Mass Quantum Research Articles

A glimpse into Quantum Gravity : A Noncommutative Spacetime results in Quantization of Area, Mass and Entropy

A glimpse into Quantum Gravity : A Noncommutative Spacetime results in Quantization of Area, Mass and Entropy

Mass-energy equation ε = mc2 and the quantum mass

Einstein’s relativistic mass-energy equation (ME) and quantum mass (QM) are obtained from Bohr’s theory. The QM is also expressed using the expectation value of the kinetic energy. The ME is also expressed using the kinetic energy of a body in Newtonian mechanics.

Construction of multi‐bubble blow‐up solutions to the L2$L^2$‐critical half‐wave equation

AbstractThis paper concerns the bubbling phenomena for the ‐critical half‐wave equation in dimension one. Given arbitrarily finitely many distinct singularities, we construct blow‐up solutions concentrating exactly at these singularities. This provides the first examples of multi‐bubble solutions for the half‐wave equation. In particular, the solutions exhibit the mass quantization property. Our proof strategy draws upon the modulation method in Krieger, Lenzmann and Raphaël [Arch. Ration. Mech. Anal. 209 (2013), no. 1, 61–129] for the single‐bubble case, and explores the localization techniques in Cao, Su and Zhang [Arch. Ration. Mech. Anal. 247 (2023), no. 1, Paper No. 4] and Röckner, Su and Zhang [Trans. Amer. Math. Soc., 377 (2024), no. 1, 517–588] for bubbling solutions to non‐linear Schrödinger equations (NLS). However, unlike the single‐bubble or NLS cases, different bubbles exhibit the strongest interactions in dimension one. In order to get sharp estimates to control these interactions, as well as non‐local effects on localization functions, we utilize the Carlderón estimate and the integration representation formula of the half‐wave operator, and find that there exists a narrow room between the orders and for the remainder in the geometrical decomposition. Based on this, a novel bootstrap scheme is introduced to address the multi‐bubble non‐local structure.

Effective potential between static sources in quenched light-front Yukawa theory

We compute a nonperturbative effective potential between two static fermions in light-front Yukawa theory as a Hamiltonian eigenvalue problem. Fermion pair production is suppressed, to make possible an exact analytic solution in the form of a coherent state of bosons that form clouds around the sources. The effective potential is essentially an interference term between individual clouds. The model is regulated with Pauli-Villars bosons and fermions, to achieve consistent quantization and renormalization of masses and couplings. This extends earlier work on scalar Yukawa theory where Pauli-Villars regularization did not play a central role. The key result is that the nonperturbative solution restores rotational symmetry even though the light-front formulation of Yukawa theory, with its preferred axis, appears antithetical to such a symmetry. Published by the American Physical Society 2024

Multi-bubble Bourgain-Wang solutions to nonlinear Schrödinger equations

We study a general class of focusing L 2 L^2 -critical nonlinear Schrödinger equations with lower order perturbations, in the possible absence of the pseudo-conformal symmetry and the conservation law of energy. In dimensions one and two, we construct multi-bubble Bourgain-Wang type blow-up solutions, which behave like a sum of pseudo-conformal blow-up solutions that concentrate at K K distinct singularities, 1 ≤ K > ∞ 1\leq K>{\infty } , and a regular profile. Moreover, we obtain the uniqueness in the energy class where the convergence rate is within the order ( T − t ) 4 + (T-t)^{4+} , for t t close to the blow-up time T T . These results in particular apply to the canonical nonlinear Schrödinger equations and, through the pseudo-conformal transform, yield the existence and conditional uniqueness of non-pure multi-solitons, which behave asymptotically as a sum of multi-solitons and a dispersive part. Thus, the results provide new examples of the mass quantization conjecture and the soliton resolution conjecture. Furthermore, through a Doss-Sussman type transform, we obtain multi-bubble Bourgain-Wang solutions for stochastic nonlinear Schrödinger equations, where the driving noise is taken in the sense of controlled rough path.

ON MASS QUANTIZATION

The problem of the mass spectrum of elementary particles is considered from the positions of reductionism and holism. It is shown that in the holistic description, the concept of substance (energy) is of paramount importance, and elementary particles are understood as emergent states that play a secondary role. A system of axioms is given that defines the basic definitions of the spectrum of matter. In this case, the spectrum of states (“elementary particles”) appears as a result of mass (energy) quantization. A mass formula is derived that depends on the quantum numbers defining the eigenvalues of the Casimir operators of the Lorentz group.

Oscillating gravity, non-singularity and mass quantization from Moffat stochastic gravity arguments

In Moffat stochastic gravity arguments, the spacetime geometry is assumed to be a fluctuating background and the gravitational constant is a control parameter due to the presence of a time-dependent Gaussian white noise In such a surrounding, both the singularities of gravitational collapse and the Big Bang have a zero probability of occurring. In this communication, we generalize Moffat’s arguments by adding a random temporal tiny variable for a smoothing purpose and creating a white Gaussian noise process with a short correlation time. The Universe accordingly is found to be non-singular and is dominated by an oscillating gravity. A connection with a quantum oscillator was established and analyzed. Surprisingly, the Hubble mass which emerges in extended supergravity may be quantized.

