Search Results (61)

We discuss different quench protocols for Ising and XY spin chains in a transverse magnetic field. With a sudden local magnetic field quench as a starting point, we generalize our approach to a large class of local non-sudden quenches. Using finite time path field theory (FTPFT) perturbative methods, we show that the difference between the sudden quench and a class of quenches with non-sudden switching on the perturbation vanishes exponentially with time, apart from non-substantial modifications that are systematically accounted for. As the consequence of causality and analytic properties of functions describing the discussed class of quenches, this is true at any order of perturbation expansion and thus for the resummed perturbation series. The only requirements on functions describing the perturbation strength switched on at a finite time $t=0$ are as follows: (1) their Fourier transform $f\left(p\right)$ is a function that is analytic everywhere in the lower complex semiplane, except at the simple pole at $p=0$ and possibly others with $\Im \left(p\right)<0$; and (2) $f\left(p\right)/p$ converges to zero at infinity in the lower complex semiplane. A prototypical function of this class is $tanh\left(\eta t\right)$, to which the perturbation strength is proportional after the switching at time $t=0$. In the limit of large $\eta$, such a perturbation approaches the case of a sudden quench. It is shown that, because of this new type of universal behavior of Loschmidt echo (LE) that emerges in an exponentially short time scale, our previous results for the sudden local magnetic field quench of Ising and XY chains, obtained by the resummation of the perturbative expansion, extend in the long-time limit to all non-sudden quench protocols in this class, with non-substantial modifications systematically taken into account. We also show that analogous universal behavior exists in disorder quenches, and ultimately global ones. LE is directly connected to the work probability distribution, and the described universal behavior is therefore appropriate in potential concepts of quantum technology related to spin chains. Full article

The continual production of long wavelength gravitons during primordial inflation endows graviton loop corrections with secular growth factors. During a prolonged period of inflation, these factors eventually overwhelm the small loop-counting parameter of $G{H}^2$, causing perturbation theory to break down. A technique was recently developed for summing the leading secular effects at each order in non-linear sigma models, which possess the same kind of derivative interactions as gravity. This technique combines a variant of Starobinsky’s stochastic formalism with a variant of the renormalization group. Generalizing the technique to quantum gravity is a two-step process, the first of which is the determination of the gauge fixing condition that will allow this summation to be realized; this is the subject of this paper. Moreover, we briefly discuss the second step, which shall obtain the Langevin equation, in which secular changes in gravitational phenomena are driven by stochastic fluctuations of the graviton field. Full article

We present a study of relic gravitational waves based on a foliated gauge field theory defined over a spacetime endowed with a noncommutative algebraic–geometric structure. As an ontological extension of general relativity—concerning manifolds, metrics, and fiber bundles—the conventional space and time coordinates, typically treated as classical numbers, are replaced by complementary quantum dual fields. Within this framework, consistent with the Bekenstein criterion and the Hawking–Hertog multiverse conception, singularities merge into a helix-like cosmic scale factor that encodes the topological transition between the contraction and expansion phases of the universe analytically continued into the complex plane. This scale factor captures the essence of an intricate topological quantum-leap transition between two phases of the branching universe: a contraction phase preceding the now-surpassed conventional concept of a primordial singularity and a subsequent expansion phase, whose transition region is characterized by a Riemannian topological foliated structure. The present linearized formulation, based on a slight gravitational field perturbation, also reveals a high sensitivity of relic gravitational wave amplitudes to the primordial matter and energy content during the universe’s phase transition. It further predicts stochastic homogeneous distributions of gravitational wave intensities arising from the interplay of short- and long-spacetime effects within the non-commutative algebraic framework. These results align with the anticipated future observations of relic gravitational waves, expected to pervade the universe as a stochastic, homogeneous background. Full article

Using a Dyson–Schwinger approach, we perform an analysis of the non-trivial ground state of thermal $SU\left(N\right)$ Yang–Mills theory in the non-perturbative regime where chiral symmetry is dynamically broken by a mass gap. Basic thermodynamic observables such as energy density and pressure are derived analytically, using Jacobi elliptic functions. The results are compared with the lattice results. Good agreement is found at low temperatures, providing a viable scenario for a gas of massive glue states populating higher levels of the spectrum of the theory. At high temperatures, a scenario without glue states consistent with a massive scalar field is observed, showing an interesting agreement with lattice data. The possibility is discussed that the results derived in this analysis open up a novel pathway beyond lattice to precision studies of phase transitions with false vacuum and cosmological relics that depend on the equations of state in strong coupled gauge theories of the type of Quantum Chromodynamics (QCD). Full article

