The analysis of interacting relativistic many-particle systems provides a theoretical basis for further work in many diverse fields of physics. After a discussion of the nonrelativisticN-particle systems we describe two approaches for obtaining the canonical equations of the corresponding relativistic forms. A further aspect of our approach is the consideration of the constants of the motion.

Following Dirac's generalized canonical formalism, we develop a quantization scheme for theN-dimensional system described by the Lagrangian $L_0 (\dot y,y) = \frac{1}{2}h_{ij} (y)\dot y^i \dot y^j + b_i (y)\dot y^i - w(y)$ which is supposed to be invariant under the gauge transformation $y^i \to y\prime ^i = y^i + (\rho ^i _\alpha + \sigma ^i _{\alpha j} \dot y^j )\delta \Lambda ^\alpha + \tau ^i _\alpha \delta \dot \Lambda ^\alpha$ . The gauge invariance necessarily implies that the Lagrangian (...) is singular. The identities imposed by the gauge invariance are enumerated and reduced to simpler forms. There are primary and secondary constraints, both of which are of first class. The reduced identities are solved explicitly for the case where the secondary constraints constitute the generators of the groupSO(M), and thus an explicit expression for the manifestly gauge-invariant Lagrangian is obtained. By fixing the gauge appropriately, the unphysical variables are eliminated and a quantization is achieved using only physical variables. Our formulation is covariant under an arbitrary point transformation of physical variables. The problem of formulating a quantum action principle is also commented on briefly. (shrink)

This dissertation is intended to provide a formalism for those generics that trigger nonmonotonic inferences. The formalism is to reflect intentionality and exception-tolerating features of generics, and has an emphasis on the axiomatization of generic reasoning that encodes nonmonotonicity. ;A modal conditional approach is taken to formalize the nonmonotonic reasoning in general at the level of object language. A serial of logic systems---MN, NID, NCUM, N STCUM---are constructed in an increasing strength of the characterized nonmonotonic inference relation. In (...) these systems, two binary modal operators ⩾ and > are introduced in their syntax, and a ⊛ function lifted from the traditional * function is deployed in their semantics. These systems are shown to be sound and complete with respect to certain classes of frames defined in the semantics. They are decidable as well. The nonmonotonic inference is argued to be a ternary relation "[phi], Gamma |∼ alpha", and is defined in the system NSTCUM. Many widely discussed nonmonotonic inference patterns such as Defeasible Modus Ponens, Defeasible Transitivity, the Penguin Principle etc. are justified. The specificity rule is proved to be a theorem of the system N STCUM. The impact of negated defaults on an inference is also investigated and accounted for. ;A canonical form to read off generics is proposed: All generic sentences with subject-predicate structure can be re-written into their canonical form S . If S is a plural noun phrase, it can be further refined to be . Normal objects are selected based on the "meaning" of the subject and predicate terms. The second parameter provides an aspect with respect to which certain objects of a kind are considered normal. Due to such a way to select normal objects, the drowning problem is solved. ;The inference behaviors of generics are axiomatized in the system G, which is a quantificational extension of the system NSTCUM. It is proved to be sound and complete with respect to the class of L⩾,G -frames. Those benchmark examples of generic inferences are examined in the system G. (shrink)

The canonical proper time formulation of relativistic dynamics provides a framework from which one can describe the dynamics of classical and quantum systems using the clock of those very systems. The framework utilizes a canonical transformation on the time variable that is used to describe the dynamics, and does not transform other dynamical variables such as momenta or positions. This means that the time scales of the dynamics are described in terms of the natural local time coordinates, which (...) is the most meaningful parameterization of phenomena such as the approach to equilibrium, or the back reaction of interacting systems. We summarize the formalism of the canonical proper time framework, and provide example calculations of the eigenvalues of the hydrogen atom and near horizon description of a scalar field near a Schwarzschild black hole. (shrink)

We construct a consistent theory of a quantum massive Weyl field. We start with the formulation of the classical field theory approach for the description of massive Weyl fields. It is demonstrated that the standard Lagrange formalism cannot be applied for the studies of massive first-quantized Weyl spinors. Nevertheless we show that the classical field theory description of massive Weyl fields can be implemented in frames of the Hamilton formalism or using the extended Lagrange formalism. Then we (...) carry out a canonical quantization of the system. The independent ways for the quantization of a massive Weyl field are discussed. We also compare our results with the previous approaches for the treatment of massive Weyl spinors. Finally the new interpretation of the Majorana condition is proposed. (shrink)

