Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userNoncommutativity and the lightfront
169
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We discuss various limits which transform configuration space into phase space, with emphasis on those related to lightfront field theory, and show that they are unified by spectral flow. Examples include quantising in `almost lightfront coordinates and the appearance of lightlike noncommutativity from a strong background laser field. We compare this with the limit of a strong magnetic field, and investigate the role played by lightfront zero modes.
rate research
Read More
We analyze renormalizability properties of noncommutative (NC) theories with a bifermionic NC parameter. We introduce a new 4-dimensional scalar field model which is renormalizable at all orders of the loop expansion. We show that this model has an infrared stable fixed point (at the one-loop level). We check that the NC QED (which is one-loop renormalizable with usual NC parameter) remains renormalizable when the NC parameter is bifermionic, at least to the extent of one-loop diagrams with external photon legs. Our general conclusion is that bifermionic noncommutativity improves renormalizablility properties of NC theories.
In this article we considered models of particles living in a three-dimensional space-time with a nonstandard noncommutativity induced by shifting canonical coordinates and momenta with generators of a unitary irreducible representation of the Lorentz group. The Hilbert space gets the structure of a direct product with the representation space, where we are able to construct operators which realize the algebra of Lorentz transformations. We study the modified Landau problem for both Schrodinger and Dirac particles, whose Hamiltonians are obtained through a kind of non-Abelian Bopps shift of the dynamical variables from the ones of the usual problem in the normal space. The spectrum of these models are considered in perturbation theory, both for small and large noncommutativity parameters. We find no constraint between the parameters referring to no-commutativity in coordinates and momenta but they rather play similar roles. Since the representation space of the unitary irreducible representations SL(2,R) can be realized in terms of spaces of square-integrable functions, we conclude that these models are equivalent to quantum mechanical models of particles living in a space with an additional compact dimension.
We discuss the formulation of classical field theoretical models on $n$-dimensional noncommutative space-time defined by a generic associative star product. A simple procedure for deriving conservation laws is presented and applied to field theories in noncommutative space-time to obtain local conservation laws (for the electric charge and for the energy-momentum tensor of free fields) and more generally an energy-momentum balance equation for interacting fields. For free field models an analogy with the damped harmonic oscillator in classical mechanics is pointed out, which allows us to get a physical understanding for the obtained conservation laws. To conclude, the formulation of field theories on curved noncommutative space is addressed.
The central theme of this thesis is noncommutativity in string theory. We explore in detail how noncommutative structures can emerge in case of the interacting bosonic string and even in the fermionic sector of superstring theory. We have shown in various approaches that string coordinates must be noncommutative in order to be compatible with boundary conditions. These noncommutative structures lead to new involutive algebra of constraints but generate same Virasoro algebra, indicating the internal consistency of our analysis
In this work, we comment on two special points in the paper by S. Ghosh [Phys. Rev. D 74, 084019 (2006)]. First of all, the Lagrangian presented by the author does not describe the Magueijo- Smolin model of Doubly Special Relativity since it is equivalent to the Lagrangian of the standard free relativistic particle. We also show that the introduction of noncommutative structures is not relevant to the problem of Lorentz covariance in Ghosh formalism.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
