"In theoretical physics, quantum field theory (QFT) is a theoretical framework combining classical field theory, special relativity, and quantum mechanics."
Explores the difficulties and challenges of describing interacting quantum fields and introduces perturbation theory.
Classical field theory: Classical field theory establishes the foundation for quantum field theory by describing the behavior of classical fields, such as the electromagnetic field, and their associated particles.
Path integrals: Path integrals are a mathematical tool for calculating the probability of a system transitioning from one state to another, and are crucial to quantum field theory.
Relativistic quantum mechanics: Relativistic quantum mechanics is the study of quantum mechanics in the context of special relativity, and is necessary to incorporate relativity into quantum field theory.
Second quantization: Second quantization is a technique for transforming a quantum mechanical system from using single-particle wavefunctions to using a field operator that describes the behavior of many particles.
Canonical quantization: Canonical quantization is a mathematical procedure for transforming a classical field into a quantum mechanical one, and is a fundamental aspect of quantum field theory.
Renormalization: Renormalization is the process of removing divergences that arise in quantum field theory, and is necessary to ensure that calculations are finite and physically meaningful.
Symmetries in quantum field theory: Quantum field theory is heavily dependent on symmetry principles, such as gauge symmetry, chiral symmetry, and conformal symmetry.
Perturbation theory: Perturbation theory is a method for calculating approximate solutions to problems in quantum field theory by expanding the solution as a power series.
Feynman diagrams: Feynman diagrams are graphical representations of particle interactions in quantum field theory, and are a powerful tool for calculating probabilities.
Effective field theory: Effective field theory is a technique for approximating the behavior of a complex system by describing it with a simpler, easier-to-calculate field theory.
Gauge theories: Gauge theories are quantum field theories that exhibit local gauge symmetry, such as the electroweak and strong nuclear forces.
Topological quantum field theory: Topological quantum field theory is a branch of quantum field theory that focuses on the topological properties of space and time.
Conformal field theory: Conformal field theory is a field theory that is invariant under conformal transformations, and plays a crucial role in the study of quantum critical phenomena.
String theory: String theory is a theoretical framework that attempts to unify all fundamental forces and particles by describing them as different vibrational modes of tiny one-dimensional strings.
Black holes in quantum field theory: Quantum field theory is important for understanding the behavior of black holes, which are extreme gravitational objects that can only be studied using a combination of general relativity and quantum mechanics.
Scalar field: This is the most basic type of quantum field, which has no spin and is described by a scalar value at each point in space-time. Examples include the Higgs field, which is responsible for giving particles mass.
Vector field: This type of quantum field has spin 1 and is described by a vector value at each point in space-time. These fields are responsible for mediating the electromagnetic force, as well as the weak and strong nuclear forces.
Fermionic field: These fields have spin 1/2 and are described by spinor values at each point in space-time. Fermionic fields describe matter particles, such as electrons and quarks, and are subject to the Pauli exclusion principle.
Ghost field: A type of quantum field that appears in gauge theories, such as quantum electrodynamics (QED). Ghost fields are used to remove unphysical degrees of freedom in certain calculations.
Tensor field: These fields have spin 2 and are described by tensor values at each point in space-time. They are used to describe gravity in general relativity.
Pseudo-scalar field: These fields are similar to scalar fields but have an odd parity under parity transformations. The axion is an example of a pseudo-scalar field that is being studied as a possible dark matter candidate.
Bundle field: Bundle fields are used in topological field theories to describe topological defects such as vortices and monopoles.
Conformal field: Conformal fields are used in conformal field theory, which is an area of quantum field theory that describes scale-invariant systems.
Topological field: Topological fields are used in topological quantum field theory to describe topological states of matter, such as topological insulators.
"QFT is used in particle physics to construct physical models of subatomic particles."
"QFT is used in condensed matter physics to construct models of quasiparticles."
"QFT treats particles as excited states (also called quanta) of their underlying quantum fields."
"Quantum fields, which are more fundamental than the particles."
"The equation of motion of the particle is determined by minimization of the action computed for the Lagrangian."
"The Lagrangian is a functional of fields associated with the particle."
"Interactions between particles are described by interaction terms in the Lagrangian involving their corresponding quantum fields."
"Each interaction can be visually represented by Feynman diagrams."
"According to perturbation theory in quantum mechanics."
"A theoretical framework combining classical field theory, special relativity, and quantum mechanics."
"Quantum fields are more fundamental than the particles."
"The equation of motion of the particle is determined by minimization of the action computed for the Lagrangian."
"Interactions between particles are described by interaction terms in the Lagrangian involving their corresponding quantum fields."
"Each interaction can be visually represented by Feynman diagrams."
"QFT is used in particle physics to construct physical models of subatomic particles."
"QFT is used in condensed matter physics to construct models of quasiparticles."
"Particles are treated as excited states (quanta) of quantum fields."
"The minimization of the action computed for the Lagrangian."
"Interactions between particles manifest as interaction terms in the Lagrangian."