The essential role of classical mechanics in the “old quantum theory” is well known. With the rise of a genuine quantum formalism, classical analogies remained a powerful heuristic tool. However, classical insights soon proved problematic, and in some cases, even counterproductive. The case of the implementation of quantum canonical transformations provides a distinguished case study for the historian studying the circumstances which led to the transformation theory of London, Dirac and Jordan. -/- The attempts to use canonical (...) transformations in strict analogy to classical practice met serious difficulties as soon as one tried to accommodate the action-angle scheme. At some point, the very consistency of quantization went addressed because of the unclear quantum equivalence of classically equivalent Hamiltonians. -/- The early attempts, often beset with ill-defined problems, are illustrative of the lack of understanding of the underlying mathematical scheme. The latter had to be properly appraised before the problem of the meaning of changing variables in quantum theory could be solved. This is why the latter proved instrumental in the discovery of transformation theory. -/- Some of the problems which arose then are still highly instructive from the foundational point of view, and worth to be rediscovered, beyond their historical interest. (shrink)

It is shown that the Hilbert space formalism of quantum mechanics can be derived as a corrected form of probability theory. These constructions yield the Schrödinger equation for a particle in an electromagnetic field and exhibit a relationship of this equation to Markov processes. The operator formalism for expectation values is shown to be related to anL 2 representation of marginal distributions and a relationship of the commutation rules for canonically conjugate observables to a topological relationship of two (...) manifolds is indicated. (shrink)

The analysis of the temporal structure of canonical general relativity and the connected interpretational questions with regard to the role of time within the theory both rest upon the need to respect the fundamentally dual role of the Hamiltonian constraints found within the formalism. Any consistent philosophical approach towards the theory must pay dues to the role of these constraints in both generating dynamics, in the context of phase space, and generating unphysical symmetry transformations, in the context of (...) a hypersurface embedded within a solution. A first denial of time in the terms of a position of reductive temporal relationalism can be shown to be troubled by failure on the first count, and a second denial in the terms of Machian temporal relationalism can be found to be hampered by failure on the second. A third denial of time, consistent with both of the Hamiltonian constraints roles, is constituted by the implementation of a scheme for constructing observables in terms of correlations and leads to a radical Parmenidean timelessness. The motivation for and implications of each of these three denials are investigated. (shrink)

Given the generic canonical probability in phase φ=exp[β(Ψ-H)], contact is traditionally made with phenomenological thermodynamics by comparing the identity δ〈φ〉=0 with the relationTδS=δU+δW, δ indicating an arbitrary infinitesimal variation of the thermodynamic coordinates and angular brackets ensemble means. This paper is concerned with the inverse problem of finding both the generic form of the phase functionw such thatS=〈w〉 and the explicit form φ=αexp[(F-H)/kT] of the canonical distribution on the basis of the requirement that the consequences of the phenomenological (...) laws must be safeguarded, i.e., the relations between the quantities which are their concomitants must also be satisfied by their statistical representatives. Given the generic statistical formalism and specifically thatU=〈H〉, δW=−〈δH〉, the problem is soluble, granted the following generic assumption: “the statistical representative of the entropy is the ensemble mean of a function which depends upon the phase through φ alone.”. (shrink)

The algebraic structure of the 8-spinor formalism is discussed, and the general form of the 8-component wave equation, equivalent to the second-order 4-component one, is presented. This allows a canonical formulation that will be the first stage of the future Clebsch parametrization, i.e., a relativistic generalization of the Bohm-Schiller-Tiomno pioneering work on the Pauli equation.

v. 1. Proceedings, Rome, 2001-2004 -- v. 2. Giornate di studi, 2005-2008.

