Narrow Results

Does massless (λΦ⁴)₄ theory exhibit spontaneous symmetry breaking (SSB)? The raw one-loop result implies that it does, but the "RG-improved" result implies the opposite. We argue that the appropriate "low-energy effective theory" is a nonlocal field theory involving an attractive, long-range interaction Φ²(x)Φ²(y)/|x-y|⁴. RG improvement then requires running couplings for both this interaction and the original pointlike interaction. A crude calculation in this framework yields SSB even after "RG improvement" and closely agrees with the raw one-loop result.

We compute the cosmological constant in a scale invariant scalar field theory. The gravitational action is also suitably modified to respect scale invariance. Due to scale invariance, the theory does not admit a cosmological constant term. The scale invariance is broken by a recently introduced mechanism called cosmological symmetry breaking. This leads to a nonzero cosmological constant. We compute the one-loop corrections to the cosmological constant and show that it is finite.

We analyze a recent proposal to map a massless scalar field theory onto a Yang–Mills theory at classical level. It is seen that this mapping exists at a perturbative level when the expansion is a gradient expansion. In this limit the theories share the spectrum, at the leading order, that is the one of a harmonic oscillator. Gradient expansion is exploited maintaining Lorentz covariance by introducing a fifth coordinate and turning the theory to Euclidean space. These expansions give common solutions to scalar and Yang–Mills field equations that are so proved to exist by construction, confirming that the selected components of the Yang–Mills field are indeed an extremum of the corresponding action functional.

In this work, using a different theoretical approach, we study a homogeneous and isotropic cosmological spacetime filled with a perfect fluid. Using the framework of Brans–Dicke (BD) and Gauss–Bonnet (GB) theories and including a scalar potential, we obtain the analytical solution of the field equations and find the field functions and the relevant expansion parameter of the spacetime. We assume that the BD and GB media can interact with each other, and hence that there is an energy transfer between these two components. Using this approach, we assume that the BD scalar field is related to intrinsic properties of the GB medium. We introduced a power-law scalar field $\varphi (t)={\varphi }_0{t}^p$ and found the appropriate dynamical functions for the different powers p. We found that the expansion rate of spacetime also behaves as a power-law, and the accelerating expansion is always satisfied for this model. We also analyze the stability for physically acceptable critical points for a given scale factor.

We prove the existence of a strong coupling expansion for a classical λϕ⁴ field theory in agreement with the duality principle in perturbation theory put forward in a paper: M. Frasca, Phys. Rev. A58, 3439 (1998). The leading order solution is a snoidal wave taking the place of plane waves of the free theory. We compute the first-order correction and show that higher-order terms do renormalize the leading order solution.

We show that a recent analysis in the strong coupling limit of the λϕ⁴ theory proves that this theory is indeed trivial giving in this limit the expansion of a free quantum field theory. We can get in this way the propagator with the renormalization constant and the renormalized mass. As expected the theory in this limit has the same spectrum as a harmonic oscillator. Some comments about triviality of the Yang–Mills theory in the infrared are also given.

We derive the spectrum in the broken phase of a λϕ⁴ theory, in the limit λ→∞, showing that this goes as even integers of a renormalized mass in agreement with recent lattice computations.

We consider the simplest example of a nonstationary quantum system which is quantum mechanical oscillator with varying frequency and $\lambda {\varphi }^4$ self-interaction. We calculate loop corrections to the Keldysh, retarded/advanced propagators and vertices using Schwinger–Keldysh diagrammatic technique and show that there is no physical secular growth of the loop corrections in the cases of constant and adiabatically varying frequency. This fact corresponds to the well-known adiabatic theorem in quantum mechanics. However, in the case of nonadiabatically varying frequency we obtain strong IR corrections to the Keldysh propagator which come from the “sunset” diagrams, grow with time indefinitely and indicate energy pumping into the system. It reveals itself via the change in time of the level population and of the anomalous quantum average.

The exact renormalization group (ERG) is formulated implementing the decimation of degrees of freedom by means of a particular momentum integration measure. The definition of this measure involves a distribution that links this decimation process with the dimensional regularization technique employed in field theory calculations. Taking the dimension $d=4-ϵ$, the one-loop solutions to the ERG equations for the scalar field theory in this scheme are shown to coincide with the dimensionally regularized perturbative field theory calculation in the limit $ϵ\to 0^{-}$, if a particular relation between the scale parameter $\mu$ and $ϵ$ is employed. In general, it is shown that in this scheme the solutions to the ERG equations for the proper functions coincide when $ϵ\to 0^{-}$ with the complete diagrammatic contributions appearing in field theory for these functions and this theory, provided that exact relations between $\mu$ and $ϵ$ hold. In addition, a nonperturbative approximation is considered. This approximation consists in a truncation of the ERG equations, which by means of a low-momentum expansion leads to reasonable results.

We examine the recently introduced idea of Spin-Field Correspondence (SFC) focusing on the example of the spin system described by the XXZ Heisenberg model with external magnetic field. The Hamiltonian of the resulting nonlinear scalar field theory is derived for arbitrary value of the anisotropy parameter $\mathrm{\Delta }$. We show that the linear scalar field theory is reconstructed in the large spin limit. For $\mathrm{\Delta }=1$, a nonrelativistic scalar field theory satisfying the Born reciprocity principle is recovered. As expected, for the vanishing anisotropy parameter $\mathrm{\Delta }\to 0$, the standard relativistic Klein–Gordon field is obtained. Various aspects of the obtained class of the scalar fields are studied, including the fate of the relativistic symmetries and the properties of the emerging interaction terms. We show that, in a certain limit, the so-called polymer quantization of the field variables is recovered. This and other discussed properties suggest a possible relevance of the considered framework in the context of quantum gravity.

