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J. Gamboa

Publications and source records attributed to J. Gamboa.

At least 73 records · Page 4Linked to original sources
arXiv2003

Noncommutativity in Field Space and Lorentz Invariance Violation

The connection between Lorentz invariance violation and noncommutativity of fields in a quantum field theory is investigated. A new dispersion relation for a free field theory with just one additional noncommutative parameter is obtained. While values for the noncommutative scale much larger than 10^{-20} eV^{-1} are ruled out by the present experimental status, cosmic ray physics would be compatible with and sensible to a noncommutativity arising from quantum gravity effects. We explore the matter-antimatter asymmetry which is naturally present in this framework.

hep-th↗
arXiv2003

Quantum Theory of Noncommutative Fields

Generalizing the noncommutative harmonic oscillator construction, we propose a new extension of quantum field theory based on the concept of "noncommutative fields". Our description permits to break the usual particle-antiparticle degeneracy at the dispersion relation level and introduces naturally an ultraviolet and an infrared cutoff. Phenomenological bounds for these new energy scales are given.

hep-th↗
arXiv2002

Testing spatial noncommutativiy via the Aharonov-Bohm effect

The possibility of detecting noncommutative space relics is analyzed using the Aharonov-Bohm effect. We show that, if space is noncommutative, the holonomy receives non-trivial kinematical corrections that will produce a diffraction pattern even when the magnetic flux is quantized. The scattering problem is also formulated, and the differential cross section is calculated. Our results can be extrapolated to high energy physics and the bound $θ\sim [ 10 {TeV}]^{-2}$ is found. If this bound holds, then noncommutative effects could be explored in scattering experiments measuring differential cross sections for small angles. The bound state Aharonov- Bohm effect is also discussed.

hep-th↗
arXiv2001

Noncommutativity and the Aharonov-Bohm Effect

The possibility of detecting noncommutive space relics is analyzed by using the Aharonov-Bohm effect. If space is non-commutative, it turns out that the holonomy receives kinematical corrections that tend to diffuse the fringe pattern. This fringe pattern has a non-trivial energy dependence and, therefore, one could observe noncommutative effects by modifying the energy of the incident electrons beam in the Tonomura experimental arrangement

hep-th↗
arXiv2001

Nonrelativistic Fermions in Magnetic Fields: a Quantum Field Theory Approach

The statistical mechanics of nonrelativistic fermions in a constant magnetic field is considered from the quantum field theory point of view. The fermionic determinant is computed using a general procedure that contains all possible regularizations. The nonrelativistic grand-potential can be expressed in terms polylogarithm functions, whereas the partition function in 2+1 dimensions and vanishing chemical potential can be compactly written in terms of the Dedekind eta function. The strong and weak magnetic fields limits are easily studied in the latter case by using the duality properties of the Dedekind function.

hep-th↗
arXiv2001

Noncommutative Quantum Mechanics: The Two-Dimensional Central Field

Quantum mechanics in a noncommutative plane is considered. For a general two dimensional central field, we find that the theory can be perturbatively solved for large values of the noncommutative parameter ($θ$) and explicit expressions for the eigenstates and eigenvalues are given. The Green function is explicitly obtained and we show that it can be expressed as an infinite series. For polynomial type potentials, we found a smooth limit for small values of $θ$ and for non-polynomial ones this limit is necessarily abrupt. The Landau problem, as a limit case of a noncommutative system, is also considered.

hep-th↗
arXiv2001

Non-Commutative Quantum Mechanics

A general non-commutative quantum mechanical system in a central potential $V=V(r)$ in two dimensions is considered. The spectrum is bounded from below and for large values of the anticommutative parameter $θ$, we find an explicit expression for the eigenvalues. In fact, any quantum mechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction $V(r)$ is replaced by $V = V ({\hat H}_{HO}, {\hat L}_z)$, where ${\hat H}_{HO}$ is the hamiltonian of the two-dimensional harmonic oscillator and ${\hat L}_z$ is z- component of the angular momentum. For other finite values of $θ$ the model can be solved by using perturbation theory.

hep-th↗
arXiv2001

The Landau problem and noncommutative quantum mechanics

The conditions under which noncommutative quantum mechanics and the Landau problem are equivalent theories is explored. If the potential in noncommutative quantum mechanics is chosen as $V= Ω\aleph$ with $\aleph$ defined in the text, then for the value ${\tilde θ} = 0.22 \times 10^{-11} cm^2$ (that measures the noncommutative effects of the space), the Landau problem and noncommutative quantum mechanics are equivalent theories in the lowest Landau level. For other systems one can find differents values for ${\tilde θ}$ and, therefore, the possible bounds for ${\tilde θ}$ should be searched in a physical independent scenario. This last fact could explain the differents bounds for $\tilde θ$ found in the literature.

