Search Results (117)

We develop a unified Koopman–von Neumann (KvN) operator and Weyl–Wigner phase-space framework for inviscid ideal (barotropic) Euler flows. Our approach reformulates the nonlinear fluid dynamics as a linear KvN evolution on an enlarged field phase space, thereby enabling us to apply tools developed for quantum mechanics (Weyl quantization, Moyal ⋆-products, and Wigner functionals) to a classical fluid. We construct the appropriate KvN generator (including the required Jacobian term for unitarity) and derive the evolution equation for the corresponding Wigner functional. This framework clarifies when the classical Liouville (Vlasov) description is exact—namely, in quadratic or linear regimes where the Moyal bracket reduces to the Poisson bracket—and when higher-order quantum-like corrections become significant in fully nonlinear regimes. As an analytic example, we obtain a closed-form Wigner solution for a one-dimensional Burgers flow (pressureless Euler) and verify, term by term, that it reproduces the expected Liouville transport (with distributional contributions at the shock). We also compare the phase-space approach with a kinetic (Vlasov–monokinetic) formulation and outline the extension of the framework to three-dimensional flows using a Clebsch variable representation. Full article

The derivations presented in this paper suggest an intimate relationship between geometry and the electroweak sector at the Planck scale. A Lorentz-invariant maximally symmetric stochastically perturbed spacetime transformed to spherical coordinates reveals an emergent Schwarzschild metric, entirely a statistical structure of stochastic spacetime. Similarly, the transition from a maximally symmetric universe with a complex $SU\left(2\right)$ scalar doublet $\varphi$, comprising four independent real scalar fields with a zero vacuum expectation value (VEV), to spherical coordinates at the Planck scale reveals the spontaneously broken electroweak (EW) sector. Working in the unitarity gauge, the resulting EW potential can be simultaneously mapped in space at the Planck scale and across the EW sector. In space, the resulting EW potential includes a deep well within the Schwarzschild sphere and a shallow well just outside corresponding to an accretion disk. The same potential mapped in the EW space provides an entire family of possible sombrero hat potentials with fourth-order coupling specific to a point in space. At the minimum points of the potential in space, inside the Schwarzschild sphere and at the accretion disk, the $\lambda$ corresponding to the Standard Model (SM) fourth-order coupling is instead derived as $\frac{\lambda }{5}$. The factor of $\frac{1}{5}$ is a simple consequence of the conservation of the EW VEV and the fact that the SM formulation of the EW potential does not account for situations where the perturbations in $\varphi$ dominate. A more general formulation of the EW potential restores the SM quartic coupling and preserves $\lambda$ in space. An emergent Higgs field inside the Schwarzschild black hole is found to directly relate to the stochastic spacetime fields normalized by the Schwarzschild radius. The corresponding Higgs vacuum has both a ground and excited state and the possibility of both positive and negative vacuum entropy. Finally, the scalar-field VEV degeneracy in EW space of the metastable Higgs vacuum appears instead differentiated in space with possible probability, tunneling, and entropy implications. Full article

The string-inspired running vacuum model (StRVM) of inflation is based on a Chern–Simons (CS) gravity effective action in which the only four-spacetime-derivative-order term is a gravitational anomalous CS–Pontryagin density coupled to an axion. In this work, we revisit curvature-squared string-inspired effective actions from the point of view of appropriate local field redefinitions, leaving the perturbative string scattering matrices invariant. We require simultaneously unitarity and torsion interpretation of the field strength of the Kalb–Ramond antisymmetric tensor, features characterizing the (3+1)-dimensional StRVM cosmology. Unlike the higher-dimensional case, the above features are possible in the context of (3+1)-dimensional spacetimes, obtained after string compactification. We demonstrate that the unitarity and torsion interpretation requirements lead to a single type of extra four-derivative terms in the effective gravitational action, not discussed in the previous literature on StRVM, which is, however, shown to be subleading by many orders of magnitude compared to the terms of the StRVM framework. Hence, its presence has no practical implications for the relevant inflationary (and, hence, postinflationary) physics of the StRVM. This demonstrates the phenomenological completeness of the StRVM cosmological scenario, which is thus fully embeddable in the UV-complete (quantum gravity-compatible) string theory framework. Full article

The Stueckelberg wave equation is transformed into a quantum telegraph equation and a set of stationary states is obtained as unitary solutions. As it has been shown previously that this PDE relates to the Dirac operator, and on the other hand it is a linearized Hamilton–Jacobi–Bellman PDE, from which the Schrödinger equation can be deduced in a nonrelativistic limit, it is clear that it is the key equation in relativistic quantum mechanics. We give a Bayesian interpretation for the measurement problem. The stationary solution is understood as a maximum entropy prior distribution and measurement is understood as a Bayesian update. We discuss the interpretation of the single electron experiments in the light of finite speed propagation of the transition probability field and how it relates to the interpretation of quantum mechanics more broadly. Full article

