Related papers: The relativistic virial theorem and scale invarian…
This is the second of a sequence of papers proving the quantum invariance for ordinary flops over an arbitrary smooth base. In this paper, we complete the proof of the invariance of the big quantum rings under ordinary flops of splitting…
From the relativistic law of motion we attempt to deduce the field theories corresponding to the force law being linear and quadratic in 4-velocity of the particle. The linear law leads to the vector gauge theory which could be the abelian…
A second order extension of the QED Lagrangian (including boson-boson coupling) has been used to describe q\bar q hadrons. Assuming massless elementary fermions (quantons) this results in a finite theory without open parameters, which may…
Finsler geometry motivates a generalization of the Riemannian structure of spacetime to include dependence of the spacetime metric and associated invariant tensor fields on the four-velocity coordinates as well as the spacetime coordinates…
Variational methods play an important role in the study of quantum many-body problems, both in the flavor of classical variational principles based on tensor networks as well as of quantum variational principles in near-term quantum…
A deformation of the canonical algebra for kinematical observables of the quantum field theory in Minkowski space-time has been considered under the condition of Lorentz invariance. A relativistic invariant algebra obtained depends on…
We show that a variety of nonequilibrium dynamics of interacting many-body systems are universally characterized by an elegant relation, which we call the dynamic virial theorem. The out-of-equilibrium dynamics of quantum correlations is…
A continuum version of the virial theorem is derived for a radiating self-gravitating accretion disc around a compact object. The central object is point-like, but we can avoid the regularization of its gravitational potential. This is…
This article develops a variational formulation of relativistic nature applicable to the quantum mechanics context. The main results are obtained through basic concepts on Riemannian geometry. Standards definitions such as vector fields and…
The Dirac method of quantizing Hamiltonian systems with constraints is applied to the massless Thirring model. We solve the quantum Hamiltonian equation for the energy-momentum tensor and obtain a violation of the classical conservation…
The adiabatic theorem refers to a setup where an evolution equation contains a time-dependent parameter whose change is very slow, measured by a vanishing parameter $\epsilon$. Under suitable assumptions the solution of the…
We show that the standard Lorentz transformations admit an invariant mass (length) scale, such as the Planck scale. In other words, the frame independence of such scale is built-in within those transformations, and one does not need to…
Properties of eigenstates of one-particle Quantum Hall Hamiltonians localized near the boundary of a two-dimensional electron gas - so-called edge states - are studied. For finite samples it is shown that edge states with energy in an…
A generalization of virial theorems and virial stresses to micropolar continuum mechanics is explored. The linear momentum balance in dyadic product with translation leads to (i) the first virial theorem of micropolar continuum mechanics…
For a quantum theory that includes exponentially decaying states and Breit-Wigner resonances, which are related to each other by the lifetime-width relation $\tau=\frac{\hbar}{\Gamma}$, where $\tau$ is the lifetime of the decaying state and…
The quark-antiquark bound states are discussed using the relativistic spectator (Gross) equations. A relativistic covariant framework for analyzing confined bound states is developed. The relativistic linear potential developed in an…
The problem of a particle in a box is probably the simplest problem in quantum mechanics which allows for significant insight into the nature of quantum systems and thus is a cornerstone in the teaching of quantum mechanics. In relativistic…
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic…
When tetrad (metric) fields are not invertible, the standard canonical formulation of gravity cannot be adopted as it is. Here we develop a Hamiltonian theory of gravity for non-invertible tetrad. In contrast to Einstein gravity, this phase…
The field theoretical description of the general relativity (GR) is further developed. The action for the gravitational field and its sources is given explicitely. The equations of motion and the energy-momentum tensor for the gravitational…