Quantum field theory (QFT) and string theory are both frameworks in theoretical physics that aim to describe the fundamental interactions of particles and the nature of the universe. While they share some similarities, they also have key differences in their fundamental assumptions and mathematical structures.
Fundamental Assumptions:
- Quantum Field Theory: QFT is based on the principles of quantum mechanics and special relativity. It postulates that particles are excitations of underlying quantum fields, which permeate all of spacetime. These fields interact with each other through exchange of particles, resulting in the fundamental forces of nature.
- String Theory: String theory, on the other hand, posits that the fundamental constituents of the universe are not point-like particles but tiny, vibrating strings of energy. It suggests that the universe has more than the familiar three spatial dimensions and includes additional spatial dimensions that are curled up or "compactified."
Description of Particles:
- Quantum Field Theory: QFT describes particles as localized excitations of quantum fields. It provides a framework for understanding the behavior of particles such as electrons, photons, and quarks, and how they interact through the exchange of other particles like photons and gluons.
- String Theory: In string theory, particles arise as different vibrational modes of the fundamental strings. These vibrations determine the particle's properties, such as its mass and charge. String theory also predicts the existence of additional particles called "string excitations" or "string modes," which are more massive than the particles described by QFT.
Mathematical Framework:
- Quantum Field Theory: QFT employs a mathematical framework known as perturbation theory, which involves expanding calculations in terms of Feynman diagrams. This approach allows for the calculation of probabilistic outcomes of particle interactions to high precision.
- String Theory: String theory requires a more elaborate mathematical framework. It relies on the principles of quantum mechanics, but its formulation includes a consistent theory of gravity, which is absent in QFT. String theory uses advanced mathematical tools such as conformal field theory and supersymmetry to study the behavior of strings and their interactions.
Applications to Each Other:
- String theory can be seen as an extension or generalization of quantum field theory. In certain limits, string theory reduces to specific quantum field theories. For example, when the strings are compactified in a particular way, string theory can yield QFTs with known particle content and interactions.
- String theory has provided insights into certain strongly interacting quantum field theories. The AdS/CFT correspondence, also known as the gauge/gravity duality, relates a specific type of string theory (string theory in Anti-de Sitter space) to a quantum field theory living on its boundary. This duality has allowed researchers to study strongly coupled QFTs using the more tractable framework of string theory.
- Quantum field theory techniques, particularly those developed for perturbative calculations, have been applied to certain aspects of string theory. For example, Feynman diagram techniques and other calculational tools from QFT have been employed to study scattering amplitudes and other properties of string theory.
It's worth noting that both quantum field theory and string theory are highly complex and active areas of research. While they have made significant contributions to our understanding of fundamental physics, particularly in the realm of particle physics and gravity, many aspects of both theories are still being explored and refined.