"In theoretical physics, quantum field theory (QFT) is a theoretical framework combining classical field theory, special relativity, and quantum mechanics."
Relativistic quantum mechanics, quantization of fields, and the standard model of elementary particles.
Foundations of Quantum Mechanics: The fundamental postulates and peculiarities of quantum mechanics, such as wave-particle duality, uncertainty principle, and superposition principle, are central to understanding quantum field theory.
Special Relativity: Quantum field theory is based on the principles of special relativity, which describes how the laws of physics are the same for all observers in uniform motion.
Classical Field Theory: Classical field theory provides a useful introduction to the concepts of quantum fields and how they translate into particles.
Lagrangian Formalism: This mathematical framework provides a way to describe the dynamics of quantum fields using a set of equations that govern the fundamental interactions between particles.
Hamiltonian Formalism: Similar to the Lagrangian formalism, the Hamiltonian formalism allows for the description of the dynamics of particles in terms of interactions, and can be used to determine the energy levels of a quantum system.
Path Integrals: These mathematical formalisms can be used to describe the dynamics of particles in a probabilistic manner, enabling accurate predictions about particle behavior.
Feynman Diagrams: These diagrams provide a graphical representation of the interactions between particles and are a powerful tool for visualizing complex quantum field theoretic processes.
Renormalization: This mathematical technique is used to eliminate certain classes of divergences within quantum field theory calculations, making predictions more accurate.
Symmetries and Conservation Laws: Symmetries underlie the behavior of particles in quantum field theory, and conservation laws ensure that certain physical quantities, such as energy or momentum, are always preserved.
Gauge Theories: Gauge theories, like quantum electrodynamics, model the interaction of particles with electromagnetic fields, and use mathematical formulations to predict particle behavior.
Quantum Chromodynamics: This branch of QFT models the strong nuclear force that binds quarks together to form neutrons and protons, allowing us to understand the behavior of atomic nuclei.
Higgs Mechanism: The Higgs mechanism is a quantum field theoretic process that gives particles mass, and is central to our understanding of the fundamental building blocks of the universe.
String Theory: A modern extension of QFT, string theory attempts to unify general relativity and quantum mechanics, and describes all particles as vibrational modes of infinitesimal strings, rather than foundational point particles.
Relativistic Quantum Field Theory: A framework for describing the interactions of particles that moves at relativistic speeds.
Non-Relativistic Quantum Field Theory: A framework for describing non-relativistic systems, such as atoms and molecules.
Gauge Field Theory: The application of quantum mechanics to the study of fields with gauge symmetry, such as electromagnetism and the strong and weak nuclear forces.
Conformal Field Theory: A type of quantum field theory that describes the behavior of conformally invariant systems.
Superstring Theory: A theoretical framework that includes gravity and unifies all the fundamental forces in nature.
Topological Quantum Field Theory: A mathematical framework that describes the topology of space and time.
Perturbative Quantum Field Theory: A framework that uses series expansions to calculate the effects of small interactions between particles.
Non-Perturbative Quantum Field Theory: A framework that uses numerical methods and other techniques to calculate the effects of large-scale interactions between particles.
Lattice Quantum Field Theory: A numerical approach to studying quantum fields on a discrete space-time lattice.
Effective Field Theory: A mathematical framework for describing low-energy excitations of a system using simplified models.
"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."