We investigate the isomorphism between the formulations of quantum mechanics in a finite-dimensional complex Hilbert space and in a real Kähler space. This investigation establishes a direct correspondence between Hermitian operators in the complex Hilbert space and real operators in the Kähler space. In this real formulation, we note the emergent property of spectral degeneracy. Moreover, we show that the structure of the Kähler space provides a natural description of composite systems in real quantum mechanics.
We consider the kinetics of a linearly polarized, spatially homogeneous, quasiclassical electric field passing through graphene within the Narozhny–Nikishov model. We obtain optical coefficients (of absorption, reflection, and transmission) numerically and analytically as functions of the field amplitude and duration. We analyze the range of applicability of the Dirac approximation using a parameter θ , which represents the ratio of the quasielectron energy to the quantum energy of the external field. We numerically obtain the energy of quantum radiation produced by the electron-hole plasma.
We investigate the strong decays of the exotic charmonium-like Y(4230) state, recently reported by the BES III Collaboration, using the covariant confined quark model. The Y state is interpreted as a four-quark state with a molecular-type interpolating current. We evaluate the hidden-charm decay width of the Y state into a vector and a scalar, with the latter subsequently decaying into a pair of charged pseudoscalar mesons. The strong decay mode Y→π^+π^-J/ψ is studied by accounting for both the f_0(500) and f_0(980) scalar resonances (treated as quark-antiquark states), whereas the Y→ K^+K^-J/ψ mode is analyzed using the f_0(980) scalar resonance. The estimated branching ratio and calculated partial widths for the strong decay of the Y(4230) state are consistent with latest experimental data and can be verified in future measurements.
We study the eigenfunctions of the continuous spectrum of the Hamiltonian of a three-particle system with pairwise interactions. The eigenfunctions are considered as distributions over the angular variables of momentum. This is equivalent to considering linear combinations of solutions to the scattering problem for the Schrödinger equation on the eigensubspace. The key singularities of these distributions are studied in the momentum representation. In the coordinate representation, a uniform asymptotic behavior of these distributions is obtained.
We present and implement two approaches for including the strangeness potential in the holographic equation of state together with the baryon chemical potential. The first approach is based on the concept of a free quark gas, taking into account symmetry considerations, while the second is based on the thermodynamic properties of the hadron gas. The goal of this paper is to study the effect of strangeness on the evolution of quark–gluon plasma within the framework of hydrodynamic modeling of heavy-ion collisions. The parameters of the holographic model are calibrated to lattice quantum chromodynamics data with the physical masses of quarks using machine learning methods. The equation of state is integrated into the MUSIC and vHLLE packages, and multistage modeling of ion collisions is performed using the iEBE-MUSIC and SMASH-vHLLE frameworks. It is shown that the inclusion of strangeness based on the hadron gas leads to better agreement with the experimental spectra of K^+ mesons compared to the hypothesis of a quark gas, and the sensitivity to the choice of the hypothesis strongly depends on the hydrodynamic package used.
We study the general properties of static, spherically symmetric, charged topological geons supported by a self-gravitating, minimally coupled scalar field with negative kinetic energy and an arbitrary self-interaction potential. In the most general case, it turns out that the gravitational mass of such a geon is completely determined by its electric charge and size (for a given scalar field), that is, the size of the corresponding wormhole throat. We discuss the properties of the charged Ellis–Bronnikov–Sorkin geon and argue that it can be considered as a possible classical model of elementary particles beyond the Standard Model, in particular, as dark matter particles.
A mathematical model for the development of spherical perturbations in a cosmological medium of a scalar-charged fluid with a Higgs scalar field is investigated. The system of equations for the perturbations is decomposed into two independent subsystems. One of these, a system of ordinary differential equations, corresponds to the singular part of the perturbations and describes the evolution of the total mass and charge of a singular source, while the second—a system of partial differential equations with respect to the nonsingular parts of the perturbations—is analyzed. Exact solutions of the evolution equations for the total mass and charge near singular points of the background cosmological model are found. These solutions demonstrate the impossibility of a sufficiently rapid growth of the singular source mass at these points. Conversely, numerical integration of the evolution equations at nonsingular points of the cosmological model demonstrates the possibility of anomalously rapid growth of the singular mass (by a factor of 10^24 ) over times on the order of several hundred Planck times. The maximum rate of this process is achieved in models with small scalar particle charges g∼ 10^-5 and small values of the effective cosmological constant.
We compare the deviations of circular orbits in the nonrelativistic and relativistic cases. General solutions of the deviation equations are obtained. We find the potentials for the nonrelativistic case and the metric components in general relativity for which trajectories close to circular ones are closed curves. Explicit expressions for the pericenter shift of an orbit close to a circular one in a static spherically symmetric spacetime are obtained. Estimates of the cosmological constant effect on the orbit pericenter shift are given. Finally, we find the spherically symmetric metric in which the Shirokov effect is absent.
In the paper, graviton mass constraints are obtained by analyzing the trajectory of a bright star in the vicinity of the center of our Galaxy, using observations from the GRAVITY and Keck groups. Other astronomical ways to limit the graviton mass are briefly discussed.
