first: Measuring in relativity: clocks, light signals and four-momentum - #### [Holography and quantum gravity](https://sandboxphysics.com/stories/holography/) Under stated assumptions, how does information in a boundary quantum state map to geometry in the bulk, and which pictures are only analogies? Read first: Quantum field theory, renormalization and critical phenomena, Quantum many-body numerics: entanglement, MPS and DMRG, Conformal field theory and the bootstrap, Measuring in relativity: clocks, light signals and four-momentum - #### [Measuring in relativity: clocks, light signals and four-momentum](https://sandboxphysics.com/stories/relativity-measurement/) Why are seeing an event, assigning it a coordinate time and timing it on your own clock three different operations? No route to read first; the textbook basics are enough. ### Quantum optics and many-body physics - #### [Time–frequency quantum optics: photon sources, modes and pulse gates](https://sandboxphysics.com/stories/time-frequency-quantum-optics/) Why can two photon-pair sources with the same joint spectral intensity give heralded photons of very different purity? No route to read first; the textbook basics are enough. - #### [Cavity and waveguide QED: from one photon to several](https://sandboxphysics.com/stories/waveguide-qed/) Bound states and echoes are clear with one excitation. What is left of them when two photons arrive together? Read first: Time–frequency quantum optics: photon sources, modes and pulse gates - #### [Quantum optomechanics: cooling, measurement and back-action](https://sandboxphysics.com/stories/quantum-optomechanics/) Why does a stronger optical readout both measure a mechanical oscillator better and disturb its motion more? Read first: Time–frequency quantum optics: photon sources, modes and pulse gates - #### [Quantum many-body numerics: entanglement, MPS and DMRG](https://sandboxphysics.com/stories/tensor-networks/) The state space grows exponentially with system size. How does entanglement structure keep some many-body states computable, and where does that stop? No route to read first; the textbook basics are enough. ### Physical chemistry - #### [Molecular electronic structure: correlation, DFT and bond breaking](https://sandboxphysics.com/stories/molecular-electronic/) Why can an electronic model that works well near the equilibrium bond length give the wrong physics once the bond is stretched? No route to read first; the textbook basics are enough. - #### [Nonadiabatic dynamics: conical intersections and reaction branching](https://sandboxphysics.com/stories/nonadiabatic-dynamics/) When electronic and nuclear motion cannot be separated, how do we tell which product a reaction will reach? Read first: Molecular electronic structure: correlation, DFT and bond breaking - #### [Free energy and rare events: enhanced sampling and kinetics](https://sandboxphysics.com/stories/free-energy/) Why can trajectories that look well sampled still give a wrong free energy and a badly wrong reaction rate? Read first: Stochastic thermodynamics: work, heat and hidden entropy - #### [Nonlinear and two-dimensional spectroscopy](https://sandboxphysics.com/stories/multidimensional-spectroscopy/) Peaks that overlap in a linear spectrum: how do several laser pulses separate their coupling, dephasing and chemical exchange? Read first: Molecular electronic structure: correlation, DFT and bond breaking - #### [Electrochemistry and ion transport](https://sandboxphysics.com/stories/electrochemistry/) When current passes through an electrolyte and an electrode surface, how do charge storage, ion depletion and fluid flow change one another? No route to read first; the textbook basics are enough. - #### [Dynamic interfaces: capillary waves, dewetting and Marangoni flow](https://sandboxphysics.com/stories/dynamic-interfaces/) Surface tension usually smooths an interface. Why does it make thin films, liquid threads and heated surfaces change shape faster? No route to read first; the textbook basics are enough. ### Biophysics - #### [Single-molecule biophysics: optical tweezers and molecular motors](https://sandboxphysics.com/stories/single-molecule/) How does one bead held in optical tweezers reveal a molecule’s elasticity, its random unfolding and its energy-burning steps? Read first: Stochastic thermodynamics: work, heat and hidden entropy - #### [Membranes and vesicles: bending, tethers and shapes](https://sandboxphysics.com/stories/membrane-mechanics/) How does a soft membrane with no skeleton hold a stable shape, and how do its thermal ripples reveal its bending stiffness? Read first: Single-molecule biophysics: optical tweezers and molecular motors, Geometric elasticity: sheets, shells and multistability - #### [Morphogenesis: reaction–diffusion and mechanical feedback](https://sandboxphysics.com/stories/morphogenesis/) How does a uniform tissue grow a spatial pattern by itself, and how can we tell the roles of diffusion, boundaries and mechanics apart? No route to read first; the textbook basics are enough. - #### [Active matter: self-propelled particles and moving defects](https://sandboxphysics.com/stories/active-matter/) Why