This is of course just for humour. The languages are very different, yet very similar (tongue). Feel free to add any elements to the table.

MathematicsPhysics
CurvatureField Strength
ConnectionGauge Potential
A section of the fibre bundleA Gauge Choice
Selecting a section of the fibre bundleFixing the Gauge
Lie Group

Continuous Symmetry Group

Lie AlgebraInfinitesimal Transformations
Exact FormWork Form
SymplectomorphismCanonical Transformation
Pseudo-riemannian manifoldSpacetime
Applying isomorphism induced by metricLowering the Index
Applying inverse of isomorphism induced by metricRaising the Index
An Element of the Projective Space of a Hilbert Space of L2 FunctionsA state in the Hilbert Space