Physics / advanced
Quantized fields and relativistic particles
Develop canonical quantum fields in detail through mode expansions, locality, spin-statistics, normal ordering, and the particle interpretation of free theories.
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Module 01 advanced
Quantized fields and relativistic particles
Develop canonical quantum fields in detail through mode expansions, locality, spin-statistics, normal ordering, and the particle interpretation of free theories.
- 01
Scalar field mode expansion and normalization
Construct a real Klein–Gordon field from positive and negative frequencies while keeping box, continuum, and relativistic state normalizations distinct.
33 min - 02
Canonical field commutators and Hamiltonians
Recover the free scalar dynamics from a canonical bracket and a positive quadratic Hamiltonian while distinguishing a formal density from its regulated operator.
33 min - 03
Vacuum energy and normal ordering
Separate volume and ultraviolet divergences, define free-vacuum Wick ordering, and identify what vacuum subtraction does and does not establish.
33 min - 04
Charged scalar fields and antiparticles
Quantize a complex Klein–Gordon field with two oscillator families and distinguish positive energy, signed charge, and particle-number conventions.
33 min - 05
Dirac spinors and completeness relations
Fix gamma-matrix and spinor conventions before using on-shell spin sums as matrices in a relativistic field expansion.
33 min - 06
Fermionic anticommutators and positive energy
Quantize the first-order Dirac field using canonical anticommutators, explain the antiparticle energy sign, and derive exclusion in a regulated mode basis.
33 min - 07
Free photon polarizations and gauge redundancy
Reduce free Maxwell theory to transverse oscillators and keep canonical brackets consistent with Gauss constraints and gauge-dependent potentials.
33 min - 08
Poincaré generators in field theory
Connect Noether stress energy to quantum translations, rotations, and boosts, with explicit generator signs and domain assumptions.
33 min - 09
Microcausality and local observable algebras
Distinguish spacelike vanishing commutators from nonzero vacuum correlations, and express causal compatibility through smeared local observable algebras.
33 min - 10
Spin–statistics assumptions and consequences
State the scope of the relativistic spin–statistics connection and distinguish its field-theoretic assumptions from finite-mode consequences and auxiliary gauge constructions.
33 min