This paper presents a novel approach to solving the Yang–Mills existence and mass gap problem using quantum information theory. We develop a rigorous mathematical framework that reformulates the Yang–Mills theory in terms of quantum circuits and entanglement structures. Our method provides a concrete realization of the Yang–Mills theory that is manifestly gauge-invariant and satisfies the Wightman axioms. We demonstrate the existence of a mass gap by analyzing the entanglement spectrum of the vacuum state, establishing a direct connection between the mass gap and the minimum non-zero eigenvalue of the entanglement Hamiltonian. Our approach also offers new insights into non-perturbative phenomena such as confinement and asymptotic freedom. We introduce new mathematical tools, including entanglement renormalization for gauge theories and quantum circuit complexity measures for quantum fields. The implications of our work extend beyond the Yang–Mills theory, suggesting new approaches to quantum gravity, strongly coupled systems, and cosmological problems. This quantum information perspective on gauge theories opens up exciting new directions for research at the intersection of quantum field theory, quantum gravity, and quantum computation. Full article

Making use of the well-known renormalization group (RG) scale dependences of the gravitational couplings in the framework of the two-parameter Einstein–Hilbert (EH) theory of gravity, the single scalar field-driven cosmological inflation is discussed in a spatially homogeneous, isotropic, and flat model universe. The inflaton field is represented by a one-component real, non-self-interacting, massive scalar field minimally coupled to gravity. Cases without and with the incorporation of the RG scaling of the inflaton mass are compared with each other and with the corresponding classical case. It is shown that the quantum improvement drastically alters the timing of the slow-roll inflation with the desirable number $\underset{,}{\mathrm{N}}\approx 60$ e-foldings, as compared with the classical case. Furthermore, accounting for the RG flow of the inflaton mass has an enormous effect on the timing of the desirable slow roll, too. Although providing the desirable slow-roll inflation, none of the versions of the investigated quantum-improved toy models provide a realistic value of the amplitude of the scalar perturbations. Full article

This is a review/research paper on anomalies applied in a bottom–up approach to standard model and gravity. It is divided into two parts. The first consists of a proper review of anomalies in quantum field theories. Anomalies are analyzed according to three different methods: a perturbative one based on a Feynman diagram, a non-perturbative one relying on the Schwinger–DeWitt approach, and, third, one hinging on the Atiyah–Singer family’s index theorem. The three methods are applied both to chiral gauge anomalies and trace anomalies. The fundamental distinction, which our presentation leads to, is between obstructive (O) and non-obstructive (NO) anomalies. The former is tied to the non-existence of fermion propagators, which fatally maim the corresponding theory. In the second part, we apply this analysis to the SM and a variety of its extensions, which are immersed in a gravitational background, and we find that they are all plagued by a residual chiral trace anomaly. To completely eliminate all kinds of dangerous anomalies in SM-like theories, we propose a somewhat unconventional scheme and exemplify it by means of an explicit model. The latter is a left–right symmetric model. We embed it in a Weyl geometry to render it a conformal invariant. We then deal with some of its quantum aspects, particularly its even (NO) trace anomalies and the means to preserve its conformal invariance at the quantum level. We briefly review renormalization and unitarity in the framework of similar models discussed in the existing literature. Finally, we present a possible (conjectural) application of the model to describe the junction between cosmology and quantum field theory. Full article

About twelve years ago, the use of standard functional manipulations was demonstrated to imply an unexpected property satisfied by the fermionic Green’s functions of $QCD$. This non-perturbative phenomenon has been dubbed an effective locality. In a much simpler way than in $QCD$, the most remarkable and intriguing aspects of effective locality have been presented in a recent publication on the Yang-Mills theory on Minkowski spacetime. While quickly recalled in the current paper, these results are used to calculate the problematic gluonic propagator in the Yang-Mills non-perturbative regime. This paper is dedicated to the memory of Professor Herbert M. Fried (1929–2023), whose inspiring manner, impressive command of functional methods in quantum field theories, enthusiasm for a broad range of topics in Theoretical Physics, and warm friendship are missed greatly by the authors. Full article