We develop an informational extension of spacetime thermodynamics in which local entropy production is coupled to spacetime curvature within an effective covariant framework. Spacetime is modeled as a continuum limit of finite-capacity information registers, giving rise to a coarse-grained entropy field whose gradients define an informational flux. Within a nonminimally coupled scalar–tensor formulation, the resulting field equations imply that the local divergence of this flux is sourced by the Ricci scalar, establishing a direct relation between curvature and entropy production. The corresponding integral form links cumulative entropy generation to the integrated spacetime curvature over a causal region. In stationary limits, the framework reproduces the Bekenstein–Hawking entropy of horizons, while in homogeneous expanding cosmologies it yields monotonic entropy growth consistent with the observed arrow of time. The construction remains compatible with unitarity at the microscopic level and with holographic entropy bounds in the stationary limit. Numerical solutions in flat FLRW backgrounds are used as consistency checks of the coupled evolution equations and confirm the expected curvature–entropy behavior across cosmological epochs. Overall, the results provide a thermodynamically consistent interpretation of curvature as a geometric source of irreversible information flow, without modifying the underlying gravitational field equations. Full article

The asymptotic safety program assumes that quantum gravity becomes renormalizable through ultraviolet fixed points in metric-based couplings. We demonstrate that this approach encounters fundamental symmetry violations across multiple independent criteria, all traceable to a single fundamental cause: the breakdown of general covariance and BRST symmetries above the gravitational cutoff scale. Rigorous canonical quantization proves that general covariance cannot be maintained quantum mechanically in dimensions greater than two, while recent path integral calculations reveal persistent gauge parameter dependence in quantum gravitational corrections, signaling BRST symmetry violation. These dual proofs establish that the metric tensor ceases to exist as a valid quantum degree of freedom above ${\Lambda }_{\mathrm{grav}}$∼${10}^{18}$ GeV, rendering the search for ultraviolet fixed points in metric-based theories problematic from a foundational physical perspective. We provide comprehensive analysis demonstrating that asymptotic safety exhibits persistent gauge parameter dependence where fixed-point properties vary with arbitrary gauge choices, non-convergent truncation schemes extending to the 35th order showing no approach to stable values, experimental tensions with electroweak precision tests by orders of magnitude, matter content requirements incompatible with the Standard Model, absence of concrete graviton predictions due to gauge and truncation dependence, unitarity challenges through ghost instabilities and propagator negativity, and fundamental Wick rotation obstructions preventing reliable connection between Euclidean calculations and physical Lorentzian spacetime. Each limitation independently challenges the program; collectively they establish fundamental incompatibility with quantum consistency requirements. We contrast this with the Unified Standard Model with Emergent Gravity framework, which recognizes general relativity as an effective field theory valid only below the covariance breakdown scale, systematically avoids all asymptotic safety pathologies, yields an emergent spin-2 graviton with transverse-traceless polarization confirmed by LIGO-Virgo observations, and provides definite experimental signatures across multiple domains. The fundamental limitations of asymptotic safety, established through theoretical analysis and experimental tension, demonstrates that consistent quantum gravity requires recognizing spacetime geometry as emergent rather than fundamental. Full article

We study basis-independent structures in the Type-I seesaw mechanism for light Majorana neutrinos, assuming the canonical scenario with three heavy right-handed (sterile) neutrinos. Let $m_{\nu }$ denote the $3\times 3$ mass matrix of light neutrinos, obtained at tree level from heavy Majorana singlets with a diagonal mass matrix $D_N=\mathrm{diag}(M_1,M_2,M_3)$ and a Dirac matrix $m_D$. We show that all right actions F on the seesaw matrix that leave $m_{\nu }$ unchanged form the group $G=D_N^{1/2}O(3,\mathbb{C})D_N^{-1/2}$. While oscillation data determine the PMNS matrix $U_{\mathrm{PMNS}}$ and the mass-squared splittings, they do not fix the F-class within G. We classify basis-invariant quantities into those that are class-blind (e.g., $det \eta$) and class-sensitive (e.g., $\mathrm{Tr}\eta$, $\mathrm{Tr}{\eta }^2$, an alignment measure, and CP-odd traces relevant to leptogenesis), where $\eta$ denotes the non-unitarity matrix of the light sector. We provide explicit formulas and both high-scale and GeV-scale benchmark examples that illustrate these invariant fingerprints and their scaling with $D_N$. This converts the degeneracy at fixed $m_{\nu }$ into measurable, basis-invariant fingerprints. Full article

