Related papers: A general comparison theorem
The equivalence theorem states that the leading part of the amplitude for a process with external longitudinally polarized vector bosons is given by the amplitude in which the longitudinal vector bosons are replaced by the corresponding…
In Part I of the present series of papers, we adumbrate our idea of Riemannian geometry to higher order in the infinitesimals and derive expressions for the appropriate generalizations of parallel transport and the Riemannian curvature…
General relativity can be presented in terms of other geometries besides Riemannian. In particular, teleparallel geometry (i.e., curvature vanishes) has some advantages, especially concerning energy-momentum localization and its…
In this article, we prove an extension of the mean value theorem and a comparison theorem for subharmonic functions. These theorems are used to answer the question whether we can conclude that two subharmonic functions which agree almost…
Quantum mechanics postulates the existence of states determined by a particle position at a single time. This very concept, in conjunction with superposition, induces much of the quantum-mechanical structure. In particular, it implies the…
General relativity differs from other forces in nature in that it can be made to disappear locally. This is the essence of the equivalence principle. In general relativity the equivalence principle is implemented using differential…
The status of experimental tests of general relativity and of theoretical frameworks for analyzing them are reviewed and updated. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eotvos experiment, tests…
The motion of a system of particles under electromagnetic interaction is considered. Under the assumption that the force acting on an electric charge is given by the sum of the electromagnetic fields produced by any other charged particles…
General Equilibrium Theory is the benchmark of economics, especially its results concerning the efficient allocation of resources, known as the First and Second Welfare Theorems. Yet, General Equilibrium Theory is beyond the scope of most…
We establish the Hamiltonian formulation of the teleparallel equivalent of general relativity, without fixing the time gauge condition, by rigorously performing the Legendre transform. The time gauge condition, previously considered,…
Heat always flows from hotter to a colder temperature until thermal equilibrium be finally restored in agreement with the usual (zeroth, first and second) laws of thermodynamics. However, Tolman and Ehrenfest demonstrated that the relation…
This paper establishes a new comparison principle for the minimum eigenvalue of a sum of independent random positive-semidefinite matrices. The principle states that the minimum eigenvalue of the matrix sum is controlled by the minimum…
Classically general covariance is found from the idea that a vector is a physical quantity which exists independently of choice of coordinate system and is unchanged by a change of coordinate system. It is often assumed that there exists…
We suppose: (1) that the ground-state eigenvalue E = F(v) of the Schroedinger Hamiltonian H = -Delta + vf(x) in one dimension is known for all values of the coupling v > 0; and (2) that the potential shape can be expressed in the form f(x)…
We show that the locally constant force necessary to get a stable hyperbolic motion regime for classical charged particles, actually, is a subtle combination of an applied external force and the radiation reaction force. It suggests, as the…
To enhance the consistency between the quantum descriptions of waves and particles, we quantise mechanical point particles in this paper in the same physically-motivated way as we previously quantised light in quantum electrodynamics…
This paper investigates the strict comparison theorem under the framework of $G$-expectation, i.e., let $X\leq Y$ q.s., if $X,Y$ satisfy some additional conditions, then $\E[X]<\E[Y]$.
We present a model unifying general relativity and quantum mechanics. The model is based on the (noncommutative) algebra \mbox{{\cal A}} on the groupoid \Gamma = E \times G where E is the total space of the frame bundle over spacetime, and…
A generalized Heisenberg-Euler formula is given for an Abelian gauge theory having vector as well as axial vector couplings to a massive fermion. So, the formula is applicable to a parity-violating theory. The gauge group is chosen to be…
Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories…