Theoretical and Mathematical Physics最新文献

In this work, we employ a field-theoretic renormalization group approach to study a paradigmatic model of directed percolation. We focus on the perturbative calculation of the equation of state, extending the analysis to three-loop order in the expansion parameter (varepsilon=4-d). We show that a large group of the necessary three-loop Feynman diagrams can be mapped onto already existing three-loop results and develop a technique to calculate the remaining—truly novel—ones. The described semianalytic procedure is further used to verify existing two-loop results. The main aim of this study is to provide an update on this ongoing work, as full three-loop calculations utilizing the described procedure are in progress.

We consider four-dimensional (mathcal{N}=4), (SU(N)) super-Yang–Mills theory formulated in terms of (mathcal{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.

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.

Following a nonperturbative formulation of strong-field QED developed in our earlier works, we consider photon emission accompanying vacuum instability under the action of a quasi-constant strong electric field of finite duration (T). We construct closed formulas for the total probabilities and study the photon emission accompanying electron–positron pair creation from the vacuum. We establish the domain of applicability of the locally constant field approximation (LCFA) for the photon emission. We study angular and polarization distribution of the emission as well as emission characteristics in a high-frequency approximation with respect of (1/T). The results presented in this work are suitable to a further development of the LCFA proposed in [Phys. Rev. D 95, 076013 (2017)].

This paper investigates stochastic solenoidal magnetohydrodynamics within the field-theoretic Martin–Siggia–Rose–Janssen–De Dominicis formalism, with a specific focus on the stability of the system when spatial mirror (parity) symmetry is explicitly broken. Under helical forcing, the one-particle-irreducible magnetic response function already at one-loop order contains a curl-type contribution that dominates the bare resistive term in the infrared limit, leading to exponential instability of the trivial state (langle boldsymbol brangle= boldsymbol 0). We re-examine a stabilization mechanism proposed by L. T. Adzhemyan et al. in [Theor. Math. Phys. 72, 940–950 (1987)], in which the system evolves into a phase with dynamically induced spontaneously broken rotational symmetry and a generated mean magnetic field (langle boldsymbol brangle= boldsymbol B_0). By deriving a self-consistency condition for ( boldsymbol B_0), we show that for any physically admissible (infrared) form of the pumping function, the model admits only a singular solution. We illustrate this with the standard power-law and “massive” pumping functions. We further show that previous claims of a finite ( boldsymbol B_0) arose from an inconsistent truncation of asymptotic expansions. We argue that a consistent physical resolution requires the inclusion of a bare curl term in the stochastic induction equation, which naturally arises from a parity-violating modification of Ohm’s law. With this modification, stabilization of the system by spontaneous symmetry breaking becomes a viable field-theoretic description of large-scale mean-field generation (turbulent dynamo) in helical turbulent magnetohydrodynamics.

Within the Symanzik approach, we consider a massless real scalar field in Euclidean spacetime in the presence of (n) planar (delta)-plates with an interaction potential (V(z)=sum_{i=1}^n lambda_idelta(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 (ntimes 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 ((lambdatoinfty)), which is associated with Dirichlet boundary conditions, is considered. In addition, we show that in the case where the number of plates (ntoinfty) and the separation (Lto0), at fixed thickness (T=nL) and with weak coupling constant (lambda), the system of (delta)-films approaches a finite-thickness slab. The results are verified for the particular cases (n=2) and (n=3).

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.

A homogeneous polynomial (S(x_1, ldots, x_n)) of degree (r) in (n) variables possesses a discriminant (D_{n|r}(S)), which vanishes if and only if the system of equations (partial S / partial x_i = 0) has nontrivial solutions. We provide an explicit formula for the discriminants of symmetric (under permutations of (x_1, ldots, x_n)) homogeneous polynomials of degree (r) in (n geq r) variables. This formula is highly effective from a computational perspective: symbolic computer calculations using this formula take seconds even for (n approx 20). We work out the cases (r = 2), (3), and (4) in detail. We also consider the case of completely antisymmetric polynomials.

We develop a unified, field-theoretic framework for coherent dynamics in the near-horizon environment of rotating (Kerr) black holes that bridges general-relativistic geometry, nonequilibrium phase transitions, and multimessenger diagnostics. Starting from a covariant effective action with a Landau–Ginzburg potential for a complex order parameter (A) coupled to a slow reservoir (X) (curvature/density proxy), we identify a critical ridge (X_{mathrm c}) that organizes metastability and defines the natural control parameter (varepsilon=X-X_{mathrm c}). Linearization in a corotating Kerr patch yields a dispersion relation in which Doppler shifting and Lense–Thirring precession enter explicitly, while coupling to (X) reshapes the unstable band and links superradiant/corotation amplification to pattern-forming thresholds. Near onset, a multiple-scale reduction leads to a complex Ginzburg–Landau (TDGL/CGL) envelope governing nonlinear self-organization. The resulting states exhibit quantized defects and rotating spiral morphologies whose core precession and arm-pass motion set a pattern clock. Energy and angular momentum cycle quasi-periodically between (A) and (X), producing windowed anti-correlations with an entropy-like coherence measure and establishing scale links via core radius and interface width. GW-like and EM-like proxies display a common dominant peak with sidebands and finite coherence, with frequencies and bandwidths that track the Kerr spin (a_ast) and the unified coupling strength. Together, these results provide a minimal, predictive backbone for interpreting horizon-scale morphology, energy transport, and partially coherent GW/EM spectra around rotating black holes.