Doing research in quantum field theory (QFT), string theory, and general relativity involves a combination of theoretical study, mathematical analysis, and computational techniques. Here are the general steps a theoretical physicist might take in their research:
Deepening Theoretical Knowledge:
- Theoretical physicists start by acquiring a solid foundation in the relevant theories, including quantum mechanics, special relativity, and classical mechanics. They study advanced topics in quantum field theory, such as renormalization, gauge theories, and symmetry principles.
- For string theory, researchers delve into the mathematical structures and formalism of string theory, such as conformal field theory, supersymmetry, and the various string compactifications.
- General relativity requires a strong grasp of differential geometry and tensor calculus. Physicists study Einstein's field equations, the principles of curvature and geodesics, and gravitational wave theory.
Mathematical Analysis:
- Researchers use advanced mathematical techniques to analyze the theories. This includes manipulating equations, performing calculations, and solving mathematical models relevant to the theories being investigated.
- In quantum field theory, physicists often utilize perturbative techniques such as Feynman diagrams and diagrammatic methods to compute scattering amplitudes, cross-sections, and other observables. They also employ mathematical tools like group theory, functional analysis, and operator algebras.
- String theory involves a rich interplay of mathematics, including algebraic geometry, complex analysis, differential geometry, and topological methods. Physicists apply these mathematical tools to study string scattering amplitudes, symmetries, and the behavior of strings in various backgrounds.
Computational Techniques:
- Computer simulations and numerical calculations play a significant role in certain aspects of research. For instance, lattice field theory is employed to study strongly interacting quantum field theories, where the equations are too complex for analytical solutions.
- In string theory, numerical methods are used to explore the behavior of strings in certain backgrounds or to study properties of black holes and cosmological solutions.
Collaboration and Discussion:
- Theoretical physicists often collaborate with colleagues, forming research groups or participating in collaborations. They discuss ideas, exchange insights, and work together on challenging problems.
- They also attend conferences, workshops, and seminars where they present their research, receive feedback, and stay updated on the latest developments in their field.
Publishing and Peer Review:
- As researchers make progress, they prepare scientific papers detailing their findings and submit them to peer-reviewed scientific journals for publication. Peer review ensures the quality and validity of the research by subjecting it to critical evaluation by experts in the field.
Continuous Learning and Adaptation:
- Theoretical physicists must stay up-to-date with the latest advancements in their fields. They read scientific literature, attend conferences, and engage in ongoing learning to remain at the forefront of research.
It's important to note that research in these areas is highly specialized and requires years of study and dedication. The process may vary among researchers, and different projects may emphasize different aspects depending on the specific research goals and interests of the physicist.