The Euler–Maruyama approximation to the discrete-time Langevin equation with multiplicative noise is used to construct a functional representation for the generating functional of correlation and response functions. Closed loops of propagators are shown to be absent in the corresponding perturbation theory, which reproduces the results of averaging the iteration solution of the stochastic difference equation. The continuous-time generating functional is defined in terms of perturbation theory by the continuous-time limit of the ordinary integral sums of the Feynman diagrams of the discrete-time perturbation theory. Compensation terms needed to exclude graphs with self-contracted propagators due to the usual Feynman rules in the continuum case are described in terms of the normal-form representation of perturbative field theory. The generating functional for the Stratonovich interpretation is obtained as the white-noise limit of multiplicative Ornstein–Uhlenbeck process noise.
We consider a cosmological scenario in a Cuscuton theory with an additional scalar field consisting of the Genesis stage followed by the conventional expansion epoch. We discuss the physical scope of these multicomponent theories within early-time cosmology on general grounds and address the possible issues of stability at the perturbation level.
We construct renormalization group equations for the effective potential in the leading logarithmic approximation. These equations are valid for arbitrary SO(N) -symmetric scalar field theories, including nonrenormalizable ones, in four dimensions on a curved background with nonminimal coupling. The solutions to these equations represent the sum of leading logarithms in all orders of perturbation theory for two contributions to the effective potential: one that is linear in curvature and another that corresponds to the effective potential on a flat background. In the renormalizable case, the obtained equations reduce to the standard renormalization group equations. Finally, we consider possible cosmological applications of the solutions to the renormalization group equations.
Embedding theory is a possible modification of general relativity that provides a framework for explaining the observed effects typically attributed to dark matter. The idea of this modification is to consider our spacetime as a four-dimensional surface in a ten-dimensional flat ambient space. The equations of motion in embedding theory can be reformulated as a set of Einstein equations with the contribution of some additional fictitious matter and of equations describing this matter. We analyze static solutions of these equations, which are reduced to fictitious-matter configurations of the wall, string, and ball types. The string case is ultimately described by the Liouville equation, and the ball case is described by its three-dimensional analogue. For the string case, we show that as the density contribution decreases at infinity, all solutions to the Liouville equation are rotationally symmetric. For the case of the ball, we show that under the assumption of spherical symmetry, there exists a unique one-parameter family of solutions that are smooth at the center.
A systematic method is proposed for deriving hydrodynamic equations for microscopic quantum field models. All terms of the equations are constructed from composite operators based on the Schwinger equations and are subsequently transformed into closed form using functional integral techniques. This scheme is applied to derive an analog of the Navier–Stokes equation for a quantum Bose liquid. The critical dimensions of the shear and bulk viscosity coefficients near the λ point are presented.
Within the Symanzik approach, we consider a massless real scalar field in Euclidean spacetime in the presence of n planar δ -plates with an interaction potential V(z)=∑_i=1^n λ_iδ(z-z_i) . Using functional integration and the Sylvester identity, the interaction energy density (per unit area) can be reduced to the logarithm of the determinant of an n× n matrix. After subtracting the self-energy contribution, the geometry of the system allows the problem to be reduced to calculating the determinant of a tridiagonal matrix, which is evaluated using a recurrence relation. For a system of identical plates with equal separations, we obtain a closed expression in terms of Chebyshev polynomials. As an illustration of the efficiency of the method, an explicit form for n=20 is written out, and the limiting case of infinitely strong interaction ( λ→∞ ), which is associated with Dirichlet boundary conditions, is considered. In addition, we show that in the case where the number of plates n→∞ and the separation L→0 , at fixed thickness T=nL and with weak coupling constant λ , the system of δ -films approaches a finite-thickness slab. The results are verified for the particular cases n=2 and n=3 .
We consider four-dimensional 𝒩=4 , SU(N) super-Yang–Mills theory formulated in terms of 𝒩=1 superfields where the leading low-energy contributions to the effective action are given by the chiral effective potential. This effective potential is calculated in the one-loop and higher-loop approximations. We show that this potential is automatically finite and proportional to the classical chiral potential. All quantum corrections are found explicitly and factored into a coefficient of the classical potential.
Recently, a second Higgs-like boson h' with a mass near 0.5 TeV was predicted from a dual holographic model describing the hypothetical strongly coupled sector beyond the Standard Model. We analyze the conditions under which this prediction can be obtained within the framework of more traditional models for describing a strongly coupled field theory—the spectral sum rules and the Nambu–Jona-Lasinio model in the scalar channel. It is shown that the results of both approaches are close and lead to this prediction if their covariant four-momentum cutoff is identified with the unitarity bound on the Higgs boson mass, and also under the assumption that the strongly coupled sector beyond the Standard Model is described by some quantum field theory based on the SU(2) gauge group. We also present additional arguments suggesting that a mass of about 0.5 TeV would be natural for a heavy analogue of the Higgs boson, if it exists.
