Quantum Field Theory: Conservation Laws

In course

Description

This lecture focuses on deriving conserved currents in classical field theory and quantum field theory, emphasizing the importance of symmetries and equations of motion. The instructor explains the difference between conserved quantities in classical mechanics and field theory, highlighting the role of Noether's theorem. Through detailed mathematical derivations, the lecture covers the application of symmetries to Lagrangians, transformations of fields under translations, and the conservation of currents. The instructor also provides insights into the significance of infinitesimal shifts in coordinates and the implications of Gal's theorem. By exploring the relationship between symmetries, Lagrangians, and conserved currents, the lecture offers a comprehensive understanding of the fundamental principles underlying quantum field theory.

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Official source

https://mediaspace.epfl.ch/media/0_jaz4jcd4

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Related concepts (37)

Lagrangian (field theory)

Lagrangian field theory is a formalism in classical field theory. It is the field-theoretic analogue of Lagrangian mechanics. Lagrangian mechanics is used to analyze the motion of a system of discrete particles each with a finite number of degrees of freedom. Lagrangian field theory applies to continua and fields, which have an infinite number of degrees of freedom.

Scalar field theory

In theoretical physics, scalar field theory can refer to a relativistically invariant classical or quantum theory of scalar fields. A scalar field is invariant under any Lorentz transformation. The only fundamental scalar quantum field that has been observed in nature is the Higgs field. However, scalar quantum fields feature in the effective field theory descriptions of many physical phenomena. An example is the pion, which is actually a pseudoscalar.

Quantum field theory

In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles.

Classical field theory

A classical field theory is a physical theory that predicts how one or more physical fields interact with matter through field equations, without considering effects of quantization; theories that incorporate quantum mechanics are called quantum field theories. In most contexts, 'classical field theory' is specifically intended to describe electromagnetism and gravitation, two of the fundamental forces of nature. A physical field can be thought of as the assignment of a physical quantity at each point of space and time.

Classical unified field theories

Since the 19th century, some physicists, notably Albert Einstein, have attempted to develop a single theoretical framework that can account for all the fundamental forces of nature – a unified field theory. Classical unified field theories are attempts to create a unified field theory based on classical physics. In particular, unification of gravitation and electromagnetism was actively pursued by several physicists and mathematicians in the years between the two World Wars.