On the subtelties of nonrelativistic reduction and applications

Abstract

Various subtleties and problems associated with nonrelativistic (NR) reduction of a scalar field theory to the Schroedinger theory are discussed. Contrary to the usual approaches that discuss the mapping among the equations of motion or the actions, we highlight the mapping among the space time generators. Using a null reduction we show the embedding of the conformal generators of the Schroedinger theory to that of a complex scalar theory in one higher dimension. As applications we reveal the conformal symmetry in hydrodynamics and the obtention of NR diffeomorphism symmetry from the relativistic one. A geometrical connection based on Horava-Lifshitz and Newton-Cartan spacetime is discussed.

29 pages, no figure

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Cited by in corpus (14)

• Galilean gauge theory from Poincare gauge theory
• New formulation of Galilean relativistic Maxwell theory
• Uniqueness of Galilean and Carrollian limits of gravitational theories and application to higher derivative gravity
• Non-relativistic Reduction of Spinors, New Currents and their Algebra
• Sengupta Transformations and Carrollian Relativistic Theory
• Action principle of Galilean relativistic Proca theory
• Duality Between Dirac Fermions in Curved Spacetime and Optical solitons in Non-Linear Schrodinger Model: Magic of $1+1$-Dimensional Bosonization
• Formulation of Galilean relativistic Born-Infeld theory
• Covariant Formulation of the Newton-Hooke Particle and its Canonical Analysis
• Canonical Formulation for a Non-relativistic Spinning Particle Coupled to Gravity
• Characterizing Klein-Fock-Gordon-Majorana particles in (1+1) dimensions
• Geometry of Nonrelativistic string
• Gauge interactions and the Galilean limit
• Null reduction and dynamical realization of Carrollian conformal symmetries