Publications

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    Vladimir Cuesta Sánchez
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    ABSTRACT: In the present book we studied two Lagrangians in such a way that the Lagrangians produce the same equations of motion and its difference is not the time derivative of a function of coordinates and time. In fact, some potentials admit the construction and we deduced its dependence. When we do the Hamiltonian formalism, in one case we have the usual formalism, in the second case we obtain a noncanonical formalism, we studied the quantization and three dimensional systems, too. We present certain matrices in such a way that the matrices will define symplectic structures, we choose the entries of the matrices in such a way that we will have square roots of minus the identity matrix, we made our studies for 6x6 and 8x8 matrices and we made a general discussion for the 2nx2n case, too.
    1 05/2014; Kindle., ISBN: B00K488NQG
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    Vladimir Cuesta Sánchez
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    ABSTRACT: In the present book we found general solutions for the components of a symplectic structure, in the solutions we can take some components as arbitrary functions, we analyze two dimensional, four dimensional and six dimensional phase spaces. When we choose a symplectic structure and the equations of motion for a specific system, we found that in some cases we can not find a Hamiltonian formalism. In a second study, we take a symplectic structure, we use integrability conditions and we find the equations of motion for systems in such a way that we can use the symplectic structure to construct a Hamiltonian formulation. In another study, we choose a symplectic structure and when we want to find the generators of translations and rotations, we found that there are not generators for all the cases.
    1 edited by Vladimir Cuesta Sánchez, 03/2014; Kindle., ISBN: ASIN: B00IVXR844
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    Vladimir Cuesta Sánchez
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    ABSTRACT: En el libro se presentan varios métodos para encontrar Hamiltonianos y estructuras simplécticas no canónicos. También, por primera vez se estudian oscilaciones eléctricas (circuitos LC) y mecánicas acopladas, además de oscilaciones pequeñas usando justo Hamiltonianos y paréntesis de Poisson no canónicos.
    1 01/2014; Kobo., ISBN: 1230000209223
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    Vladimir Cuesta Sánchez
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    ABSTRACT: Chaotic attractors can be described with three variables (x, y, z) and three differential equations, we can mention the Lorenz attractor, Chen's attractor and more chaotic systems. In the present book we added an odd number of variables and we construct Lagrangian and Hamiltonian formalisms in the usual way. In the procedures we have the same equations of motion for the variables x, y and z, plus the equations of motion for the additional variables. We followed three different approaches: in the first approach we presented a phase space and the Hamiltonian, in the second approach we presented the Lagrangian and we obtained the Hamiltonian, we had not constraints, in the last procedure we considered the Lagrangian formalism and we obtained constraints.
    12/2013; , ISBN: ASIN: B00HLADSU6
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    Vladimir Cuesta Sánchez
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    ABSTRACT: In the book we construct models with two degrees of freedom where sl(2, R) is the Lie algebra of constraints, in some cases a constraint looks like a General Relativity constraint, we present some topological models where the Lie algebra for the first class constraints has two generators, we studied methods to find first class constraints with a specific Lie algebra, we calculated its equations of motion and we studied quantum theories. For the Lee model, we use complex Bogoliubov transformations and we show that we can construct states with positive norm in the non hermitian regime. The Lee model was studied as a part of a postdoc position at the Institute of Nuclear Sciences in the National Autonomous University of Mexico. I would like to dedicate my book to Natasha, she is my daughter.
    10/2013; Kobo.., ISBN: 1230000193451
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    Vladimir Cuesta Sánchez
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    ABSTRACT: In the present work we studied some Lie algebras. We can choose a Lie algebra L over the field R, when we use matrix representations for the elements in the base, we can use it to construct vector fields over a manifold M with the same commutation relations for the elements in the base, we find one parameter groups and we studied if the vector fields can be Killing vectors. We use matrix representations to construct models with the first class constraints in a gauge system, we found complete observables and we obtained the Lie algebra of observables, too. We illustrate the methods with gl(2), sp(2, R), sl(3) and so on.
    1 10/2013; Kindle.., ISBN: B00FZKTMRM
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    Vladimir Cuesta Sánchez
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    ABSTRACT: In the present book the classical and quantum dynamics are studied for the three-dimensional isotropic harmonic oscillator, when noncanonical symplectic structures are used, in a classical level we found different couples of hamiltonians and symplectic structures for the usual set of equations of motion, the quantizations were made with Darboux maps and with the help of creation and annhilation operators. The book presents a new method to find complete observables, the method begins with a partial observable and one clock or a set of clocks and we finish with a complete observable. The present work studied the self adjointness for the quantum operators of gauge invariant systems, too.
