Week 1 Flashcards
Where are quantum field theory (QFT) applicable?
In particle physics experiments, in the evolution of astrophysical objects, in the physics of rays and in cosmology
QFT is a framework that combines…
non-relativistic quantum mechanics with special relativity
Difference between non-relativistic quantum mechanics and QFT
Choice of dynamical variables. (QM: Lagrangian coordinates, QFT: fields)
The Principle of Special Relativity
The laws of physics take the same from in all inertial coordinate systems. Inertial coordinate systems are related by the Lorentz transformations. This implies that the laws of physics must be covariant under Lorentz transformations
Determinant of a proper Lorentz transformation matrix
+1
Wavevector in terms of momentum
k=p/h
Fine structure constant in terms of constants
e^2/4pihbar*c~=1/137
What is the Causality Problem?
The amplitude for a free particle to propagate between two positions is nonzero for all times and positions in quantum mechanics
How does QFT solve the causality problem?
By introducing antiparticles which amplitude cancel that of the free particle in the tails.
What’s the real reason to study QFT?
It’s the best model for scattering cross section, particle lifetimes and other observables
Inertial coordinate systems are related by what transformations?
Lorentz transformations
The principle of special relativity implies the equations of physics must be _______ under Lorentz transformations
covariant
Are the number of particles conserved in relativistic processes?
No
Coulomb gauge
nabla cdot A = 0
Principle of least action
“When a system evolves from one given configuration to another between times t_1 and t_2 it does so along a ‘path’ in configuration space for which the action S is an extremum (normally minimum)”