We revisit the constraint proposed by T. Appelquist, A. G. Cohen, and M. Schmaltz (ACS) on asymptotically free field theories, which relates the number of infrared (IR) degrees of freedom to those in the ultraviolet (UV). The original ACS analysis examined several examples—both supersymmetric and non-supersymmetric—and identified only one interacting IR fixed point with a superpotential: Seiberg dual of an $SU\left(N_c\right)$ gauge theory. Here, we extend their analysis to $SO\left(N_c\right)$ and $Sp\left(2N_c\right)$ gauge groups near Banks–Zaks fixed points. We further test the ACS inequality in theories featuring conjectured accidental IR symmetries and nontrivial superpotential deformations. Beginning with ADE-type deformations, we then investigate three chiral theories by estimating decoupled chiral-ring invariants using a-maximization and unitarity bounds. In all cases, we find no violation of the ACS conjecture. Full article

We present a comprehensive quantum field theoretical analysis of graviton self-energy and mass generation in 3+1 dimensional BTZ black hole spacetime, incorporating axion interactions within the framework of dark matter theory. Using a novel mathematical approach based on ultrahyperfunctions, generalizations of Schwartz tempered distributions to the complex plane, we derive exact quantum relativistic expressions for graviton and axion self-energies without requiring ad hoc regularization procedures. Our approach extends the Gupta–Feynman quantization framework to BTZ gravity while introducing a new constraint that eliminates unitarity violations inherent in previous formulations, thereby avoiding the need for ghost fields. Through systematic application of generalized Feynman parameters, we evaluate both bradyonic and tachyonic graviton modes, revealing distinct quantum correction patterns that depend critically on momentum, energy, and mass parameters. Key findings include (1) natural graviton mass generation through cosmological constant interactions, yielding $m^2=2\left|\mathsf{\Lambda }\right|/\kappa (1-\kappa )$; (2) qualitatively different quantum behaviors between bradyonic and tachyonic modes, with bradyonic corrections reaching amplitudes 6 times larger than their tachyonic counterparts; (3) the discovery of momentum-dependent quantum dissipation effects that provide natural ultraviolet regulation; and (4) the first explicit analytical expressions and graphical representations for 17 distinct graviton self-energy contributions. The ultrahyperfunction formalism proves essential for handling the non-renormalizable nature of the theory, providing mathematically rigorous treatment of highly singular integrals while maintaining Lorentz invariance. Our results suggest observable consequences in gravitational wave propagation through frequency-dependent dispersive effects and modifications to black hole thermodynamics, potentially bridging theoretical quantum gravity with experimental constraints. Full article

In this paper, we investigate the memory effects introduced by the time-fractional Schrödinger equation proposed by Naber on quantum entanglement and quantum dense coding under amplitude damping noise. Two formulations are analyzed: one with fractional operations applied to the imaginary unit and one without. Numerical results show that the formulation without fractional operations on the imaginary unit may be more suitable for describing non-Markovian (power-law) behavior in dissipative environments. This finding provides a more physically meaningful interpretation of the memory effects in time-fractional quantum dynamics and indirectly addresses fundamental concerns regarding the violation of unitarity and probability conservation in such frameworks. Our work offers a new perspective for the application of fractional quantum mechanics to realistic open quantum systems and shows promise in supporting the theoretical modeling of decoherence and information degradation. Full article

We present an analytic continuation of the central charge c in two-dimensional conformal field theory (2D CFT), modeled as a Nevanlinna function—an analytic map from the upper half-plane to itself. Motivated by the structure of vacuum energies arising from the quantization of spin-j conformal fields on the circle, we derive a discrete spectrum of central charges $c\left(j\right)=1+6j(j+1)$ and extend it continuously via $c\left(z\right)=1+6z$. The Möbius-inverted form $f\left(z\right)=1-6/z$ satisfies the conditions of a Nevanlinna function, providing a physically consistent analytic structure that captures both the unitarity of minimal models ($c<1$) and the continuous spectrum for $c\ge 1$. This unified framework highlights the connection between spectral theory, analyticity, and conformal symmetry in quantum field theory. Full article