    09/2013; Kindle.., ISBN: B00FGQZQTI
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    Vladimir Cuesta Sánchez
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    ABSTRACT: En el presente trabajo se obtienen lagrangianos con las mismas ecuaciones de movimiento de un sistema, los lagrangianos que se encuentran no son la diferencia entre las energías cinética y potencial de la formulación usual y tampoco difieren de ésta en una derivada total de una función de coordenadas y del tiempo. El estudio se realiza para el oscilador harmónico isótropo en 2 y 3 dimensiones, para oscilaciones acopladas tanto eléctricas como mecánicas. Se realiza la formulación hamiltoniana y en un caso se estudia el teorema de Noether a nivel lagrangiano. También se muestran diferentes modelos que tienen constricciones de primera clase, en tales modelos se emplean métodos para encontrar constantes de movimiento y posteriormente, se encuentra el álgebra de Lie de observables. Finalmente, se estudia al oscilador harmónico unidimensional y a una partícula cargada en un campo magnético constante pero con formulaciones hamiltonianas no canónicas. En particular se estudia la cuantización del sistema usando mapeos de Darboux.
    09/2013; BibliotEca.
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    Vladimir Cuesta Sánchez
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    ABSTRACT: En el presente trabajo se muestra que existen 16 reglas para expresar el cambio de dos celdas adyacentes en una cuando cada celda puede estar en uno de dos estados (blanco o negro), tales reglas están en una correspondencia uno a uno a determinadas estructuras algebraicas. Usando cada una de las reglas se estudia el cambio en un tiempo discreto de cadenas cortas divididas en celdas para tres elecciones: cadenas cerradas, cadenas abiertas con un extremo fijo y cadenas abiertas con los extremos fijos. También se estudian cadenas cortas (abiertas y cerradas) para el caso de algunos autómatas celulares lineales usuales. En cualquier caso se observa que al fijar uno, o bien dos extremos los resultados que se obtienen cambian de manera significativa respecto a los casos de cadenas cerradas.
    1 07/2013; Publicia.., ISBN: 978-3639551198
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    Vladimir Cuesta Sánchez
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    ABSTRACT: En el presente trabajo se muestra que una transformación de Lorentz y adicionalmente una rotación permiten encontrar nuevas soluciones a las ecuaciones de la teoría de Kaluza-Klein, partiendo de conocidas; lográndose encontrarlas en realidad a las ecuaciones de Einstein-Maxwell acopladas con un campo escalar. El método se basa en la existencia de algunas simetrías de las soluciones de partida. En forma adicional, se presentan acciones lagrangianas cuyas ecuaciones de movimiento incluyen a las ecuaciones de la llamada dinámica de Cartan. Finalmente, se estudian las regiones del plano que va cubriendo un objeto si a este se le permite moverse en regiones descritas con parámetros continuos.
    1 01/2013; Editorial Académica Española.., ISBN: 978-3847352686
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    Vladimir Cuesta Sánchez
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    ABSTRACT: En el siguiente trabajo se encuentran diferentes hamiltonianos y estructuras simplécticas para el oscilador harmónico isótropo en 3D que originan las mismas ecuaciones de movimiento, se estudian los generadores de traslaciones y rotaciones, se estudia su cuantización. Además, se estudia la compatibilidad de norma y frontera para sistemas no invariantes de norma e invariantes de norma cuando se agregan términos a la frontera, usando estructuras simplécticas no canónicas. Finalmente, las ecuaciones estructurales de Cartan y las identidades de Bianchi se interpretan como ecuaciones de movimiento, se da el principio de acción, se estudia su relación con teorías BF y más.
    1 02/2012; Editorial Académica Española.., ISBN: 978-3847363804
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    ABSTRACT: In this work we consider scale anisotropic transformations between space and time in classical mechanics. The degree of anisotropy is measure by the dynamical exponent z. We build an action that is consistent with the dispersion relation of Hořava gravity [1]. For z = 2 our model corresponds to the conformal mechanics of Alfaro, Fubini and Furlan. Furthermore, we introduce a canonical transformation which connects directly the Hořava type particle with the relativistic particle.
    AIP Conference Proceedings. 09/2011; 1361(1):344-348.
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    Vladimir Cuesta Sánchez
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    ABSTRACT: En el siguiente trabajo se introduce una conexión compatible con una métrica pero con torsión, ésto permite definir momentos lineal y angular en forma cuasilocal para ciertos espacios-tiempo tipo D.
    1 08/2011; Editorial Académica Española.., ISBN: 978-3845485973
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    Vladimir Cuesta, J David Vergara
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    ABSTRACT: An Ar threesome: Matrix models, 2d conformal field theories, and 4d N = 2 gauge theories J. Math. Phys. 51, 082304 (2010) Eightfold way from dynamical first principles in strongly coupled lattice quantum chromodynamics
    XII Mexican Workshop on Particles and Fields; 01/2011
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    Vladimir Cuesta, David Vergara, Merced Montesinos
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    ABSTRACT: We work with gauge systems and using gauge invariant functions we study its quantum counterpart and we find if all these operators are self adjoint or not. Our study is divided in two cases, when we choose clock or clocks that its Poisson brackets with the set of constraints is one or it is different to one. We show some transition amplitudes.
