introduction
Quantum Field Theory (QFT) is a theory in physics that describes elementary particles and their interactions. It is based on the basic principles of quantum mechanics, quantizes the concepts in classical field theory, and describes the physical system as a collection of qubits. These qubits travel through space and time and interact to form various physical phenomena.
concept
Quantum field theory includes many concepts and methods, some of the main concepts include:
Classic field
A classical field is a continuous physical quantity that can be defined at every point in space and time. For example, electromagnetic field, gravitational field and temperature field can all be regarded as classical fields.
quantum field
Corresponding to the classical field, the quantum field is a discrete physical system that cannot be directly observed, only its particle state can be observed. The state of a quantum field can be described by a quantum state, which is a state vector containing a large number of qubits.
regular quantization
Canonical quantization is a method of quantizing canonical equations in classical field theory. It transforms the evolution equation of the classical field into the state equation of the quantum field by introducing the quantum operators and quantum states of the classical field.
path integral
Path integral is another important tool in quantum field theory. It is a method used to calculate the physical quantities and regulations of quantum fields. The basic idea of path integral is to regard the evolution of the quantum field as the superposition of all possible paths, and then perform a weight calculation on each path, and finally obtain an integral expression that includes the contributions of all paths.
Two point correlation function
The two-point correlation function is an important concept in quantum field theory, which describes the correlation between two points in space. The two-point correlation function can be used to calculate the probability distribution of particles in space, measurement errors, and interactions between particles.
Feynman diagram
Feynman diagrams are another important tool in quantum field theory, which describe the interactions and evolution of particles. A Feynman diagram is a graph composed of a series of arrows and lines with arrows, where the arrows represent the direction of movement of particles, and the lines with arrows represent the process of interaction.
renormalization
Renormalization is another important concept in quantum field theory, which is used to eliminate the influence of unstable states to achieve the stability of quantum fields. There are many methods of renormalization, the most common of which is overdetermined renormalization .
Overdetermined renormalization is a method of dealing with infinite divergences that eliminates divergences by redefining physical quantities. In overdetermined renormalization, physical quantities are divided into active and passive parts. The active part is the part that interacts with the particles, and the passive part is the part that does not interact with the particles. By renormalizing the passive part, the influence of the active part on the system can be eliminated, thereby achieving the stability of physical quantities.
Overdetermined renormalization is an effective method that can solve many theoretical problems. However, it also has some problems, such as the selection of renormalization parameters and the consistency of the theory. Therefore, in practical applications, it is necessary to choose the appropriate processing method according to the specific situation.
Summarize
In summary, quantum field theory is an important theory in physics that provides a framework for describing elementary particles and their interactions. By quantizing classical fields and introducing evolution equations of quantum fields, we can describe various physical phenomena and calculate the corresponding physical quantities. Although there are some problems in practical application, through continuous improvement and development of theory, we can better understand the nature and laws of nature.