- Adjoint Dirac equation
- Adjoint Dirac equation: explicit solutions
- Alternative normalization for Dirac spinors
- Anticommutation relations and Hamiltonian for Dirac field
- Anticommutators, creation and annihilation operators in the Dirac equation
- Canonical momenta for electromagnetic fields
- Causality in the Klein-Gordon field
- Causality in the Klein-Gordon field: commutators and measurements
- Chirality projection operator and eigenvectors of gamma-5
- Complex scalar field - Hamiltonian
- Complex scalar field - quantization, particles and antiparticles
- Coordinate transformations in classical field theory
- Coupled oscillators in terms of creation and annihilation operators; phonons
- Creation and annihilation operators for the 3-d harmonic oscillator
- Creation and annihilation operators in the harmonic oscillator
- Creation and annihilation operators in the harmonic oscillator: a few theorems
- Creation and annihilation operators: commutators and anticommutators
- Creation and annihilation operators: normalization
- Creation and destruction operators for a free scalar field
- Delta function: a couple of alternative derivations
- Dirac equation
- Dirac equation as four coupled differential equations
- Dirac equation in quantum field theory: Lagrangian density
- Dirac equation in relativistic quantum mechanics: summary
- Dirac equation: 4 solution vectors
- Dirac equation: adjoint solutions
- Dirac equation: angular momentum
- Dirac equation: conserved probability current
- Dirac equation: gamma matrices and \gamma^{5}
- Dirac equation: inner products of spinors
- Dirac equation: linear independence of matrices
- Dirac equation: lorentz covariance
- Dirac equation: matrix properties
- Dirac equation: non-relativistic limit
- Dirac equation: nonuniqueness of solutions
- Dirac equation: orthogonality of solutions
- Dirac equation: positive probabilities and negative energies
- Dirac equation: set of independent matrices
- Dirac equation: spin of a moving particle
- Dirac equation: spin of a particle at rest
- Dirac equation: spinors near the speed of light
- Dirac equation: the gamma matrices
- Dirac spin operator in quantum field theory
- Dirac spinors: Gordon identity
- Dirac spinors: normalization
- Dirac spinors: products of spinors
- Discrete Fourier transforms
- Eigenfunctions of position and momentum; unit operators
- Eigenspinors of the Pauli spin matrices
- Energy-momentum tensor for a general Lagrange density
- Energy projection operators in the Dirac equation
- Euler-Lagrange equations for particle & field theories; Lagrangian density
- Euler-Lagrange equations: a couple of examples
- Evolution operator
- Explicit solutions of Dirac equation in Dirac-Pauli representation
- Explicit solutions of Dirac equation from particle's rest frame
- Fermat's principle of least time and Snell's law
- Fermion wave functions; the Slater determinant
- Feynman propagator as a contour integral
- Feynman propagator for a complex scalar field: Time ordering
- Feynman propagator as a single real integral
- Feynman propagator for a scalar field (Lahiri & Pal)
- Feynman propagator for scalar fields
- Feynman propagator in terms of commutators
- Feynman propagator: from commutator to integral
- Field operators for the infinite square well
- Fock space - Number operator
- Free scalar Hamiltonian as an integral of the Hamiltonian density
- From mattress to field
- Functional derivative: a 4-dimensional example
- Functional derivatives and the Lagrangian
- Functional derivatives: more examples
- Functionals and functional derivatives
- Gamma matrices: a curious example
- Gamma matrices: contractions
- Gamma matrices in Dirac-Pauli representation
- Gamma matrices: Objects behaving like vectors or tensors
- Gaussian integrals: averages of powers of x
- Gaussian integrals: averages over matrix components and the Wick contraction
- Gaussian integrals: single variable & matrix exponents
- Generators of the Lorentz group
- Generators of the Lorentz group - alternative derivation of the Commutators
- Generators of the Lorentz group - Commutators
- Generators of the Lorentz group - Momentum Commutators
- Green's function for Klein-Gordon equation
- Hamilton's equations and Poisson brackets
- Hamilton's equations for relativistic fields; conjugate momentum
- Hamilton's equations of motion in classical field theory
- Hamiltonian density for the Dirac equation
- Hamiltonian for complex scalar field
- Hamiltonian for the Dirac equation
- Harmonic oscillator ground state from annihilation operator
- Helicity and chirality are equal for massless fermions
- Helicity of one-particle Dirac states
- Helicity operator in the Dirac equation
- Helicity operator in the Dirac equation (Lahiri & Pal)
- Helicity projection operator in the Dirac equation
- Helicity projection operator: Properties and commutators
- Hermitian Lagrangian for the Dirac field
- Interactions of fields - basics
- Klein-Gordon equation
- Klein-gordon equation - derivation and continuity equations
- Klein-Gordon equation for fields; derivation from the Lagrangian
