arXiv subjects

Tomohiro Inagaki

Publications and source records attributed to Tomohiro Inagaki.

At least 19 recordsLinked to original sources

arXiv2026

Instability diagram of the massive gauge quantum fields around the nonlinear massive classical wave solution

The stability and instability in the time dynamics of quantum fluctuation of the massive gauge field coupling to the nonlinear massive wave solution is studied. In particular, the instability in the transverse polarization and longitudinal polarization modes are obtained as the two dimensional plot of the initial field value parameter and the spatial momentum of the quantum massive gauge fields with the help of the theory of the Hill's equation. We present the formalism to analyze the massive gauge field by taking into account Proca constraint and we found that our formalism can predict the time dynamics of the unstable quantum mode by the Floquet index. The resulting polarization-resolved Floquet maps show that the transverse modes possess only narrow parametric-resonance bands, whereas the longitudinal modes exhibit substantially broader regions generated by both parametric and spinodal instabilities. We also find additional low-momentum instability regions for the $W$ boson that are absent or strongly suppressed in the $Z$ sector.

hep-ph↗

arXiv2026

Localized scalar modes of $O(3)$ critical bubbles: partial-wave continuum mergers and wave-function deformation

At phase coexistence, a degenerate quartic scalar potential admits an exact planar kink whose normal fluctuation operator is the modified P\"oschl--Teller operator, with translational and positive shape states below a continuum beginning at $\Lambda=4$. We continue the two connected spectral bands through finite supercooling in a smooth one-component quartic benchmark and resolve $\ell=0,1,2$. The $O(3)$ bounce is obtained by singular collocation, while the radial Euclidean Hessian is analyzed by finite-difference diagonalization and independent threshold shooting. The positive $\ell=2$ and $\ell=1$ branches reach the common false-vacuum continuum threshold at $\delta_{{\rm merge},2}=0.0900472$ and $\delta_{{\rm merge},1}=0.1410162$, respectively. At each endpoint, $u_\ell\propto\rho^{-\ell}$ is square integrable and defines a threshold eigenstate; beyond the endpoint, however, no normalizable eigenstate continuation exists for the corresponding branch. The $\ell=0$ shape state remains bound up to the geometric wall crossover. Its planar-mode overlap, radial centroid, and distinct interior and exterior decay lengths reveal asymmetric wave-function deformation. Thus, angular spectral dissolution and the later geometric loss of a true-vacuum-like core are separate phenomena, revealing two distinct finite-supercooling fates of the planar shape mode.

hep-ph↗

arXiv2025

Instability of quantum fluctuation around classical nonlinear massive wave solution in Higgs potential and particle creations

We discuss the dynamics of the quantum fluctuation around the nonlinear massive wave solution in the Higgs potential. In particular, we analyze the stability and instability of the mode function. Using the stability condition for Hill's equation, we obtain the instability region of the mode function in the quantum fluctuation as the function of the parameters in the mode equation. We show that the two types of the instabilities of the system in the particle number can be understood by the Floquet's exponents in the instability parameter region. The analysis will be useful to understand the dynamics of the quantum field theory around the nonlinear massive wave solution when the classical background slightly deviates from the constant background during the middle stage of the phase transition.

hep-ph↗

arXiv2025

Classification of $T^2/Z_m$ orbifold boundary conditions in $SO(N)$ gauge theories

We generally classify the equivalence classes of the $T^2/Z_m$ $(m=2,3,4,6)$ orbifold boundary conditions (BCs) for the $SO(N)$ gauge group. Higher-dimensional gauge theories are defined by gauge groups, matter field contents, and the BCs. The numerous patterns of the BCs are classified into the finite equivalence classes, each of which consists of the physically equivalent BCs. In this paper, we reconstruct the canonical forms of the BCs for the $SO(N)$ gauge group through the ``re-orthogonalization method." All the possible equivalent relations between the canonical forms are examined by using the trace conservation laws. The number of the equivalence classes in each orbifold model is obtained.

hep-th↗

arXiv2025

Exploring the universal $\bar{\mathcal{I}}-\mathcal{C}$ relations for relativistic stars in $f(Q)$ gravity

