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A Generalized Kinetic Theory was proposed in order to have the possibility to treat particles which obey a very general statistics. By adopting the same approach, we generalize here the Kinetic Theory of electrons and phonons. Equilibrium…

A positive mass theorem for General Relativity Theory is proved. The proof is 4-dimensional in nature, and relies completely on arguments pertaining to causal structure, the basic idea being that positive energy-density focuses null…

A quantum version of the action principle is considered in the case of a free relativistic particle. The classical limit of the quantum action is obtained.

Energy conditions are attempts to summarise the properties of realistic descriptions of matter via constraints on the energy-momentum tensor. This is, for example, useful when one wants to understand the types of spacetime geometry that can…

Some useful kinematical relations for the absorption of a photon by a nucleus and its recoil are derived for the relativistic incident energies. These expressions provided for the relativistic kinematics of photoabsorption reactions, though…

A general set of fluid equations that allow for energy-conserving momentum transport by gyroscopic motion of fluid elements is obtained. The equations are produced by a class of action principles that yield a large subset of the known fluid…

The correct quantum description for a curvature squared term in the action can be obtained by casting the action in the canonical form with the introduction of a variable which is the negative of the first derivative of the field variable…

An action principle for the generalized harmonic formulation of general relativity is presented. The action is a functional of the spacetime metric and the gauge source vector. An action principle for the Z4 formulation of general…

A hypothetical energy quantization condition is imposed in [1] (Francisco A. Cruz Neto {\it et al.}, arXiv : 1910.11701 [gr-qc]) in order to show consistent of the result with those in [2] but fail or unable to show consistency with those…

We use the recently discovered universality of Einstein equations in the first order formalism to suggest a positive definite Euclidean action. Possible implications for quantum gravity are considered. We discuss the Hawking and Coleman…

We give an introduction to the canonical formalism of Einstein's theory of general relativity. This then serves as the starting point for one approach to quantum gravity called quantum geometrodynamics. The main features and applications of…

We have previously proposed a conjecture stating that quantum mechanical transition amplitudes can be parametrized in terms of a quantum action. Here we give a proof of the conjecture and establish the existance of a local quantum action in…

The quantum theory of General Relativity at low energy exists and is of the form called "effective field theory". In this talk I describe the ideas of effective field theory and its application to General Relativity.

An energy condition, in the context of a wide class of spacetime theories (including general relativity), is, crudely speaking, a relation one demands the stress-energy tensor of matter satisfy in order to try to capture the idea that…

It is well known that the spectrum condition, i.e. the positivity of the energy in every inertial coordinate system, is one of the central conceptual ingredients in model-independent approaches to relativistic quantum field theory. When one…

The derivation of the recently proposed nonlinear quantum evolution of gravity from an action principle is considered in this brief note. It is shown to be possible if a set of consistency conditions are satisfied that are analogous to the…

A review is given of the various approaches to and expressions for total energy-momentum and mass in the presence of a positive cosmological constant in Einstein's field equations, together with a discussion of the key conceptual questions,…

The energy and time variables of the elementary classical dynamical systems are described geometrically, as canonically conjugate coordinates of an extended phase-space. It is shown that the Galilei action of the inertial equivalence group…

A generalization of the force approach to radiation reaction is given, taken into consideration an arbitrary motion of the charged particle . The expression obtained brings about the expression already given for the linear an the circular…

The energy and momentum for different cosmological models using various prescriptions are evaluated. In particular, we have focused our attention on the energy and momentum for gravitational waves and discuss the results. It is concluded…