Longstanding anomalies in the Cosmic Microwave Background (CMB), including the low quadrupole moment and hemispherical power asymmetry, have recently been linked to an underlying parity asymmetry. We show here how this parity asymmetry naturally arises within a quantum framework that explicitly incorporates the construction of a geometric quantum vacuum based on parity ($\mathcal{P}$) and time-reversal ($\mathcal{T}$) transformations. This framework restores unitarity in quantum field theory in curved spacetime (QFTCS). When applied to inflationary quantum fluctuations, this unitary QFTCS formalism predicts parity asymmetry as a natural consequence of cosmic expansion, which inherently breaks time-reversal symmetry. Observational data strongly favor this unitary QFTCS approach, with a Bayes factor, the ratio of marginal likelihoods associated with the model given the data $p\left(M|D\right)$, exceeding 650 times that of predictions from the standard inflationary framework. This Bayesian approach contrasts with the standard practice in the CMB community, which evaluates $p\left(D|M\right)$, the likelihood of the data under the model, which undermines the importance of low-ℓ physics. Our results, for the first time, provide compelling evidence for the quantum gravitational origins of CMB parity asymmetry on large scales. Full article

We pose and address the radical question of whether quantum mechanics, known for its firm internal structure and enormous empirical success, carries in itself the genomes of larger quantum theories that have higher internal intricacy and phenomenological versatility. In other words, we consider, at the basic level of closed quantum systems and regardless of interpretational aspects, whether standard quantum theory (SQT) harbors quantum theories with context-based deformed principles or structures, having definite predictive power within much broader scopes. We answer this question in the affirmative following complementary evidence and reasoning arising from quantum-computation-based quantum simulation and fundamental, general, and abstract rationales within the frameworks of information theory, fundamental or functional emergence, and participatory agency. In this light, as we show, one is led to the recently proposed experience-centric quantum theory (ECQT), which is a larger and richer theory of quantum behaviors with drastically generalized quantum dynamics. ECQT allows the quantum information of the closed quantum system’s developed state history to continually contribute to defining and updating the many-body interactions, the Hamiltonians, and even the internal elements and “particles” of the total system. Hence, the unitary evolutions are continually impacted and become guidable by the agent system’s experience. The intrinsic interplay of unitarity and non-Markovianity in ECQT brings about a host of diverse behavioral phases, which concurrently infuse closed and open quantum system characteristics, and it even surpasses the theory of open systems in SQT. From a broader perspective, a focus of our investigation is the existence of the quantum interactome—the interactive landscape of all coexisting, independent, context-based quantum theories that emerge from inferential participatory agencies—and its predictive phenomenological utility. Full article

Recent work has demonstrated a correspondence that bridges quantum information processing and high-energy physics: discrete quantum cellular automata (QCA) can, in the continuum limit, reproduce quantum field theories (QFTs). This QCA/QFT correspondence raises fundamental questions about how matter/energy, information, and the nature of spacetime are related. Here, we show that free QED is equivalent to the continuous-space-and-time limit of Fermi and Bose QCA theories on the cubic lattice derived from quantum random walks satisfying simple symmetry and unitarity conditions. In doing so, we define the Fermi and Bose theories in a unified manner using the usual fermion internal space and a boson internal space that is six-dimensional. We show that the reduction to a two-dimensional boson internal space (two helicity states arising from spin-1 plus the photon transversality condition) comes from restricting the QCA theory to positive energies. We briefly examine common symmetries of QCAs and how time-reversal symmetry demands the existence of negative-energy solutions. These solutions produce a tension in coupling the Fermi and Bose theories, in which the strong locality of QCAs seems to require a non-zero amplitude to produce negative-energy states, leading to an unphysical cascade of negative-energy particles. However, we show in a 1D model that, by extending interactions over a larger (but finite) range, it is possible to exponentially suppress the production of negative-energy particles to the point where they can be neglected. Full article

In a number of previous publications, scattering theory for N-pole semiconductor quantum devices was developed. In the framework of the Landauer–Büttiker formalism, an S-matrix was constructed with the aid of an R-matrix providing a mapping of the in-going waves onto the out-going waves. These waves include propagating waves and evanescent waves, the latter of which decay exponentially in the leads which are connected to the active region of the N-pole device. In order to formulate the current conservation in the N-pole device, it is necessary to define the current S-matrix schematically as $\tilde{S}=k^{1/2}S{k}^{-1/2}$, where k contains the information about the k-vectors of the mentioned in- and out-going waves. In this paper, we show how the complete current S-matrix is calculated including the coupling between the propagating and evanescent components and coupling to the bound states in the active device region. One then finds a sub-matrix of $\tilde{S}$ which is unitary and which is restricted to the space of the propagating components. We demonstrate that current conservation is associated with the unitarity just of this sub-matrix. Full article