hep-th↗
arXiv2001

Quantum Gravity at Very High Energies

The problem of time and the quantization of three dimensional gravity in the strong coupling regime is studied following path integral methods. The time is identified with the volume of spacetime. We show that the effective action describes an infinite set of massless relativistic particles moving in a curved three-dimensional target space, i.e. a tensionless 3-brane on a curved background. If the cosmological constant is zero the target space is flat and there is no ` ` graviton" propagation (i.e., $G[g_{ij} (2), g_{ij} (1)] = 0$). If the cosmological constant is different from zero, 3D gravity is both classical and quantum mechanically soluble. Indeed, we find the following results: i) The general exact solutions of the Einstein equations are singular at $t=0$ showing the existence of a big-bang in this regime and ii) the propagation amplitude between two geometries $ $ vanishes as $t \to 0$, suggesting that big-bang is suppressed quantum mechanically. This result is also valid for $D>3$.

hep-th↗
arXiv2000

Scattering in Three Dimensional Extremal Black Holes

An approach to scattering theory in three dimensional AdS spaces is proposed. Firstly we consider the scattering of spinless relativistic particles by a three dimensional extremal black hole and compute the absorption cross section $σ_{abs} =J_{abs}/J_{\infty}$ without using {\it in} and {\it out} states. Secondly, we posit a reciprocal space ${\cal H}$ where {\it in} and {\it out} states and the scattering amplitude is defined as in usual scattering theory. We show that both descriptions are equivalent and ${\cal H}$ could be considered as the space where the scattering processes in AdS should be defined.

hep-th↗
arXiv2000

Off-Shell Effective Lagrangian for NRQCD and Heavy Quarks Effective Theory

derivation of the effective lagrangian for non-relativistic quantum chromodynamics and the heavy quarks effective field theory is given. Our calculation provides of a simple and systematic method of calculation of the full off shell effective lagrangian at tree level including all the $1/m$ corrections.

hep-ph↗
arXiv2000

Fermions on Non-Trivial Topologies

An exact expression for the Green function of a purely fermionic system moving on the manifold $\Re \times Σ^{D-1}$, where $Σ^{D-1}$ is a $(D-1)$-torus, is found. This expression involves the bosonic analog of $χ_n = e^{inθ}$ corresponding to the irreducible representation for the n-th class of homotopy and in the fermionic case for D=2 and 3, $χ_n$ is a measure of the statistics of the particles. For higher dimensions ($D \geq 4$), there is no analogue interpretation however this could, presumably, indicate a generation of mass as in quantum field theories at finite temperature.

hep-th↗
arXiv1998

Topological Excitations in the Thirring model

The quantization of the massless Thirring model in the light-cone using functional methods is considered. The need to compactify the coordinate $x^-$ in the light-cone spacetime implies that the quantum effective action for left-handed fermions contains excitations similar to abelian instantons produced by composite of left-handed fermions. Right-handed fermions don't have a similar effective action. Thus, quantum mechanically, chiral symmetry must be broken as a result of the topological excitations. The conserved charge associated to the topological states is quantized. Different cases with only fermionic excitations or bosonic excitations or both can occur depending on the boundary conditions and the value of the coupling.

hep-th↗
arXiv1996

Global Anomalies and Anyons in 1+1 Dimensions

We consider the analog in one spatial dimension of the Bose-Fermi transmutation for planar systems. A quantum mechanical system of a spin 1/2 particle coupled to an abelian gauge field, which is classically invariant under gauge transformations and charge conjugation is studied. It is found that unless the flux enclosed by the particle orbits is quantized, and the spin takes a value $n+ 1/2$, at least one of the two symmetries would be anomalous. Thus, charge conjugation invariance and the existence of abelian instantons simultaneously force the particles to be either bosons or fermions, but not anyons.

hep-th↗
arXiv1996

Anomaly and Condensate in the Light-Cone Schwinger Model

The axial anomaly and fermion condensate in the light cone Schwinger model are studied following path integral methods. This formalism allows for a simple and direct calculation for these and other vacuum dependent phenomena.

hep-th↗
arXiv1996

On the Initial Singularity Problem in Two Dimensional Quantum Cosmology

The problem of how to put interactions in two-dimensional quantum gravity in the strong coupling regime is studied. It shows that the most general interaction consistent with this symmetry is a Liouville term that contain two parameters $(α, β)$ satisfying the algebraic relation $2β- α=2$ in order to assure the closure of the diffeomorphism algebra. The model is classically soluble and it contains as general solution the temporal singularity. The theory is quantized and we show that the propagation amplitude fall tozero in $τ=0$. This result shows that the classical singularities are smoothed by quantum effects and the bing-bang concept could be considered as a classical extrapolation instead of a physical concept.

hep-th↗