Local and global behavior of solutions to 2 D-elliptic equation with exponentially-dominated nonlinearities

We study the family of blowup solutions to semilinear elliptic equations in two-space dimensions with exponentially-dominated nonnegative nonlinearities. Such a family admits an exclusion of the boundary blowup, finiteness of blowup points, and pattern formation. Then, Hamiltonian control of the location of blowup points, residual vanishing, and mass quantization arise under the estimate from below of the nonlinearity. Finally, if the principal growth rate of nonlinearity is exactly exponential and the residual part has a gap relative to this term, there is a locally uniform estimate of the solution which ensures its asymptotic non-degeneracy.

Electron Mass Is Specified by Five Fundamental Constants, <i>a</i>, <i>ħ</i>, <i>G</i>, Λ, and Ω<sub>Λ</sub>, from Quantum Mechanics and General Relativity

Electron mass has been considered a fundamental constant of nature that cannot be calculated from other constants such as Planck’s constant ħ and gravitational constant G. In contrast, holographic analysis takes account of the finite amount of information available to describe the universe and specifies electron mass to six significant figures in terms of five fundamental constants: fine structure constant a, ħ , G, cosmological constant Λ, and vacuum fraction ΩΛ of critical density. A holographic analysis accounts for charge conservation, mass quantization, and baryon/antibaryon ratio. A holographic analysis relates electromagnetism and gravitation, specifies electron Compton wavelength in terms of Planck length and cosmological event horizon radius, and has implications for charged Standard Model fermion masses, minimum stellar mass at redshift z, and use of continuum mathematics in a discontinuous universe.

Dynamics of a Quantum Particle Interacting With an Electromagnetic Field

Essentially, we solve the particle-field equations obtained in the matter distribution quantum mechanics. In the framework of this theory, a particle is described by a density amplitude function, we call wave function, as a packet of waves with the time dependent phases proportional to the relativistic Lagrangian. The mass quantization of such a particle, as a distribution of matter, is obtained from the equality of the spatial integral of the density with the mass as a characteristic of the relativistic dynamics of this matter. The particle dynamics, as a motion of a mass spatial distribution, is obtained from the equality of the wave propagation velocities with the distribution coordinate velocities. This description is a physical one, compared to the Schrödinger-Heisenberg description leading to unphysical results as a null velocity for the kinetic energy as a constant of motion, or Zitterbewegung. The description of a particle interaction with an electromagnetic field by additional Lagrangian terms, with a vector potential conjugated to coordinates, as in the Aharonov-Bohm effect, and an electric potential conjugated to time, leads to the Lorentz force, and the Maxwell equations. In the two conjugated spaces, of the coordinates and of the momentum, the dynamics of a quantum particle is described by propagation operators, depending on the coordinate-momentum product, applied to time dependent wave functions satisfying matter-field equations.  Unlike the standard Schrödinger or Schrödinger-Dirac equations, depending only on the Hamiltonian operator, instead of the Hamiltonian these equations contain the Lagrangian, which, besides the Hamiltonian, include additional terms with an explicit dependence on velocity, as it is expected in a relativistic theory. We obtain the wave function of a particle-antiparticle system interacting with an electromagnetic field, as a wave packet of spinors propagating in space with finite dimensions, given by the finite definition domain of the density function, in the space of the matter-field momentum, as a constant of motion. We show that an electrically charged quantum particle, rotating in a central electric field, generates a vector potential with a magnetic field perpendicular to the rotational plane and an electric field in this plane. By a quantum transition, a photon is emitted in the particle rotational plane, with the magnetic field perpendicular to this plane, and the electric field contained in this plane. In this framework, the vector potential rotation is correlated to a particle momentum rotation, for the canonical matter-field momentum as a constant of motion, without any electromagnetic field radiated outside.

Possible light neutral boson and particle mass quantization * *Supported by the National Natural Science Foundation of China (10175091, 11305007)

Qualities of nucleons, such as the fundamental parameter mass, might be modified in extreme conditions relative to those of isolated nucleons. We show the ratio of the EMC-effect tagged nucleon mass to that of the free one ( ); these values are derived from the nuclear structure function ratio between heavy nuclei and deuterium measured in the electron Deep Inelastic Scattering (DIS) reaction in 0.3 0.7. The increase in with is phenomenologically interpreted via the release of a color-singlet cluster formed by sea quarks and gluons in bound nucleons holding high momentum in the nucleus, from which the mass and fraction of non-nucleonic components in nuclei can be deduced. The mass of color-singlet clusters released per short range correlated (SRC) proton in the high momentum region ( 2 fm ) is extracted to be 16.890 0.016 MeV/c , which evidences the possibility of a light neutral boson and quantized mass of matter.

