Quantum field theory (QFT) and string field theory (SFT) are two closely related frameworks used to describe the fundamental interactions of particles and fields in physics. Here's a brief overview of the role of quantum field theory in string field theory:
Quantum Field Theory (QFT): Quantum field theory is a mathematical framework that combines quantum mechanics and special relativity to describe the behavior of quantum fields. In QFT, elementary particles are described as excitations of their respective quantum fields. The interactions between these particles are represented by mathematical objects known as Feynman diagrams, which are used to calculate probabilities of different particle interactions.
String Theory: String theory is a theoretical framework that aims to provide a unified description of all fundamental particles and forces in the universe. According to string theory, particles are not considered point-like entities but rather tiny, one-dimensional strings. The vibrations and modes of these strings give rise to various particles with different properties.
String Field Theory (SFT): String field theory is an extension of string theory that incorporates the principles of quantum field theory. While traditional string theory describes the behavior of strings in a fixed background, string field theory treats the string itself as a dynamic object. In SFT, the fundamental entities are string fields, which are analogous to quantum fields in QFT.
Interaction Vertex: In string field theory, interactions between strings are described by interaction vertices, similar to how interactions between particles are described by Feynman vertices in QFT. These interaction vertices represent the joining and splitting of strings during interactions, and they are crucial for calculating the scattering amplitudes associated with different string interactions.
Feynman Diagrams in SFT: Feynman diagrams, which are integral to QFT calculations, can also be employed in string field theory. These diagrams involve the joining and splitting of strings at interaction vertices. However, due to the higher-dimensionality of strings compared to point particles, Feynman diagrams in SFT become more complex, involving the propagation and splitting of strings in multiple dimensions.
In summary, quantum field theory plays a crucial role in string field theory by providing a framework to describe the interactions of string fields and calculating scattering amplitudes using interaction vertices and Feynman diagrams. It allows for the incorporation of quantum mechanical principles into the study of string interactions, leading to a deeper understanding of the fundamental structure of the universe.