A Bicycle Built for Two: The Galilean and U(1) Gauge Invariance of the Schrödinger Field

Details A Bicycle Built for Two: The Galilean and U(1) Gauge Invariance of the Schrödinger Field A Bicycle Built for Two: The Galilean and U(1) Gauge Invariance of the Schrödinger Field

2008-02-17

arxiv.org/abs/0802.2401v2

Physics

Mathematical Physics

13 pages, 0 figures, Physical Review A format, Section on Maxwell's Eqns added

Scientific paper

This paper undertakes a study of the nature of the force associated with the local U (1) gauge symmetry of a non-relativistic quantum particle. To ensure invariance under local U (1) symmetry, a matter field must couple to a gauge field. We show that such a gauge field necessarily satisfies the Maxwell equations, whether the matter field coupled to it is relativistic or non-relativistic. This result suggests that the structure of the Maxwell equations is determined by gauge symmetry rather than the symmetry transformation properties of space-time. In order to assess the validity of this notion, we examine the transformation properties of the coupled matter and gauge fields under Galilean transformations. Our main technical result is the Galilean invariance of the full equations of motion of the U (1) gauge field.

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