Foundations Of Field Theory Research Articles

Role of Skew-Symmetric Differential Forms in Mathematical Physics and Field Theory

Skew-symmetric differential forms possess properties that enable one to carry out a qualitative investigation of the equations of mathematical physics and the foundations of field theories. In the paper we call attention to a unique role in field theory of closed exterior skew-symmetric differential forms, which correspond to conservation laws for physical fields (to conservative quantities). At the same time, it was shown that such closed exterior forms can be derived from skew-symmetric differential forms, which follow from the mathematical physics equations describing material media such as thermodynamic, gas-dynamic, cosmic media. This points a connection the field theory equations with the mathematical physics equations. Such connection discloses the properties and specific features of field theory.

Алгоритм оценки ротора векторных полей движений земной поверхности по геодезическим данным

According to the changes of geodetic elements (coordinates, heights, directions) after multiple measurements, it is possible to represent the field of geodetic points’ displacement vector. When studying the stress-strain state of the earth’s surface, the vectors obtained can be used not only to calculate the earth’s deformation tensor in the area under study, but also the differential characteristics of the vector field, called divergence and rotor (vortex, curl). The author proposes the way to determinethe rotor according to discrete geodesic observations of displacement vectors on the surface of the surveyed area. The most important continuation of this research work is the method of geodynamic systemsmathematical modeling for predictive purposes. In order to study the complex (nonlinear) geodynamic processes, an appropriate mathematical basis should be chosen. Here the attention is drawn to the attraction of the mathematical foundations of field theory. The variants of the curl definition are proposed – one of the vector fields’ differential characteristics. To assess the characteristics of vector fields when using multiple geodetic measurements, the finite element method can be used. The division of the surveyed area into triangles enables you to determine the characteristics of the deformation after calculating the elements of the strain tensor.

Discussion: Conceptual Foundations of Field Theories in Physics

This discussion provides a brief commentary on each of the papers presented in the symposium on the conceptual foundations of field theories in physics. In Section 2 I suggest an alternative to Paul Teller's (1999) reading of the gauge argument that may help to solve, or dissolve, its puzzling aspects. In Section 3 I contend that Sunny Auyang's (1999) arguments against substantivalism and for “objectivism” in the context of gauge field theories face serious worries. Finally, in Section 4 I claim that Gordon Fleming's (1999) proposal for hyperplane-dependent Newton-Wigner fields differs importantly from his previous arguments about hyperplane-dependent properties in quantum mechanics.

Remarks on gauge variables and singular lagrangians

Chela-Flores ( t975) has proposed a gauge theory of He-II superfluidity, based on the Lagrangian density 5~(k) g = ( i /2 ) (~Ot~* ¢ * ~ t ~ ) (1/2/14)[(7 +/MA)~0*] "[(V iMA)~ ] ( U / 2 ) [ ~ 14 (Mk/2 ) (V x A)" (V x A) (1) in which ~(x, t) is the condensate field, and A(x, t) is a gauge field which is interpreted (up to a sign) as the depletion velocity. See also Chela-Ftores (1977), Hu (1977), and Chela-Ftores et al. (to be published). We shall call this last paper I. The present note does not concern low-temperature physics, but rather the relevance of Aa/~ ) to the foundations of field theory. (i) Let us assumek • 0. We have shown in I the (1) implies via Noether 's theorem the existence of a conserved current that is such that, when combined with Euler-Lagrange equations (ELE), it results that all solutions with nonstatic density I ~ 12 are forbidden. This is true even if U = 0. Here a discontinuity in the Lagrangian parameters is exhibited because 5¢~o° / is the Schr6dinger Lagrangian, which certainly allows for nonstationary solutions.