Related papers: Noncommutative Sp(2,R) Gauge Theories - A Field Th…
A very simple field theory in noncommutative phase space X^{M},P^{M} in d+2 dimensions, with a gauge symmetry based on noncommutative u*(1,1), furnishes the foundation for the field theoretic formulation of Two-Time Physics. This leads to a…
We construct an Sp(2,R) gauge invariant particle action which possesses manifest space-time SO(d,2) symmetry, global supersymmetry and kappa supersymmetry. The global and local supersymmetries are non-abelian generalizations of Poincare…
A field theory formulation of two-time physics in d+2 dimensions is obtained from the covariant quantization of the constraint system associated with the OSp(n|2) worldline gauge symmetries of two-time physics. Interactions among fields can…
We generalize the connection between 2t physics and noncommutative geometry. In particular, we apply our formalism to a target spacetime of signature (2+2). Specifically, we compute an algebra of a generalized SL(2, R)-Hamiltonian…
It is shown that all possible gravitational, gauge and other interactions experienced by particles in ordinary d-dimensions (one-time) can be described in the language of two-time physics in a spacetime with d+2 dimensions. This is obtained…
We show that a simple OSp(1/2) worldline gauge theory in 0-brane phase space (X,P), with spin degrees of freedom, formulated for a d+2 dimensional spacetime with two times X^0,, X^0', unifies many physical systems which ordinarily are…
According to Two-Time Physics, there is more to space-time than can be garnered with the ordinary formulation of physics. Two-Time Physics has shown that the Standard Model of Particles and Forces is successfully reproduced by a two-time…
All possible interactions of a point particle with background electromagnetic, gravitational and higher-spin fields is considered in the two-time physics worldline formalism in (d,2) dimensions. This system has a counterpart in a recent…
Position and momentum enter at the same level of importance in the formulation of classical or quantum mechanics. This is reflected in the invariance of Poisson brackets or quantum commutators under canonical transformations, which I regard…
Double field theory is an approach for massless modes of string theory, unifying and geometrizing all gauge invariance in manifest $\mathbf{O}(D,D)$ covariant manner. In this approach, we derive off-shell conserved Noether current and…
We construct a duality between several simple physical systems by showing that they are different aspects of the same quantum theory. Examples include the free relativistic massless particle and the hydrogen atom in any number of…
We describe a simple dynamical model characterized by the presence of two noncommuting Hamiltonian constraints. This feature mimics the constraint structure of general relativity, where there is one Hamiltonian constraint associated with…
Gauge theories are formulated on the noncommutative two-sphere. These theories have only finite number of degrees of freedom, nevertheless they exhibit both the gauge symmetry and the SU(2) "Poincar\'e" symmetry of the sphere. In…
New developments in 2T-physics, that connect 2T-physics field theory directly to the real world, are reported in this talk. An action is proposed in field theory in 4+2 dimensions which correctly reproduces the Standard Model (SM) in 3+1…
We analyze properties of the Sp(2M) conformally invariant field equations in the recently proposed generalized $\half M(M+1)$-dimensional space-time $\M_M$ with matrix coordinates. It is shown that classical solutions of these field…
We write down scalar field theory and gauge theory on two-dimensional noncommutative spaces ${\cal M}$ with nonvanishing curvature and non-constant non-commutativity. Usual dynamics results upon taking the limit of ${\cal M}$ going to i) a…
In this work, we utilize the dynamic invariant method to obtain a solution for the time-dependent Schr\"odinger equation, aiming to explore the quantum theory of a $p$-form gauge field propagating in $D$-dimensional de Sitter spacetimes.…
We propose an alternative geometric mathematical structure for arbitrary phase space. The main guide in our approach is the hidden SL(2,R)-symmetry which acts on the phase space changing coordinates by momenta and vice versa. We show that…
We present numerical results for U(1) gauge theory in 2d and 4d spaces involving a non-commutative plane. Simulations are feasible thanks to a mapping of the non-commutative plane onto a twisted matrix model. In d=2 it was a long-standing…
We plan to translate the successful description of three-dimensional gravity as a gauge theory in the noncommutative framework, making use of the covariant coordinates. We consider two specific three-dimensional fuzzy spaces based on SU(2)…