do particles that keep burning energy cluster without any attraction, and why do their topological defects move on their own? No route to read first; the textbook basics are enough. - #### [Microswimming at low Reynolds number](https://sandboxphysics.com/stories/microswimming/) When inertia almost vanishes, why can a swimmer that strokes back and forth never move forward, however fast it strokes? No route to read first; the textbook basics are enough. - #### [Statistical physics of evolution and ecology](https://sandboxphysics.com/stories/evolution-statistical-physics/) Why can a variant with no local advantage still take over a whole expanding population? No route to read first; the textbook basics are enough. - #### [Statistical physics of neural systems](https://sandboxphysics.com/stories/neural-statistical-physics/) When neural recordings look close to a critical point, how do we tell real dynamics from an artifact of the analysis? Read first: Stochastic thermodynamics: work, heat and hidden entropy ### Non-equilibrium physics and materials - #### [Stochastic thermodynamics: work, heat and hidden entropy](https://sandboxphysics.com/stories/stochastic-thermodynamics/) If we observe only part of a system, can we still tell how much energy it dissipates and how far it is from equilibrium? No route to read first; the textbook basics are enough. - #### [Complex fluids: elastic instabilities and elastic turbulence](https://sandboxphysics.com/stories/complex-fluids/) How can a flow with almost no inertia still become violently unsteady in space and time? No route to read first; the textbook basics are enough. - #### [Granular matter and jamming](https://sandboxphysics.com/stories/granular-jamming/) At the same packing density, why do grains sometimes flow and sometimes suddenly bear a load? No route to read first; the textbook basics are enough. - #### [Fracture mechanics: Griffith energy, phase-field cracks and branching](https://sandboxphysics.com/stories/fracture-mechanics/) Why does a material crack along one path, and why can a faster load make the crack branch or wander? No route to read first; the textbook basics are enough. - #### [Micromagnetics: domain walls, spin waves and skyrmions](https://sandboxphysics.com/stories/micromagnetics/) When the magnetization direction is no longer set by hand, how do exchange, demagnetization, damping and driving decide the pattern? No route to read first; the textbook basics are enough. - #### [Geometric elasticity: sheets, shells and multistability](https://sandboxphysics.com/stories/geometric-elasticity/) Why does changing the lengths a thin sheet wants to have make it curl into a complex shape with no external force? No route to read first; the textbook basics are enough. - #### [Crystal defects and microstructure: dislocations, grains and dendrites](https://sandboxphysics.com/stories/crystal-defects-microstructure/) How do energy, diffusion and interface motion together choose the grains and dendrites seen under a microscope? No route to read first; the textbook basics are enough. - #### [Nanofriction: stick–slip, thermal activation and superlubricity](https://sandboxphysics.com/stories/nanofriction/) A friction coefficient looks simple. How do the atomic-scale periodic potential and the twist between lattices change the energy lost? Read first: Stochastic thermodynamics: work, heat and hidden entropy ### Waves, imaging and transport - #### [Kinetic plasma physics: Landau damping and echoes](https://sandboxphysics.com/stories/kinetic-plasma/) After the electric field dies away, is the information gone, or hidden in fine structure of the velocity distribution? No route to read first; the textbook basics are enough. - #### [Fluctuational electrodynamics: near-field heat transfer and Casimir forces](https://sandboxphysics.com/stories/fluctuational-electrodynamics/) When two surfaces are much closer than the thermal wavelength, why does the blackbody formula no longer describe the heat flow? No route to read first; the textbook basics are enough. - #### [Acoustics and ultrasound: radiation force, echoes and cavitation](https://sandboxphysics.com/stories/acoustics-ultrasound/) How can the same sound beam carry an image, push particles and drive bubbles? No route to read first; the textbook basics are enough. - #### [Magnetic resonance imaging: Bloch dynamics and k-space](https://sandboxphysics.com/stories/mri-spatial-encoding/) The coil records one total signal with no position label. How do field gradients turn it into an image that can be reconstructed? No route to read first; the textbook basics are enough. - #### [Seismology: elastic waves, source location and inversion](https://sandboxphysics.com/stories/seismic-imaging/) From a few vibration records at the surface, how well can we know the structure underground? No route to read first; the textbook basics are enough. - #### [Phonons and heat transport: ballistic flow and second sound](https://sandboxphysics.com/stories/phonon-heat-transport/) Does a temperature disturbance always spread like ink in water, or can it travel as a wave in some solids? No route to read first; the textbook basics are enough.