Related papers: Dynamical Poincare Symmetry Realized by Field-depe…
We introduce a model of Poincar\'e mappings which represents hierarchical structure of phase spaces for systems with many degrees of freedom. The model yields residence time distribution of power type, hence temporal correlation remains…
We explore the properties of polynomial Lagrangians for chiral $p$-forms previously proposed by the last named author, and in particular, provide a self-contained treatment of the symmetries and equations of motion that shows a great…
We propose a method for deforming an extended Galilei algebra that leads to a nonstandard realization of the Poincar\'e group with the Fock-Lorentz linear fractional transformations. The invariant parameter in these transformations has the…
In this paper I shall consider field theories in a space of four-dimensions which have field variables consisting of the components of a metric tensor and scalar field. The field equations of these scalar-tensor field theories will be…
We present important elements of a gauge and diffeomorphism invariant formulation of the moduli space approximation to soliton dynamics. We argue that explicit velocity-dependent modifications are determined entirely from gauge and…
We use Lie-algebraic arguments to classify Lorentz-invariant theories of massless interacting scalars that feature coordinate-dependent redundant symmetries of the Galileon type. We show that such theories are determined, up to a set of…
Totally symmetric arbitrary spin massless and massive free fields in flat and AdS spaces and conformal fields in flat space are studied. Extended gauge invariant hamiltonian action for such fields is obtained. The action is constructed out…
We study spontaneous symmetry breaking for field algebras on Minkowski space in the presence of a condition of geometric modular action (CGMA) proposed earlier as a selection criterion for vacuum states on general space-times. We show that…
We study the structure and dynamics of the infinite sequence of extensions of the Poincar{\'e} algebra whose method of construction was described in a previous paper [1]. We give explicitly the Maurer-Cartan (MC) 1-forms of the extended Lie…
The hierarchy of conformally invariant k-th powers of the Laplacian acting on a scalar field with scaling dimensions $\Delta_{(k)}=k-d/2$, k=1,2,3 as obtained in the recent work [1] is rederived using the Fefferman-Graham d+2 dimensional…
Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…
The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant subspaces that corresponds to considering an…
The following work demonstrates the viability of Poincar\'e symmetry in a discrete universe. We develop the technology of the discrete principal Poincar\'e bundle to describe the pairing of (1) a hypercubic lattice `base manifold' labeled…
Many interesting physical systems have mathematical descriptions as finite-dimensional or infinite-dimensional Hamiltonian systems. Poincare who started the modern theory of dynamical systems and symplectic geometry developed a particular…
In the following work, we pedagogically develop 5-vector theory, an evolution of scalar field theory that provides a stepping stone toward a Poincar\'e-invariant lattice gauge theory. Defining a continuous flat background via the…
A Galileon field is one which obeys a spacetime generalization of the non-relativistic Galilean invariance. Such a field may possess non-canonical kinetic terms, but ghost-free theories with a well-defined Cauchy problem exist, constructed…
We construct simple Lagrangians of vector fields which involve second derivatives, but nevertheless lead to second order field equations. These vector fields are, therefore, analogs of generalized Galileons. Our construction is given first…
The anelastic and pseudo-incompressible equations are two well-known soundproof approximations of compressible flows useful for both theoretical and numerical analysis in meteorology, atmospheric science, and ocean studies. In this paper,…
The purpose of this article is to initiate a study of a class of Lorentz invariant, yet tractable, Lagrangian Field Theories which may be viewed as an extension of the Klein-Gordon Lagrangian to many scalar fields in a novel manner. These…
Symbolic dynamics is a coarse-grained description of dynamics. By taking into account the ``geometry'' of the dynamics, it can be cast into a powerful tool for practitioners in nonlinear science. Detailed symbolic dynamics can be developed…