We analyze the performance of a perturbation theory for nonlinear cosmological dynamics, based on the Lagrangian description of hydrodynamics. In our previous paper, we solved the hydrodynamic equations for a self-gravitating fluid with pressure, given by a polytropic equation of state, using a perturbation method. Then we obtained the first-order solutions in generic background universes and t...

In this note, I will demonstrate that a theory of a massless neutrino (in 3+1-dimensional quantum field theory) can be described either as a theory of a massless Weyl fermion or as a theory of a massless four-component Majorana fermion. The two formulations are indistinguishable, as they arise from exactly the same Lagrangian when expressed in terms of two-component fermions. I will also exhibi...

New symmetry transformations for the n-dimensional Toda lattice are presented. Their existence allows for the construction of several first order Lagrangian structures associated to them. The multi-Hamiltonian structures are derived from Lagrangians in detail. The set of symmetries generates a Lie algebra.

We show that weak (Eulerian) solutions for the Semi-Geostrophic system in physical space exhibiting some mild regularity in time cannot yield point masses in dual space. However, such solutions are physically relevant to the model. Thus, we discuss a natural generalization of weak Lagrangian solutions in the physical space to include the possibility of singular measures in dual space. We prove ...

We prove some non-existence theorems for translating solutions to Lagrangian mean curvature flow. More precisely, we show that translating solutions with an L bound on the mean curvature are planes and that almost-calibrated translating solutions which are static are also planes. Recent work of D. Joyce, Y.-I. Lee, and M.-P. Tsui, shows that these conditions are optimal.

From a phenomenological view, the motivation for supersymmetry(SUSY) is that it provides us with an elegant method of dealing with the hierarchy problem. Supersymmetry solves the hierarchy problem because |λf | = λs, where λf and λs are higgs’ coupling to the Standard Model(SM) fermions and their scalar superpartners(SP) respectively. Due to this relationship between the two coupling constants ...

We classify singular fibres of a projective Lagrangian fibration over codimension one points. As an application, we obtain a canonical bundle formula for a projective Lagrangian fibration over a smooth manifold.

All norms in this section are defined elementwise. To recap, we solve the following problem: The Lagrangian of (1) is