In this work, we generalize the constant-roll condition for minimally coupled canonical scalar field inflation. Particularly, we shall assume that the scalar field satisfies the condition $\ddot{\varphi }=\alpha (\varphi )V^{\prime }(\varphi )$, and we derive the field equations under this assumption. We call the framework extended constant-roll framework. Accordingly, we calculate the inflationary indices and the corresponding observational indices of inflation. In order to demonstrate the inflationary viability, we choose three potentials that are problematic in the context of slow-roll dynamics, namely, chaotic, linear power-law and exponential inflation, and by choosing a simple power-law form for the smooth function $\alpha (\varphi )$, we show that in the extended constant-roll framework, the models are compatible with the latest 2018 Planck constraints on inflation. We also justify appropriately why we called this new framework extended constant-roll framework, and we show that the condition $\ddot{\varphi }=\alpha (\varphi )V^{\prime }(\varphi )$ is equivalent to the condition $\ddot{\varphi }=\beta (\varphi )H\dot{\varphi }$, with the latter condition being a simple generalization of the constant-roll condition. Finally, we examine an interesting physical situation, in which a general extended constant-roll scalar field model is required to satisfy the cosmological tracker condition used in quintessence models. In contrast to the slow-roll and ordinary constant-roll cases, in which case the tracker condition is not compatible with neither the slow-roll or the ordinary constant-roll conditions, the extended constant-roll condition can be compatible with the tracker condition. This feature leads to a new inflationary phenomenological framework, the essential features of which we develop in brief. The main feature of the new theoretical framework is that the function $\alpha (\varphi )$ and the potential $V(\varphi )$ are no longer free to choose, but these are directly functionally related.

In this study, we have explored a scalar field cosmological model in the axially symmetric Bianchi type-I universe. In this study, our aim is to constrain the scalar field dark energy model in an anisotropic background. For this purpose, the explicit solution of the developed field equations for the model is determined and analyzed. Constraints on the cosmological model parameters are established utilizing Markov Chain Monte Carlo (MCMC) analysis and using the latest observational datasets of OHD, BAO, and Pantheon. For the combined dataset (OHD, BAO, and Pantheon), the best-fit values of Hubble and density parameters are estimated as $H_0=71.54\pm 0.28$, ${\mathrm{\Omega }}_{m0}=0.2622\pm 0.0021$${\mathrm{\Omega }}_{\varphi 0}=0.7331\pm 0.0046$ and ${\mathrm{\Omega }}_{\sigma 0}=0.000162\pm 0.000063$. The model shows a flipping nature and redshift transition occurs at $z_t=0.6964_{-0.0006}^{+0.0136}$, and the present value of decelerated parameter is computed to be $q_0=-0.6964\pm 0.028$ for the combined dataset. We have explored characteristics like the universe’s age, particle horizon, deceleration parameter, and jerk parameter. The dynamical properties, such as energy density ${\rho }_{\varphi }$, scalar field pressure $p_{\varphi }$, and equation of state parameter ${\omega }_{\varphi }$, are analyzed and presented. We have also described the behavior of the scalar potential $V(\varphi )$ and scalar field. Furthermore, the authors also described the behavior of energy conditions in scalar-tensor cosmology. The scenario of the present accelerated expansion of the universe is described by the contribution of the scalar field.

In this study, we investigate a scalar field cosmological model with Lyra’s geometry to explain the present cosmic expansion in a homogeneous and isotropic flat FRW universe. In Einstein’s field equations, we presupposed a variable displacement vector as an element of Lyra’s geometry. In the context of the conventional theory of gravity, we suggest a suitable parametrization of the scalar field’s dark energy density in the hybrid function of redshift $z$, confirming the essential transition behavior of the universe from a decelerating era to the present accelerated scenario. We present constraints on model parameters using the most recent observational datasets from OHD, BAO/CMB and Pantheon, taking Markov Chain Monte Carlo (MCMC) analysis into account. For the proposed model, the best estimated values of parameters for the combined dataset (OHD, BAO/CMB and Pantheon) are $H_0=71.15\pm 0.26$km/s/Mpc, ${\mathrm{\Omega }}_{m0}=0.2625\pm 0.0024$, ${\mathrm{\Omega }}_{\varphi 0}=0.676\pm 0.038$, $\alpha =-0.22\pm 0.13$, $n=0.096\pm 0.079$ and $k=0.38\pm 0.32$. The model exhibits a flipping nature, and the redshift transition occurs at $z_t=0.756_{-0.015}^{+0.005}$. The current value of the decelerated parameter for the proposed model is calculated as $q_0=-0.625_{-0.085}^{+0.067}$ for the combined dataset. Some dynamical properties of the model like energy density (${\rho }_{\varphi }$), scalar field pressure ($p_{\varphi }$), EoS parameter of scalar field (${\omega }_{\varphi }$), and effective EoS parameter (${\omega }_{\mathrm{\text{eff}}}$) are analyzed and presented. Further, we have also examined the statefinder diagnosis and jerk parameters of the derived model. The total density parameter for the derived model is found to be unity which is in nice agreement with recent standard findings.