Sumários

Quantization of a complex scalar field

30 Abril 2025, 16:30 Luís Bento

Quantization of a free complex scalar field. Discretization with Fourier series and description as an infinite number of harmonic oscillators. Hamiltonean, linear momentum and U(1) charge. Their commutators with the particle and anti-particle creation operators. Exercise with a single oscillator.


Energy-momentum tensor

28 Abril 2025, 14:00 Luís Bento

Canonical and symmetrized energy-momentum tensor of the electromagnetic field.


Harmonic oscillator

16 Abril 2025, 16:30 Luís Bento

Quantization of a single harmonic oscillator and of two degenerate harmonic oscillators. Hamiltonean
and U(1) charge.


Energy-momentum tensor

14 Abril 2025, 14:00 Luís Bento

Calculation of the energy-momentum tensor for a free spinor.


Poincaré group symmetries and conservation laws

9 Abril 2025, 16:30 Luís Bento

Canonical and symmetrized energy-momentum tensor for the electromagnetic field. Energy and momentum balance equations with electromagnetic sources.
Canonical conserved tensors associated with Lorentz group symmetries. Total angular momentum and spin contribution of vector and spinor fields.
General procedure for the symmetrization of the energy-momentum tensor.