A new Galileon based charged matter theory -- a possible candidate for fracton gauge theory

We have mooted a new charged scalar field theory using a doublet of the Galileon scalar field instead of the usual Klein Gordon real scalar fields. Our model for the charged scalar field have a few remarkable properties like Poincare invariance , Abelian gauge symmetry and shift symmetries. The existence of two independent gauge symmetries is a welcome news for fracton physics.Whereas phase rotation in $phi$ space leads to the conservation of electric charge , the additional symmetries correspond to the conservation of a scalar charge and a vector charge. The system is shown to resemble matter in the fracton phase. Consequently, the results in this letter have immense possibilities in fracton physics.

Non-relativistic string in Newton-Cartan background

We formulate non-relativistic string theory on the Newton-Cartan space time using the vielbein approach mooted in the Galilean gauge theory. Geometric implication has been discussed at length. The outcome is the establishment of some points of non-relativistic diffeomorphism which has to some extent mystified in the literature.

Hamiltonian analysis of the Schroedinger field coupled with dynamic non-relativistic gravity

Using the recently mooted Galilean gauge theory we have constructed the model for the Schroedinger field interacting wuth gravity which is also dynamical. The dynamics of gravity is dictated by the Newtonian action in the Newton-Cartan spacetime. The theory is highly constrained . An elaborate analysis of the constraints of the theory have been performed. The symmetries are explicitly verified and the uniqueness of the model has been established. To the best of our knowledge both the model and its constraints structure are unique in the literature

A new approach for nonrelativistic bosonic string in flat space time

A new approach to the study of nonrelativistic bosonic string in flat space time is introduced, basing on a holistic hamiltonian analysis of the minimal action for the string. This leads to a structurally new form of the action which is, however, equivalent to the known results since, under appropriate limits, it interpolates between the minimal action (Nambu Goto type) where the string metric is taken to be that induced by the embedding and the Polyakov type of action where the world sheet metric components are independent fields. The equivalence among different actions is established by a detailed study of symmetries using constraint analysis. Various vexing issues in the existing literature are clarified. The interpolating action mooted here is shown to reveal the geometry of the string and may be useful in analyzing nonrelativistic string coupled with curved background.

Canonical Formulation for a Non-relativistic Spinning Particle Coupled to Gravity

We systematically derive an action for a nonrelativistic spinning partile in flat background and discuss its canonical formulation in both Lagrangian and Hamiltonian approaches. This action is taken as the starting point for deriving the corresponding action in a curved background. It is achieved by following our recently developed technique of localising the flat space galilean symmetry cite{BMM1, BMM3, BMM2}. The coupling of the spinning particle to a Newton-Cartan background is obtained naturally. The equation of motion is found to differ from the geodesic equation, in agreement with earlier findings. Results for both the flat space limit and the spinless theory (in curved background) are reproduced. Specifically, the geodesic equation is also obtained in the latter case.

Canonical Formulation of a New Action for a Non-relativistic Particle Coupled to Gravity

A detailed canonical treatment of a new action for a nonrelativistic particle coupled to background gravity, recently given by us, is performed both in the Lagrangian and Hamiltonian formulations. The equation of motion is shown to satisfy the geodesic equation in the Newton-Cartan background, thereby clearing certain confusions. The Hamiltonian analysis is done in the gauge independent as well as gauge fixed approaches, following Diracs analysis of constraints. The physical (canonical) variables are identified and the path to canonical quantisation is outlined by explicitly deriving the Schroedinger equation.

A New Action for Nonrelativistic Particle in Curved Background

We obtain a new form for the action of a nonrelativistic particle coupled to Newtonian gravity. The result is different from that existing in the literature which, as shown here, is riddled with problems and inconsistencies. The present derivation is based on the formalism of galilean gauge theory, introduced by us as an alternative method of analysing nonrelativistic symmetries in gravitational background.

Constrained Hamiltonian analysis of a non relativistic Schrodinger field coupled with C-S gravity

We provide a constrained Hamiltonian analysis of a non relativistic Schrodinger field in 2+1 dimensions , coupled with Chern - Simons gravity. The coupling is achieved by the recently advanced Galilean gauge theory cite{BMM1},cite{ BMM2}, cite{BM4}. The calculations are repeated with a truncated model to show that deviation from Galilean gauge theory makes the theory untenable. The issue of nonrelativistic spatial diffeomorphism is discussed in this context.

Galilean gauge theory from Poincare gauge theory

We provide an exact mapping between the Galilian gauge theory, recently advocated by us cite{BMM1, BMM2, BM}, and the Poincare gauge theory. Applying this correspondence we provide a vielbein approach to the geometric formulation of Newtons gravity where no ansatze or additional conditions are required.