Este artículo expone la emergencia de expresiones de la espiritualidad no vinculadas a la experiencia religiosa y, en particular, aquella manifestación que pretende situar esta dimensión humana como un fenómeno natural, reconocible y, por ello, transformable desde el método de las ciencias de la Naturaleza. Se presenta un amplio marco que sitúa este fenómeno en el desarrollo de las teorías que establecen un continuo entre biología y cultura. Se ofrecen ejemplos de autores que han presentado propuestas de espiritualidad sin Dios (...) y algunas que responden al llamado «problema realmente difícil», de cómo dar cuenta desde la ciencia natural de este fenómeno de la consciencia. Se cierra señalando límites y remitiendo a la presentación de una propuesta de modelo antropológico con fundamentos clínicos y teóricos, que para dar cuenta del fenómeno de la espiritualidad precisa un marco teórico que supera los límites de la ciencia natural y acude, en este caso, al psicoanálisis. Este mismo modelo muestra también que la espiritualidad elaborada sobre la experiencia religiosa del sujeto es una de las vías de maduración humana. (shrink)

The church in Africa, like its counterparts elsewhere in the world, is called to fulfil the mission of God as expressed in the call ‘Missio Dei’ and influentially remains with the integrity of the mission of Christ, which is liberative and practical. For Christ was not only concerned with the spiritual needs of the people, but also with their material well-being. The following question therefore arises: how can the church in Africa, in general, and in Zimbabwe, in particular, actively do (...) God’s mission and remain with integrity in the midst of the reality of suffering. Furthermore, how can the church for mission and reconstruction be understood in a post-colonial Zimbabwe given the contextual realities of political crises, corruption, poverty, moral decadence, defined or censored truth, leadership crises and no freedom of expression? This article argues that, although the church is faced with these arduous realities, it remains called by God to do God’s mission. While in post-colonial Zimbabwe the socio-political, socio-economic and socio-religious situation might seem hopeless, the church has remained vibrant and alive for reconstruction theology. The transformation of society is possible given the authority and mission mandate of the church. This article argues that the church is a key player in reconstruction theology and in the transformation of society. For transformation to be possible, the church should witness to the gospel of Christ without fear of being labelled, castrated and persecuted. The article asserts that the spirit of the Bible should be revived in a time of reconstruction in Zimbabwe. The assumption in this article is that Zimbabwe is ready for reconstruction discourse. For this to happen, the researchers argue that the church as a critical relevant player in reconstruction needs to ‘be church’ in its missional mandates. Integrity is essential if a church wants to be relevantly missional and reconstructive. Integrity means that the church has to embrace the risks and opportunities associated with mission. (shrink)

En los años ochenta emergió la cuestión de la licitud moral de la mejora por relación a la terapia. Para presentar la problemática actual sobre el tema se ofrece el constructo denominado Práctica de Intervención del Cuerpo caracterizado por cinco parámetros: M o la materia de la transformación, CT o la tecnociencia disponible, A o las concepciones vigentes de lo natural y lo artificial, N o las visiones de la naturaleza humana culturalmente compartidas y V o las valoraciones éticas a (...) las que se apela para legitimar la transformación. Se apunta el nivel ontológico como necesario para comprender y debatir las diferencias existentes en criterio moral. El concepto de naturaleza humana como referente normativo está en crisis, pero su ausencia deja un vacío que hace urgente una deliberación para llegar a una instancia normativa común. (shrink)

El modelo paradigmático de Justicia Transicional se caracteriza por la protección de derechos civiles y políticos y el predominio de la justicia retributiva. La exportación de este modelo a sociedades en posconflicto ha develado las conexiones entre cuestiones sociales y económicas, tales como, pobreza, corrupción y desigualdades, y el logro de una transición efectiva a la democracia. Este artículo analiza la relación entre dichas cuestiones sociales y económicas y la Justicia Transicional a la luz de la teoría del discurso y (...) de las categorías de discurso anormal y normal, utilizadas por Nancy Fraser en el análisis de la teoría de la justicia. (shrink)

El descubrimiento y desarrollo del poder instrumental de la razón en Occidente desde Galileo y Descartes se ha producido de modo unilateral: dominador, constructivo y, por tanto, encubridor de algunas de sus dimensiones esenciales. De esta forma, la ciencia, trocada en tecnociencia, se ha extrañado del mundo de la vida y la amenaza. Sólo haciendo oír la "otra voz" de la razón, su modulación femenina, el anima, podrán corregirse aquellas parcialidades y volver a establecer los vínculos necesarios entre ciencia, tecnociencia (...) y mundo de la vida. (shrink)