PHYS201 Lecture Notes - Lecture 5: Polarization Density, Quantum Field Theory

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A mathematical quantity with both a magnitude and a direction. Scalar quantities: length, area, volume, speed, mass, density, temperature, energy, work, power. Vector quantities: displacement, direction, velocity, acceleration, momentum force, lift, drag, weight. Tensor quantities: stress, strain, conductivity, polarization density, general relativity, quantum field theory. Two vectors are equal if they have the same magnitude and the same direction. If |a| = |b| and they point along parallel lines. Vector addition is very different from adding scalar quantities. When adding vectors, their directions must be taken into account. Two ways to add vectors: graphically. Tip to tail or head to tail. The resultant is drawn from the origin of the first vector to the end of the last vector. When you have many vectors, just keep repeating the process until all are included: algebraic. When two vectors are added, the sum is independent of the order of the addition.

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