Relaxed multi-marginal costs and quantization effects

We propose a duality theory for multi-marginal repulsive cost that appears in optimal transport problems arising in Density Functional Theory. The related optimization problems involve probabilities on the entire space and, as minimizing sequences may lose mass at infinity, it is natural to expect relaxed solutions which are sub-probabilities. We first characterize the N-marginals relaxed cost in terms of a stratification formula which takes into account all k interactions with k≤N. We then develop a duality framework involving continuous functions vanishing at infinity and deduce primal-dual necessary and sufficient optimality conditions. Next we prove the existence and the regularity of an optimal dual potential under very mild assumptions. In the last part of the paper, we apply our results to a minimization problem involving a given continuous potential and we give evidence of a mass quantization effect for optimal solutions.

Influence of the magnetic interactions on the mass spectrum of elementary particles

Different approaches to the problem of mass quantization are discussed. The Barut ideas of crucial influence of magnetic forces for explaining the properties of the strong interaction are considered in details. It is shown that this approach gives the possibility to understand the enormous number of elementary particles (about 400) as the excited states of stable fundamental particles (e, p, v), bounded by magnetic interactions.

Quantization of the Blow-Up Value for the Liouville Equation with Exponential Neumann Boundary Condition

In this paper, we analyze the asymptotic behavior of solution sequences of the Liouville-type equation with Neumann boundary condition. In particular, we will obtain a sharp mass quantization result for the solution sequences at a blow-up point.

Modified inertial mass from information loss

A modification of inertia (called MiHsC or quantized inertia) has been proposed that assumes that inertia is caused by Unruh radiation, and that this radiation is made inhomogeneous in space by either Rindler horizons caused by acceleration or the distant Hubble horizon. The former predicts the standard inertial mass, and the latter predicts galaxy rotation without dark matter and cosmic acceleration without dark energy. It is proposed here that this model can be derived in an alternative way by assuming that the sum of mass (M), energy (E) and the information content of horizons (I) is conserved (EMI) so that mass–energy is released in a discrete manner when the area of a Rindler horizon reduces. This model could be tested by looking for the quantization of inertial mass and acceleration at very high accelerations, and may provide an explanation for the cosmological constant problem.

MATHEMATICAL MODELING OF FEEDBACK CONTROL OF GRAVITATIONAL WAVES

We present an analysis for gravitation through space-mass quantization technique where gravitational waves is the fundamental interaction through distinct state of quantization of mass & space while remaining mathematically compatible with general relativity (GR). It also encompasses issues such as the notion of space-radiative expansion leading to order in the large radius expansion, zero point energy & also space-contraction is introduced that sets the physical scales and subleading terms. We discuss conditions under which gravitational waves is transformed locally under space-mass action. A proposal for improving the current use of scientific methods & mechanism to forge a model of gravitational waves is given. We refer this physical interpretation in rest of the text as “Quantize field Theory”.

Analytic aspects of the Tzitzéica equation: blow-up analysis and existence results

We are concerned with the following class of equations with exponential nonlinearities: $$ \Delta u+h_1e^u-h_2e^{-2u}=0 \qquad \mbox{in } B_1\subset\mathbb{R}^2, $$ which is related to the Tzitz\'eica equation. Here $h_1, h_2$ are two smooth positive functions. The purpose of the paper is to initiate the analytical study of the above equation and to give a quite complete picture both for what concerns the blow-up phenomena and the existence issue. In the first part of the paper we provide a quantization of local blow-up masses associated to a blowing-up sequence of solutions. Next we exclude the presence of blow-up points on the boundary under the Dirichlet boundary conditions. In the second part of the paper we consider the Tzitz\'eica equation on compact surfaces: we start by proving a sharp Moser-Trudinger inequality related to this problem. Finally, we give a general existence result.

On the existence and blow-up of solutions for a mean field equation with variable intensities

We study an elliptic problem with exponential nonlinearities describing the statistical mechanics equilibrium of point vortices with variable intensities. For suitable values of the physical parameters we exclude the existence of blow-up points on the boundary, we prove a mass quantization property and we apply our analysis to the construction of minimax solutions.

Position-dependent mass approach and quantization for a torus Lagrangian

We have shown that a Lagrangian for a torus surface can yield second-order nonlinear differential equations using the Euler-Lagrange formulation. It is seen that these second-order nonlinear differential equations can be transformed into the nonlinear quadratic and Mathews-Lakshmanan equations using the position-dependent mass approach developed by Mustafa (J. Phys. A: Math. Theor. 48, 225206 (2015)) for the classical systems. Then, we have applied the quantization procedure to the nonlinear quadratic and Mathews-Lakshmanan equations and found their exact solutions.

On the Blow-Up of Solutions to Liouville-Type Equations

Abstract We estimate some complex structures related to perturbed Liouville equations defined on a compact Riemannian 2-manifold. As a byproduct, we obtain a quick proof of the mass quantization and we locate the blow-up points.