This article examines the use of fractals to estimate the probability of classical events controlled by quantum processes. A hypothesis explaining the opposite charges of the positron and electron is discussed, as well as the relationship with the main modern theories of quantum mechanics, such as quantum electrodynamics (QED), string theory, etc. The relationship with the tunnel effect and the pulsed tunnel effect is considered. Examples of practical application of fractals are given, for example, in photocatalysts. The concepts of the effective mass of a photon and the quantum nature of elementary particles, the idea of their internal structure and the formation of matter from the point of view of quantum mechanics are touched upon. Particular attention is paid to the fractal structure of the quantum field as a probability associated with the formation of a positron or electron, and the mathematical connection with the Dirac equation, QED and the Schrödinger equation.This article examines the use of fractals to estimate the probability of classical events controlled by quantum processes. A hypothesis explaining the opposite charges of the positron and electron is discussed, as well as the relationship with the main modern theories of quantum mechanics, such as quantum electrodynamics (QED), string theory, etc. The relationship with the tunnel effect and the pulsed tunnel effect is considered. Examples of practical application of fractals are given, for example, in photocatalysts. The concepts of the effective mass of a photon and the quantum nature of elementary particles, the idea of their internal structure and the formation of matter from the point of view of quantum mechanics are touched upon. Particular attention is paid to the fractal structure of the quantum field as a probability associated with the formation of a positron or electron, and the mathematical connection with the Dirac equation, QED and the Schrödinger equation.

Computational nanotechnologyAug 15, 20245 citations

Theoretical Analysis of Quantum Electrodynamic

Edward B. Manoukian

De Gruyter eBooksDec 31, 19840 citations

Study of a Model of Quantum Electrodynamics

Oscar Wallace Greenberg

arXiv:hep-th/0002201Foundations of PhysicsMar 1, 20004 citations

Quantum critical point in the QED3 theory of underdoped high-temperature superconductors

Dominic J. Lee, Igor F. Herbut

We study the effect of gapless quasiparticles in a d-wave superconductor on the $T=0$ end point of the Kosterlitz-Thouless transition line in underdoped high-temperature superconductors. Starting from a lattice model that has gapless fermions coupled to three-dimensional $\mathrm{XY}$ phase fluctuations of the superconducting order parameter, we propose a continuum field theory to describe the quantum phase transition between the d-wave superconductor and the spin-density-wave insulator. Without fermions, the theory reduces to the standard Higgs scalar electrodynamics (HSE), which is known to have the critical point in the inverted $\mathrm{XY}$ universality class. Extending the renormalization group calculation for the HSE to include the coupling to fermions, we find that the qualitative effect of fermions is to increase the portion of the space of coupling constants where the transition is discontinuous. The critical exponents at the stable fixed point vary continuously with the number of fermion fields N, and we estimate the correlation length exponent $(\ensuremath{\nu}=0.65)$ and the vortex field anomalous dimension $({\ensuremath{\eta}}_{\ensuremath{\Phi}}=\ensuremath{-}0.48)$ at the quantum critical point for the physical case $N=2.$ The stable critical point in the theory disappears for the number of Dirac fermions $N>{N}_{c},$ with ${N}_{c}\ensuremath{\approx}3.4$ in our approximation. We discuss the relationship between the superconducting and the chiral (SDW) transitions, and point to some interesting parallels between our theory and the Thirring model.We study the effect of gapless quasiparticles in a d-wave superconductor on the $T=0$ end point of the Kosterlitz-Thouless transition line in underdoped high-temperature superconductors. Starting from a lattice model that has gapless fermions coupled to three-dimensional $\mathrm{XY}$ phase fluctuations of the superconducting order parameter, we propose a continuum field theory to describe the quantum phase transition between the d-wave superconductor and the spin-density-wave insulator. Without fermions, the theory reduces to the standard Higgs scalar electrodynamics (HSE), which is known to have the critical point in the inverted $\mathrm{XY}$ universality class. Extending the renormalization group calculation for the HSE to include the coupling to fermions, we find that the qualitative effect of fermions is to increase the portion of the space of coupling constants where the transition is discontinuous. The critical exponents at the stable fixed point vary continuously with the number of fermion fields N, and we estimate the correlation length exponent $(\ensuremath{\nu}=0.65)$ and the vortex field anomalous dimension $({\ensuremath{\eta}}_{\ensuremath{\Phi}}=\ensuremath{-}0.48)$ at the quantum critical point for the physical case $N=2.$ The stable critical point in the theory disappears for the number of Dirac fermions $N>{N}_{c},$ with ${N}_{c}\ensuremath{\approx}3.4$ in our approximation. We discuss the relationship between the superconducting and the chiral (SDW) transitions, and point to some interesting parallels between our theory and the Thirring model.

arXiv:cond-mat/0210182Physical review. B, Condensed matterMay 16, 20033 citations

Spectral Mechanics of Phase: Variational Structure, Spectral Dynamics, and Physical Consequences

