Papers by Marcos Rosenbaum
Journal of Mathematical Physics
General Relativity and Gravitation, 2006
We consider the quantum mechanical equivalence of the Seiberg-Witten map in the context of the We... more We consider the quantum mechanical equivalence of the Seiberg-Witten map in the context of the Weyl-Wigner-Groenewold-Moyal phase-space formalism in order to construct a quantum mechanics over noncommutative Heisenberg algebras. The formalism is then applied to the exactly soluble Landau and harmonic oscillator problems in the 2-dimensional noncommutative phase-space plane, in order to derive their correct energy spectra and corresponding Wigner distributions. We compare our results with others that have previously appeared in the literature. * Dedicated to Mike Ryan on his sixtieth birthday, who as a scientist always understood that it is nice to be good, but that it is better to be nice.
Clifford Algebras and their Applications in Mathematical Physics, 2000
Physics Letters A, 2007
We investigate the incorporation of space noncommutativity into field theory by extending to the ... more We investigate the incorporation of space noncommutativity into field theory by extending to the spectral continuum the minisuperspace action of the quantum mechanical harmonic oscillator propagator with an enlarged Heisenberg algebra. In addition to the usual ⋆-product deformation of the algebra of field functions, we show that the parameter of noncommutativity can occur in noncommutative field theory even in the case of free fields without self-interacting potentials.
Journal of Physics A: Mathematical and Theoretical, 2007
Within the spirit of Dirac's canonical quantization, noncommutative spacetime field theories are ... more Within the spirit of Dirac's canonical quantization, noncommutative spacetime field theories are introduced by making use of the reparametrization invariance of the action and of an arbitrary non-canonical symplectic structure. This construction implies that the constraints need to be deformed, resulting in an automatic Drinfeld twisting of the generators of the symmetries associated with the reparametrized theory. We illustrate our procedure for the case of a scalar field in 1+1-spacetime dimensions, but it can be readily generalized to arbitrary dimensions and arbitrary types of fields.
Advances in Applied Clifford Algebras, 2010
ABSTRACT The aim of this paper is to review the formalism of noncommutativity using canonical par... more ABSTRACT The aim of this paper is to review the formalism of noncommutativity using canonical parametrization theory. In the first part we present the formalism for the case of Quantum Mechanics, and we show that using this approach and an appropriate basis we can get the noncommutativity expressed in terms of the Moyal product from the Dirac brackets of an extended phase space. We generalize our formalism to the context of Quantum Field Theory where we discuss the case of scalar electrodynamics. The interesting result is that our approach works correctly when we consider an interaction term between the gauge field and the scalar field. Finally, we present an argument that shows that gauge theories are not deformed if we use only noncommutativity of the coordinates. Mathematics Subject Classification (2000).Primary 70S10, 70S05-Secondary 81T75, 20C20
Physics Letters A, 2006
We show that introducing an extended Heisenberg algebra in the context of the Weyl-Wigner-Groenew... more We show that introducing an extended Heisenberg algebra in the context of the Weyl-Wigner-Groenewold-Moyal formalism leads to a deformed product of the classical dynamical variables that is inherited to the level of quantum field theory, and that allows us to relate the operator space noncommutativity in quantum mechanics to the quantum group inspired algebra deformation noncommutativity in field theory.
... Report APPLICATIONS OF THE WIGNER REPRESENTATIONS TO THE THEORY OF SLOW NEUTRON SCATTERING Ma... more ... Report APPLICATIONS OF THE WIGNER REPRESENTATIONS TO THE THEORY OF SLOW NEUTRON SCATTERING Marcos Rosenbaum ORA Project 03712 ... AGGREGATE 8 2.1 The Fermi Pseudo-Potential 8 2.2 Differential Cross Section 9 2.3 Van Hove Formulism 16 III. ...
Gaceta Unam, Jul 16, 2001
Revista De La Universidad De Mexico, Mar 1, 2001
La universidad es una de las instituciones más antiguas del mundo, aun más antigua que el Estado-... more La universidad es una de las instituciones más antiguas del mundo, aun más antigua que el Estado-nación. La primera universidad propiamente dicha se fundó en Bolonia en el siglo XI; las de Parfs yOxford, en el XII. Estas añejas instituciones, ymillares de réplicas, continúan creciendo yprosperando. Aunque han cambiado, nolo han hecho hasta el punto de ser irreconocibles. La universidad moderna es la descendiente directa de la ins.titución que fue hace casi un milenio. Para cualquier estándar, esto constituye un éxito formidable: algo digno de tomarse en cuenta ante los pronunciamientos sobre '~a crisis conceptual de la academia".