We investigate the properties of neutron stars within the framework of $f(Q)$ gravity by incorporating rotational effects through a slowly rotating metric. We derive the modified TOV equations and calculate the angular velocity profiles and moments of inertia (MOI) for linear, quadratic, exponential, and logarithmic $f(Q)$ models. Our results show that deviations in the MOI are more pronounced than those in the stellar mass profiles, suggesting that rotational observables are highly sensitive to geometric corrections. We also calculate a quasi-universal relation between the dimensionless MOI and compactness ($\bar{I}$-$C$). The linear and quadratic models are generally consistent with observational data from PSR J0737-3039A, although the deviations are small and difficult to distinguish from General Relativity due to inherent EoS variability. On other hand, the logarithmic and exponential models show larger deviations (over 20 %), exceeding the EoS-induced uncertainty reported by Suleiman & Read (2024), highlighting the relation's sensitivity to the $f(Q)$ gravity model. These results indicate that $f(Q)$ gravity could potentially be tested in the strong-field regime and point to a direction for future studies, such as investigating EoS-insensitive quasi-universal relations, like the $\bar{I}(\Lambda)$ relations, within the $f(Q)$ framework. Such relations may provide a clearer pathway for exploring possible signatures in strong-field gravity when combined with more precise future observations.

gr-qc↗

arXiv2024

Non-thermal particle production in Einstein-Cartan gravity with modified Holst term and non-minimal couplings

Non-thermal fermionic particle production is investigated in Einstein-Cartan modified gravity with a modified Holst term and non-minimal couplings between the spin connection and a fermion. By using the auxiliary field method, the theory is rewritten into a pseudoscalar-tensor theory with Einstein-Hilbert action and canonical kinetic and potential terms for a pseudoscalar field. The introduced field is called Einstein-Cartan pseudoscalaron. If the potential energy of the Einstein-Cartan pseudoscalaron dominates the energy density of the early universe, it causes inflationary expansion. After the end of inflation, the pseudoscalaron develops a large value and the non-minimal couplings destabilize the vacuum. Evaluating the non-thermal fermionic particle production process, we obtain the mass and the helicity dependences of the produced particle number density. We show the model parameters to enhance the preheating and reheating processes.

gr-qc↗

arXiv2024

Neutron Star in Covariant $f(Q)$ gravity

Assuming static and spherically symmetric stars with perfect fluid matter, we used realistic equations of state to study neutron stars in covariant $f(Q)$ gravity. The structure profiles and properties of neutron stars such as mass, radius and compactness are obtained through numerical methods using quadratic, exponential, and logarithmic $f(Q)$ models. The results indicate that nonmetricity affects the interior profile deviations of the star, which in turn influence the properties of stars, as illustrated in the mass-radius relation diagram. This effect allows the star to accommodate either more or less matter compared to GR, resulting in a different total mass. For the quadratic model, we cannot generate larger masses, whereas the other two models can give consistent results for both smaller and larger masses of the observed stars. By tuning model parameters, we obtain $\mathcal{M}-\mathcal{R}$ diagrams that are compatible with observational constraints from NICER and LIGO.

gr-qc↗

arXiv2024

Trace conservation laws in $T^2/Z_m$ orbifold gauge theories

Gauge theory compactified on an orbifold is defined by gauge symmetry, matter contents, and boundary conditions. There are equivalence classes (ECs), each of which consists of physically equivalent boundary conditions. We propose the powerful necessary conditions, trace conservation laws (TCLs), which achieve a sufficient classification of ECs in U(N) and SU(N) gauge theories on $T^2/Z_m$ orbifolds $(m=2,3,4,6)$. The TCLs yield the equivalent relations between the diagonal boundary conditions without relying on an explicit form of gauge transformations. The TCLs also show the existence of off-diagonal ECs, which consist only of off-diagonal matrices, on $T^2/Z_4$ and $T^2/Z_6$. After the sufficient classification, the exact numbers of ECs are obtained.

hep-th↗

arXiv2024

Mass generation via nonlinear massive solution in Higgs potential and particle creations

