A kinetic term contains derivatives of a field and determines its free propagation. Its quadratic differential operator becomes the inverse quantum field theory propagator.
A mass term is a quadratic term without derivatives whose coefficient sets the mass scale of a free field.
A field interaction term is nonlinear in the fields and produces the interaction vertices of perturbation theory.
A continuous variational symmetry gives a current satisfying on shell. Integrating over space gives a conserved charge when boundary flux vanishes.
The Belinfante-Rosenfeld construction adds the divergence of a spin-current superpotential to the canonical stress-energy tensor, producing a symmetric conserved tensor with the same integrated four-momentum under suitable boundary conditions.
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Classical field theory is a framework in physics that describes how physical fields, such as electromagnetic fields, gravitational fields, or fluid fields, interact with matter and evolve over time. It aims to formulate physical laws in terms of fields, rather than point particles, allowing for a more comprehensive understanding of phenomena that involve continuous distributions of matter and energy. ### Key Features of Classical Field Theory: 1. **Fields**: In classical field theory, fields are functions defined over space and time.