- Klein-Gordon equation from the Heisenberg picture
- Klein-Gordon equation with anticommutators
- Klein-gordon equation - charged particles
- Klein-Gordon equation: commutators
- Klein-Gordon equation: continuous solutions
- Klein-Gordon equation from harmonic oscillator: Hamiltonian, creation and annihilation operators
- Klein-Gordon solutions from harmonic oscillator
- Klein-gordon equation - nonrelativistic limit
- Klein-Gordon equation: orthonormality of solutions
- Klein-Gordon equation: plane wave solutions
- Klein-Gordon equation: probability density and current
- Klein-Gordon equation in the Feshbach-Villars representation
- Klein-Gordon equation in Feshbach-Villars form - Operator transformations and solutions
- Klein-Gordon equation in Schrödinger form
- Klein-Gordon equation - invariance under electromagnetic gauge transformations
- Klein-Gordon equation in Schrödinger form - Lagrangian, energy-momentum tensor
- Klein-Gordon equation with Coulomb potential
- Klein-Gordon equation with Coulomb potential - charged sphere
- Klein-Gordon equation with Coulomb potential - Hypergeometric functions and numerical solutions
- Klein-Gordon equation - interaction with electromagnetic field
- Klein-Gordon equation with scalar 1/r potential
- Klein-Gordon equation with exponential potential
- Klein-Gordon equation with finite square well
- Klein-Gordon equation with finite square well - numerical solution
- Klein-Gordon Feynman propagator
- Klein-Gordon field in the Heisenberg picture; time dependence
- Klein-Gordon field in position space
- Klein-Gordon Green's function as a Fourier transform
- Lagrangian for inhomogeneous Maxwell's equations
- Lagrangian for the Dirac field
- Lagrangian for the Schrödinger equation
- Lagrangians and the principle of least action
- Lagrangians for elastic media
- Linear chain of oscillators - Classical treatment, equations of motion
- Linear chain of oscillators - Classical treatment, Hamiltonian
- Linear chain of oscillators - Quantum treatment
- Linear chain of oscillators - External force, unitary operator
- Linear chain of oscillators - External force, ground state
- Lorentz group
- Lorentz invariance in Klein-Gordon momentum states
- Lorentz transformation as product of a pure boost and pure rotation
- Lorentz transformation for infinitesimal relative velocity
- Lorentz transformations and the special linear group SL(2,C)
- Lorentz transformations as 2x2 matrices
- Lorentz transformations as rotations
- Maxwell's equations using the electromagnetic field tensor
- Momentum of a free scalar Klein-Gordon field
- Momentum of particles in a Dirac field
- Natural units
- Natural units (Lahiri & Pal)
- Natural units: the muon lifetime
- Neutral Klein-Gordon field - Fourier expansion
- Neutral Klein-Gordon field - Lagrangian and hamiltonian
- Noether's theorem
- Noether's theorem and conservation laws
- Noether's theorem and conservation of angular momentum
- Noether's theorem and conservation of energy and momentum
- Noether's theorem - internal symmetry and scaled spacetime
- Noether's theorem - internal symmetry of complex scalar field
- Noether's theorem - traceless stress-energy tensor
- Nonrelativistic field theory - Fock space to position space
- Nonrelativistic field theory for fermions
- Nonrelativistic field theory - Fourier expansion
- Nonrelativistic field theory - number, creation and annihilation operators
- Nonrelativistic field theory - Schrödinger equation
- Normal ordering
- Notation for Relativistic Quantum Mechanics
- Number operator
- Occupation number representation; delta function as a series
- One-dimensional field (displacement of a string)
- Path integrals in quantum mechanics
- Pauli-Lubansky vector and spin in the Dirac equation
- Poisson brackets and Hamilton's equations of motion
- Poisson brackets in classical field theory
- Probability density in a Klein-Gordon field
- Propagator for the Dirac field
- Propagator for the Dirac field as a time-ordered product
- Quantum field theory representation of non-relativistic quantum mechanics
- Real Klein-Gordon fields
- Real scalar field - commutators
- Real scalar field - fourier decomposition
- Rotation about an arbitrary axis in 3-D
- S-matrix
- Scalar-scalar scattering in the Yukawa interaction
- Schrödinger equation: Lagrange density & Energy-momentum tensor
- Second quantizing a single-particle operator
- Second quantizing operators - examples
- Second quantizing the tight-binding hamiltonian
- Second quantizing the tight-binding hamiltonian
- Spin projection operators in the Dirac equation
- Spin projection operators in the Dirac equation for a particle at rest
- Steepest descent and the classical limit of quantum mechanics
- Stress-energy tensor from Noether's theorem
- Stress-energy tensor: 3 examples
- Stress-energy tensor and angular momentum for Dirac field
- Unitary transformations and the Heisenberg picture
- Vacuum energy in the free Klein-Gordon field
- Violation of causality in old quantum theory
- Wick's theorem for 2 fields
- Wick's theorem - general case
- Wick's theorem - no equal time commutators