Extended Conformal Algebra and Non-commutative Geometry in Particle Theory

We show how an off shell invariance of the massless particle action allows the construction of an extension of the conformal space-time algebra and induces a non-commutative space-time geometry in bosonic and supersymmetric particle theories.Comment: 9 page

High Energy Commutators in Particle, String and Membrane Theories

We study relativistic particle, string and membrane theories as defining field theories containing gravity in (0+1), (1+1) and (2+1) spacetime dimensions respectively. We show how an off shell invariance of the massless particle action allows the construction of an extension of the conformal algebra and induces a transition to a non-commutative spacetime geometry. This non-commutative geometry is found to be preserved in the spacetime supersymmetric massless particle theory. It is then shown how the basic bosonic commutators we found for the massless particle may also be encountered in the tensionless limit of string and membrane theories. Finally we speculate on how the non-locality introduced by these commutators could be used to construct a covariant Newtonian gravitational field theory.Comment: Latex, 24 page

Free Massless Particles, Two Time Physics and Newtonian Gravitodynamics

We demonstrate how a classical Snyder-like phase space can be constructed in the Hamiltonian formalism for the free massless relativistic particle, for the two-time physics model and for the relativistic Newtonian gravitodynamic theory. In all these theories the Snyder-like phase space emerges as a consequence of a new local scale invariance of the Hamiltonian. The implications and consequences of this Snyder-like phase space in each of these theories are also considered.Comment: Latex, 26 page

Dual Gravitation

We propose a canonical relation between gravity and space-time noncommutativity

2T Physics and Quantum Mechanics

We use a local scale invariance of a classical Hamiltonian and describe how to construct six different formulations of quantum mechanics in spaces with two time-like dimensions. All these six formulations have the same classical limit described by the same Hamiltonian. One of these formulations is used as a basis for a complementation of the usual quantum mechanics when in the presence of gravity.Comment: 27 page

Gravitation with Two Times

We investigate the possibility of constructing a covariant Newtonian gravitational theory and find that the action describing a massless relativistic particle in a background Newtonian gravitodynamic field has a higher-dimensional extension with two times.Comment: Latex, 13 page

Noncommutative Two Time Physics

We present a classical formalism describing two-time physics with Abelian canonical gauge field backgrounds. The formalism can be used as a starting point for the construction of an interacting quantized two-time physics theory in a noncommutative soace-time.Comment: Latex, 11 page

Two Time Physics with a Minimum Length

We study the possibility of introducing the classical analogue of Snyder's Lorentz-covariant noncommutative space-time in two-time physics theory. In the free theory we find that this is possible because there is a broken local scale invariance of the action. When background gauge fields are present, they must satisfy certain conditions very similar to the ones first obtained by Dirac in 1936. These conditions preserve the local and global invariances of the action and leads to a Snyder space-time with background gauge fields

New Heisenberg Relations in a Non-commutative Geometry

We show how an induced invariance of the massless particle action can be used to construct an extension of the Heisenberg canonical commutation relations in a non-commutative space-time.Comment: 7 pages, LAte

Free massless particles and extended space-time algebra

We study the space-time invariances of the relativistic particle action for both the massive and massless cases. While the massive action has only the invariances associated to the Poincare algebra, we find that the invariances of the massless action give rise to the conformal algebra in four dimensions. For the free massless particle, a new invariance of the action permits the construction of an extension of the conformal algebra. The conclusion is that two distinct symmetry breaking mechanisms are necessary to arrive at the Poincare algebra.Comment: 6 pages, completed equation