Gravitation the Spacetime Structure Silarg Viii, 1994
Phys Rev D, 1988
A model problem is solved for a six-dimensional spacetime where ordinary four-space is flat and t... more A model problem is solved for a six-dimensional spacetime where ordinary four-space is flat and the two extra dimensions have the geometry of a two-sphere. The geometry is driven by coupled Yang-Mills and Higgs fields. The equations of motion are derived from a geometric theory of the canonical gravitation-Yang-Mills-Higgs fields. The constant radius of the two-sphere is determined. If certain reasonable values are taken for various arbitrary constants in the theory, the radius is of the order of the Planck length and an exact value for the coupling constant of the Yang-Mills field is obtained.
An exact solution is presented for colliding plane waves in N-italic = 1 classical supergravity. ... more An exact solution is presented for colliding plane waves in N-italic = 1 classical supergravity. Contrary to the situation in ordinary gravity, this solution is nonsingular everywhere. The Grassmann algebra is shown to be responsible for the vanishing of terms in the Raychaudhuri equation that generate the singularity in the pure gravity case.
Explicit examples of quasi-exactly-solvable $N$-body problems on the line are presented. These ar... more Explicit examples of quasi-exactly-solvable $N$-body problems on the line are presented. These are related to the hidden algebra $sl_N$, and they are of two types -- containing up to $N$ (infinitely-many eigenstates are known, but not all) and up to 6 body interactions only (a finite number of eigenstates is known). Both types degenerate to the Calogero model.
Classical and Quantum Gravity, 1987
An exact solution in N = 1 supergravity for a Kasner (Bianchi type-I) cosmological metric is pres... more An exact solution in N = 1 supergravity for a Kasner (Bianchi type-I) cosmological metric is presented. The gauge (gamma exp mu)psi(mu) = 0 is used together with the ansatz psi(0) = psi(3) = 0 and a three-generator Grassmann algebra. The stress-energy tensor for the gravitino field psi(mu) is shown to be zero, so it is a 'ghost' field. The solution corresponds to a universe that is always expanding but is singular at some time in the past where the metric, the curvature and the psi(mu) field become infinite.
Using a simplified, soluble quantum cosmology, the authors discuss the dangers of using perturbed... more Using a simplified, soluble quantum cosmology, the authors discuss the dangers of using perturbed models to predict quantum behavior.
Phys Rev D, 2000
In the present work the evolution of a coherent field structure of the sine-Gordon equation under... more In the present work the evolution of a coherent field structure of the sine-Gordon equation under quantum fluctuations is studied. The basic equations are derived from the coherent state approximation to the functional Schrödinger equation for the field. These equations are solved asymptotically and numerically for three physical situations. The first is the study of the nonlinear mechanism responsible for the quantum stability of the soliton in the presence of low momentum fluctuations. The second considers the scattering of a wave by the soliton. Finally the third problem considered is the collision of solitons and the stability of a breather. It is shown that the complete integrability of the sine-Gordon equation precludes fusion and splitting processes in this simplified model. The approximate results obtained are non-perturbative in nature, and are valid for the full nonlinear interaction in the limit of low momentum fluctuations. It is also found that these approximate results are in good agreement with full numerical solutions of the governing equations. This suggests that a similar approach could be used for the baby Skyrme model, which is not completely integrable. In this case the higher space dimensionality and the internal degrees of freedom which prevent the integrability will be responsible for fusion and splitting processes. This work provides a starting point in the numerical solution of the full quantum problem of the interaction of the field with a fluctuation.
Recent Developments in Theoretical and Experimental General Relativity Gravitation and Relativistic Field Theories, 1999
Proceedings of the Seventh Marcel Grossman Meeting on Recent Developments in Theoretical and Experimental General Relativity Gravitation and Relativistic Field Theories, 1996
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Papers by Marcos Rosenbaum