Jonatan P. camargo

Spectral Mechanics of Phase is presented as a variational formulation in which energy, dynamics, and observables emerge from a spectral structure associated with the phase $\phi = S/\hbar$ . Starting from the variational principle and spectral functional calculus, it is demonstrated that unitary evolution can be constructed via the Cayley transform of a self-adjoint operator, leading to a nonlinear relationship between energy and spectrum: \begin{equation} E(\lambda) = \hbar \frac{2}{\Delta t}\arctan(\tau \lambda). \end{equation} It is shown that standard quantum mechanics is recovered as a low-energy limit, in which the spectral relationship becomes approximately linear. In contrast, in the high-energy regime, the theory predicts energy saturation and spectral compression, arising from the limitation of the spectral phase. Applications to canonical systems, including the harmonic oscillator, infinite well, and hydrogen atom, show the presence of systematic corrections in energy levels and transition frequencies. In particular, modifications in atomic spectral series are derived that preserve the known structure in asymptotic regimes but introduce controlled deviations at higher orders. Order-of-magnitude analysis and comparison with spectroscopic data indicate that the theory is compatible with current experimental results, while providing explicit criteria for falsification. An experimental protocol based on low-energy transitions is proposed to distinguish the predictions of Spectral Mechanics of Phase from those of quantum electrodynamics. The presented formulation reproduces the established results of quantum mechanics in its domain of validity, while introducing a more general spectral structure, derived directly from the action, without the need to postulate spectral linearity or operators as primitive entities.Spectral Mechanics of Phase is presented as a variational formulation in which energy, dynamics, and observables emerge from a spectral structure associated with the phase $\phi = S/\hbar$. Starting from the variational principle and spectral functional calculus, it is demonstrated that unitary evolution can be constructed via the Cayley transform of a self-adjoint operator, leading to a nonlinear relationship between energy and spectrum: \begin{equation} E(\lambda) = \hbar \frac{2}{\Delta t}\arctan(\tau \lambda). \end{equation} It is shown that standard quantum mechanics is recovered as a low-energy limit, in which the spectral relationship becomes approximately linear. In contrast, in the high-energy regime, the theory predicts energy saturation and spectral compression, arising from the limitation of the spectral phase. Applications to canonical systems, including the harmonic oscillator, infinite well, and hydrogen atom, show the presence of systematic corrections in energy levels and transition frequencies. In particular, modifications in atomic spectral series are derived that preserve the known structure in asymptotic regimes but introduce controlled deviations at higher orders. Order-of-magnitude analysis and comparison with spectroscopic data indicate that the theory is compatible with current experimental results, while providing explicit criteria for falsification. An experimental protocol based on low-energy transitions is proposed to distinguish the predictions of Spectral Mechanics of Phase from those of quantum electrodynamics. The presented formulation reproduces the established results of quantum mechanics in its domain of validity, while introducing a more general spectral structure, derived directly from the action, without the need to postulate spectral linearity or operators as primitive entities.

May 3, 20260 citations

Theory of Quantum Transitions

D. I. Blokhint︠s︡ev

Springer eBooksJan 1, 19640 citations

We study the effect of gapless quasiparticles in a d-wave superconductor on the

T=0

end point of the Kosterlitz-Thouless transition line in underdoped high-temperature superconductors. Starting from a lattice model that has gapless fermions coupled to three-dimensional

\mathrm{XY}

phase fluctuations of the superconducting order parameter, we propose a continuum field theory to describe the quantum phase transition between the d-wave superconductor and the spin-density-wave insulator. Without fermions, the theory reduces to the standard Higgs scalar electrodynamics (HSE), which is known to have the critical point in the inverted

\mathrm{XY}

universality class. Extending the renormalization group calculation for the HSE to include the coupling to fermions, we find that the qualitative effect of fermions is to increase the portion of the space of coupling constants where the transition is discontinuous. The critical exponents at the stable fixed point vary continuously with the number of fermion fields N, and we estimate the correlation length exponent $(\ensuremath{\nu}=0.65)$ and the vortex field anomalous dimension $({\ensuremath{\eta}}_{\ensuremath{\Phi}}=\ensuremath{-}0.48)$ at the quantum critical point for the physical case

N=2.

The stable critical point in the theory disappears for the number of Dirac fermions

N>{N}_{c},

with ${N}_{c}\ensuremath{\approx}3.4$ in our approximation. We discuss the relationship between the superconducting and the chiral (SDW) transitions, and point to some interesting parallels between our theory and the Thirring model.

Spectral Mechanics of Phase is presented as a variational formulation in which energy, dynamics, and observables emerge from a spectral structure associated with the phase

\phi = S/\hbar

. Starting from the variational principle and spectral functional calculus, it is demonstrated that unitary evolution can be constructed via the Cayley transform of a self-adjoint operator, leading to a nonlinear relationship between energy and spectrum: \begin{equation} E(\lambda) = \hbar \frac{2}{\Delta t}\arctan(\tau \lambda). \end{equation} It is shown that standard quantum mechanics is recovered as a low-energy limit, in which the spectral relationship becomes approximately linear. In contrast, in the high-energy regime, the theory predicts energy saturation and spectral compression, arising from the limitation of the spectral phase. Applications to canonical systems, including the harmonic oscillator, infinite well, and hydrogen atom, show the presence of systematic corrections in energy levels and transition frequencies. In particular, modifications in atomic spectral series are derived that preserve the known structure in asymptotic regimes but introduce controlled deviations at higher orders. Order-of-magnitude analysis and comparison with spectroscopic data indicate that the theory is compatible with current experimental results, while providing explicit criteria for falsification. An experimental protocol based on low-energy transitions is proposed to distinguish the predictions of Spectral Mechanics of Phase from those of quantum electrodynamics. The presented formulation reproduces the established results of quantum mechanics in its domain of validity, while introducing a more general spectral structure, derived directly from the action, without the need to postulate spectral linearity or operators as primitive entities.