The nonlinear massive plane wave solution of the classical scalar field in the Higgs potential is revisited to study the mass generation and particle creation. In particular, by assuming that the Higgs system is in the slightly excited state in early universe and it is described by the nonlinear solution, we study the mass generation mechanism for massive vector bosons and a heavy fermion in the quantum field theory around the nonlinear massive classical field. The nonlinear massive classical solution gives the transition from the vacuum to a pair of vector bosons and fermions. We present the new formulae of the probability density of the production process for particles in the standard model of elementary particle physics. The probability densities of the particle productions vanish when the nonlinear massive solution reduces to the constant solution (the classical vacuum expectation value); while the probability densities are expressed as the function of the free parameter in the classical solution in general case. We discuss the behavior of the probability densities for the three oscillating modes in the classical solution.

hep-ph↗

arXiv2024

Approach to the arbitrariness problem of boundary conditions in $S^1/Z_2$ brane-world models

We study the arbitrariness of boundary conditions (BCs) on $S^1/Z_2$ brane-world models with the gauge group $U(N)$. The BCs are chosen independently on the branes and the bulk in this model. There are numerous choices for BCs in general, but some of the BCs are connected through gauge transformations. We show that the equivalent relations are obtained on the UV-brane without relying on specific transformation parameters. There is no other equivalent relation on the UV-brane. On the other hand, we find that a gauge transformation with a kink connects all the BCs on the bulk and IR-brane. It means that the arbitrariness of BCs is completely solved on the bulk and the IR-brane except for the UV-brane.

hep-th↗

arXiv2024

New classification method for Equivalence Classes on $S^1/Z_2$ and $T^2/Z_3$ Orbifolds

In five- and six-dimensional $U(N)$ and $SU(N)$ gauge theories compactified on $S^1/Z_2$ and $T^2/Z_3$ orbifolds, we propose a new method to classify the equivalence classes (ECs) of boundary conditions (BCs) wihtout depending on the structure of gauge transformations. Some of the BCs are connected through gauge transformations and constitute ECs, each of which contains physically equivalent BCs. Previous methods for classifying ECs have been used specific gauge transformations. In this paper, we show that a geometric property of orbifolds significantly narrows down the possibilities of connecting BCs and completes the classification of ECs.

hep-th↗

arXiv2023

Quintessential Inflation in Logarithmic Cartan $F(R)$ Gravity

We investigate the quintessential inflation in the logarithmic Cartan $F(R)$ gravity. A small logarithmic modification of the general relativity has the potential to introduce both inflation and dark energy. We evaluate the time evolution of the Universe such as inflation, reheating, and dark energy. The parameters in the model are fixed to introduce the inflation and the dark energy scales. We show that the CMB fluctuations induced by the inflation are consistent with the current observations. In the reheating process, it is possible to achieve the reheating temperature required for nucleosynthesis in Big Bang scenario. It can be seen that by choosing an appropriate value for the scalaron field after reheating, the scalaron field again dominates the energy of the Universe and causes the current accelerating expansion as dark energy.

hep-th↗

arXiv2023

Robustness of predicted CMB fluctuations in Cartan $F(R)$ gravity

The cosmology of the $F(R)$ gravity rebuilding by the Cartan formalism is investigated. This is called Cartan $F(R)$ gravity. The well-known $F(R)$ gravity has been introduced to extend the standard cosmology, e.g. to explain the cosmological accelerated expansion as the inflation. Cartan $F(R)$ gravity is based on the Riemann-Cartan geometry. The curvature $R$ can separate to two parts, one is derived from the Levi-Civita connection and the other from the torsion. Assuming the matter-independent spin connection, we have successfully rewritten the action of Cartan $F(R)$ gravity into the Einstein-Hilbert action and a scalar field with canonical kinetic and potential terms without any conformal transformations. This feature simplifies building and analysis of new model of inflation. In this paper, we study two models, the power-law model and logarithmic model, and evaluate fluctuations in the cosmological microwave background (CMB) radiation. We found the robustness of CMB fluctuation by the analytical computation and confirm this feature by the numerical calculation.