    XIV Mexican School on Particles and Fields; 01/2011
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    ABSTRACT: In this paper we implement scale anisotropic transformations between space and time in classical mechanics. The resulting system is consistent with the dispersion relation of Hořava gravity [ P. Hořava Phys. Rev. D 79 084008 (2009)]. Also, we show that our model is a generalization of the conformal mechanics of Alfaro, Fubini, and Furlan. For an arbitrary dynamical exponent we construct the dynamical symmetries that correspond to the Schrödinger algebra. Furthermore, we obtain the Boltzmann distribution for a gas of free particles compatible with anisotropic scaling transformations and compare our result with the corresponding thermodynamics of the recent anisotropic black branes proposed in the literature.
    Physical review D: Particles and fields 09/2009; 81(6).
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    ABSTRACT: Action principles of the BF type for diffeomorphism invariant topological field theories living in n-dimensional spacetime manifolds are presented. Their construction is inspired by Cuesta and Montesinos' recent paper where Cartan's first and second structure equations together with first and second Bianchi identities are treated as the equations of motion for a field theory. In opposition to that paper, the current approach involves also auxiliary fields and holds for arbitrary n-dimensional space-times. Dirac's canonical analysis for the actions is detailedly carried out in the generic case and it is shown that these action principles define topological field theories, as mentioned. The current formalism is a generic framework to construct geometric theories with local degrees of freedom by introducing addi-tional constraints on the various fields involved that destroy the topological character of the original theory. The latter idea is implemented in two-dimensional spacetimes where gravity coupled to matter fields is constructed out, which has indeed local excitations.
    Physical review D: Particles and fields 09/2008; 78.
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    Vladimir Cuesta, Merced Montesinos, David Vergara
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    ABSTRACT: Some very simple models of gauge systems with noncanonical symplectic structures having sl(2, r) as the gauge algebra are given. The models can be interpreted as noncommutative versions of the usual SL(2, R) model of Montesinos-Rovelli-Thiemann. The symplectic structures of the noncom-mutative models, the first-class constraints, and the equations of motion are those of the usual SL(2, R) plus additional terms that involve the parameters θ µν which encode the noncommutativity among the coordinates plus terms that involve the parameters Θµν associated with the noncommu-tativity among the momenta. Particularly interesting is the fact that the new first-class constraints get corrections linear and quadratic in the parameters θ µν and Θµν . The current constructions show that noncommutativity of coordinates and momenta can coexist with a gauge theory by explicitly building models that encode these properties. This is the first time models of this kind are reported which might be significant and interesting to the noncommutative community. Hamiltonian constrained systems with a finite num-ber of degrees of freedom can be written in a Hamilto-nian form by means of the dynamical equations of mo-tion (summation convention over repeated indices is used throughout) ˙ x µ = ω µν (x) ∂H ∂x ν + λ a ∂γ a ∂x ν + λ α ∂χ α ∂x ν = ω µν (x) ∂H E ∂x ν , µ, ν = 1, 2, . . . , 2N, (1) where H E = H + λ a γ a + λ α χ α is the extended Hamilto-nian, γ a (x) ≈ 0, χ α (x) ≈ 0, (2) are the constraints which define the constraint surface Σ embedded in the phase space Γ. Γ is a symplectic manifold endowed with the symplectic structure ω = 1 2 ω µν (x)dx µ ∧ dx ν , (3) where (x µ) are coordinates which locally label the points p of Γ. It is important to emphasize that the phase space Γ is considered as a single entity, i.e., Γ need not be nec-essarily interpreted as the cotangent bundle of a configu-ration space C. H is taken to be a first-class Hamiltonian, the γ's are first-class constraints while the χ's are second class, i.e., {γ a , γ b } ω = C ab c γ c + T ab αβ χ α χ β , (4a)
    hep-th/0611333. 02/2008;
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    Vladimir Cuesta, Merced Montesinos
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    ABSTRACT: Cartan’s first and second structure equations together with first and second Bianchi identities can be interpreted as equations of motion for the tetrad, the connection and a set of two-form fields TI and RJI. From this viewpoint, these equations define by themselves a field theory. Restricting the analysis to four-dimensional spacetimes (keeping gravity in mind), it is possible to give an action principle of the BF type from which these equations of motion are obtained. The action turns out to be equivalent to a linear combination of the Nieh-Yan, Pontrjagin, and Euler classes, and so the field theory defined by the action is topological. Once Einstein’s equations are added, the resulting theory is general relativity. Therefore, the current results show that the relationship between general relativity and topological field theories of the BF type is also present in the first-order formalism for general relativity.
    Physical review D: Particles and fields 11/2007; 76(10).
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    ABSTRACT: The effect of the gauge transformation in the action principle for Hamiltonian gauge systems formulated in terms of noncanonical symplectic structures is studied and, particularly, the compatibility between gauge conditions and boundary conditions is analyzed. It is shown that the complete set of commuting observables at the time boundary is now fixed by the boundary term and the symplectic structure. The theory is applied to two nontrivial models having SL(2,R) and SU(2) gauge symmetries, respectively, whose extended phase spaces are endowed with new interactions produced by noncanonical symplectic structures.
    Physical review D: Particles and fields 07/2007; 76(2).

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