Related papers: Scale-invariant phase space and the conformal grou…
We show how to cast an interacting system of M--branes into manifestly gauge-invariant form using an arrangement of higher-dimensional Dirac surfaces. Classical M--theory has a cohomologically nontrivial and noncommutative set of gauge…
We point out that the (pseudo-)conformal Universe scenario may be realized as decay of conformally invariant, metastable vacuum, which proceeds via spontaneous nucleation and subsequent growth of a bubble of a putative new phase. We study…
A family of classical integrable systems defined on a deformation of the two-dimensional sphere, hyperbolic and (anti-)de Sitter spaces is constructed through Hamiltonians defined on the non-standard quantum deformation of a sl(2) Poisson…
We investigate the geometric and conformally equivariant quantizations of the supercotangent bundle of a pseudo-Riemannian manifold $(M,g)$, which is a model for the phase space of a classical spin particle. This is a short review of our…
Modern theoretical models strongly suggest that new phenomena await discovery above the energy scale of the Standard Model (SM) of particle interactions. In this paper we argue that correct description of particle physics in the TeV energy…
In a previous publication we have shown that the gauge theory of relativistic 3-Branes can be formulated in a conformally invariant way if the embedding space is six-dimensional. The implementation of conformal invariance requires the use…
We consider classical gauge theory on a principal bundle P->X in a case of spontaneous symmetry breaking characterized by the reduction of a structure group G of P->X to its closed subgroup H. This reduction is ensured by the existence of…
The new manifestation of conformal invariance for a massless scalar particle in a Riemannian spacetime of general relativity is found. Conformal transformations conserve the Hamiltonian and wave function in the Foldy-Wouthuysen…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…
The standard Hamiltonian machinery, being applied to field theory, leads to infinite-dimensional phase spaces. It is not covariant. In this article, we present covariant finite-dimensional multimomentum Hamiltonian formalism for field…
Abelian gauge theory in $d\neq 4$ spacetime dimensions is an example of a scale invariant theory which does not possess conformal symmetry -- the special conformal transformation(SCT) explicitly breaks the gauge invariance of the theory. In…
Conformal transformations of the following kinds are compared: (1) conformal coordinate transformations, (2) conformal transformations of Lagrangian models for a D-dimensional geometry, given by a Riemannian manifold M with metric g of…
How can one fully harness the power of physics encoded in relativistic $N$-body phase space? Topologically, phase space is isomorphic to the product space of a simplex and a hypersphere and can be equipped with explicit coordinates and a…
The quantization of the most general Bianchi Type II geometry -with all six scale factors, as well as the lapse function and the shift vector, present- is considered. In an earlier work, a first reduction of the initial 6-dimensional…
The method of adiabatic invariants for time dependent Hamiltonians is applied to a massive scalar field in a de Sitter space-time. The scalar field ground state, its Fock space and coherent states are constructed and related to the particle…
Systems under holonomic constraints are classified within the generalized Hamiltonian framework as second-class constraints systems. We show that each system of point particles with holonomic constraints has a hidden gauge symmetry which…
We study the multifractal behavior of coherent states projected in the energy eigenbasis of the spin-boson Dicke Hamiltonian, a paradigmatic model describing the collective interaction between a single bosonic mode and a set of two-level…
Let $(M^m,g)$ be an $m$-dimensional closed Riemannian manifold with non-negative sectional curvatures, $m\ge 3$. We define a conformal invariant and prove that, if the conformal invariant is bounded from above by a constant depending only…
We introduce a dynamical model to reduce a large cosmological constant to a sufficiently small value. The basic ingredient in this model is a distinction which has been made between the two unit systems used in cosmology and particle…
Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same…