gr-qc↗

arXiv2023

Super Restoration of Chiral Symmetry in Massive Four-Fermion Interaction Models

The chiral symmetry is explicitly and spontaneously broken in a strongly interacting massive fermionic system. We study the chiral symmetry restoration in massive four-fermion interaction models with increasing temperature and chemical potential. At high temperature and large chemical potential, we find the boundaries where the spontaneously broken chiral symmetry can be fully restored in the massive Gross--Neveu model. We call the phenomenon super restoration. The phase boundary is obtained analytically and numerically. In the massive Nambu--Jona-Lasinio model, it was found that whether super restoration occurs depends on regularizations. We also evaluate the behavior of the dynamical mass and show the super restoration boundaries on the ordinary phase diagrams.

hep-ph↗

arXiv2023

Scalar Mode Quadrupole Radiation from Astronomical Sources in $F(R)$ Modified Gravity

We investigate the scalar mode quadrupole radiation of gravitational waves in $F(R)$ modified gravity. In $F(R)$ gravity a massive scalar mode appears in the gravitational waves. We find explicit expressions for the quadrupole radiation and the energy current of the scalar mode in general $F(R)$ gravity models. We consider a binary star and a bouncing star as astronomical sources of the gravitational waves and calculate the quadrupole radiation of the scalar and tensor modes. The scalar mode radiates under spherically symmetric conditions, but the tensor modes do not. The scalar mode mass is estimated for some typical energy scales. We show a possibility to detect the scalar mode in the future gravitational waves observation.

gr-qc↗

arXiv2022

Cartan $F(R)$ Gravity and Equivalent Scalar-Tensor Theory

We investigate the Cartan formalism in $F(R)$ gravity. $F(R)$ gravity has been introduced as a theory to explain cosmological accelerated expansion by replacing the Ricci scalar $R$ in the Einstein-Hilbert action with a function of $R$. As is well-known, $F(R)$ gravity is rewritten as a scalar-tensor theory by using the conformal transformation. Cartan $F(R)$ gravity is described based on the Riemann-Cartan geometry formulated by the vierbein. In the Cartan formalism, the Ricci scalar $R$ is divided into two parts, one derived from the Levi-Civita connection and the other from the torsion. Assuming the spin connection independent matter action, we have successfully rewritten the action of Cartan $F(R)$ gravity into the Einstein-Hilbert action and a scalar field with canonical kinetic and potential terms without any conformal transformations. The resulting scalar-tensor theory is useful in applying the usual slow-roll scenario. As a simple case, we employ the Starobinsky model and evaluate fluctuations in the cosmological microwave background radiation.

gr-qc↗

arXiv2022

Elliptically oscillating solutions in Abelian-Higgs model and electromagnetic property

The elliptically oscillating solutions in the Abelian Higgs-model are presented and the classical massive-dispersion-relation through the non-linear dynamics is discussed. The generated massive-dispersion-relation including a field value of the scalar field is derived as the consequence of the equation of motions. We discuss the property of the new solutions and its Hamiltonian density. In addition, we calculate the electromagnetic property of the system, in particular, we derive the relation between the field value and the electric field and the electric current-density.

hep-ph↗

arXiv2022

Precise Phase Structure in Four-fermion Interaction Model on Torus

We investigate finite-size effects on chiral symmetry breaking in a four-fermion interaction model at a finite temperature and a chemical potential. Applying the imaginary time formalism, the thermal quantum field theory is constructed on an $S^1$ in the imaginary time direction. In this paper, the finite-size effect is introduced by a compact $S^1$ spatial direction with a $\mathrm{U}(1)$-valued boundary condition. Thus, we study the model on a $\mathbb{R}^{D-2} \times S^1 \times S^1$ torus. Phase diagrams are obtained by evaluating the local minima of the effective potential in the leading order of the $1/N$ expansion. From the grand potential, we calculate the particle number density and the pressure, then we illustrate the correspondence with the phase structure. We obtain a stable size for which the sign of the pressure flips from negative to positive as the size decreases. Furthermore, the finite chemical potential expands the parameter range that the stable size exists.

hep-ph↗