In this work, we elaborate further on a (3+1)-dimensional cosmological Running-Vacuum-type-Model (RVM) of inflation based on string-inspired Chern-Simons(CS) gravity, involving axions coupled to gravitational-CS(gCS) anomalous terms. Inflation in such models is caused by primordial-gravitational-waves(GW)-induced condensation of the gCS terms, which leads to a linear-axion potential. We demonstrate that this inflationary phase may be metastable, due to the existence of imaginary parts of the gCS condensate. These are quantum effects, proportional to commutators of GW perturbations, hence vanishing in the classical theory. Their existence is quantum-ordering-scheme dependent. We argue in favor of a physical importance of such imaginary parts, which we compute to second order in the GW (tensor) perturbations in the framework of a gauge-fixed effective Lagrangian, within a (mean field) weak-quantum-gravity-path-integral approach. We thus provide estimates of the inflation lifetime. On matching our results with the inflationary phenomenology, we fix the quantum-ordering ambiguities, and obtain an order-of-magnitude constraint on the String-Mass-Scale-to-Planck-Mass ratio, consistent with previous estimates by the authors in the framework of a dynamical-system approach to linear-axion RVM inflation. Finally, we examine the role of periodic modulations in the axion potential induced by non-perturbative effects on the slow-roll inflationary parameters, and find compatibility with the cosmological data. Full article

A generalized scientific review with elements of additions and clarifications has been carried out on the methods of theoretical research on the electrophysical properties of crystals with ionic–molecular chemical bonds (CIMBs). The main theoretical tools adopted are the methods of quasi-classical kinetic theory as applied to ionic subsystems relaxing in layered dielectrics (natural silicates, crystal hydrates, various types of ceramics, and perovskites) in an electric field. A universal (applicable for any CIMBs class crystals) nonlinear quasi-classical kinetic equation of theoretical and practical importance has been constructed. This equation describes, in complex with the Poisson equation, the mechanism of ion-relaxation polarization and conductivity in a wide range of polarizing field parameters (0.1–1000 MV/m) and temperatures (1–1550 K). The physical model is based on a system of non-interacting ions (due to the low concentration in the crystal) moving in a one-dimensional, spatially periodic crystalline potential field, perturbed by an external electric field. The energy spectrum of ions is assumed to be continuous. Elements of quantum mechanical theory in a quasi-classical model are used to mathematically describe the influence of tunnel transitions of hydrogen ions (protons) during the interaction of proton and anion subsystems in hydrogen-bonded crystals (HBC) on the polarization of the dielectric in the region of nitrogen (50–100 K) and helium (1–10 K) temperatures. The mathematical model is based on the solution of a system of nonlinear Fokker-Planck and Poisson equations, solved by perturbation theory methods (via expanding solutions into infinite power series in a small dimensionless parameter). Theoretical frequency and temperature spectra of the dielectric loss tangent were constructed and analyzed, the molecular parameters of relaxers were calculated, and the physical nature of the maxima of the experimental temperature spectra of dielectric losses for a number of HBC crystals was discovered. The low-temperature maximum, which is caused by the quantum tunneling of protons and is absent in the experimental spectra, was theoretically calculated and investigated. The most effective areas of scientific and technical application of the theoretical results obtained were identified. The application of the equations and recurrent formulas of the constructed model to the study of nonlinear optical effects in elements of laser technologies and nonlinear radio wave effects in elements of microwave signal control systems is of the greatest interest. Full article

We analyze truncated series generated as divergent formal solutions of non-linear ordinary differential equations. Motivating the study is a specific non-linear, first-order differential equation, which is the basis of the resurgent formulation of renormalized perturbation theory in quantum field theory. We use the Borel–Padé approximant and classical analysis to determine the analytic structure of the solution using the first few terms of its asymptotic series. Afterward, we build an approximant, consistent with the resurgent properties of the equation. The procedure gives an approximate expression for the Borel–Ecalle resummation of the solution useful for practical applications. Connections with other physical applications are also discussed. Full article

In a seminal work, Hawking showed that natural states for free quantum matter fields on classical spacetimes that solve the spherically symmetric vacuum Einstein equations are KMS states of non-vanishing temperature. Although Hawking’s calculation does not include the backreaction of matter on geometry, it is more than plausible that the corresponding Hawking radiation leads to black hole evaporation which is, in principle, observable. Obviously, an improvement of Hawking’s calculation including backreaction is a problem of quantum gravity. Since no commonly accepted quantum field theory of general relativity is available yet, it has been difficult to reliably derive the backreaction effect. An obvious approach is to use the black hole perturbation theory of a Schwarzschild black hole of fixed mass and to quantize those perturbations. However, it is not clear how to reconcile perturbation theory with gauge invariance beyond linear perturbations. In recent work, we proposed a new approach to this problem that applies when the physical situation has an approximate symmetry, such as homogeneity (cosmology), spherical symmetry (Schwarzschild), or axial symmetry (Kerr). The idea, which is surprisingly feasible, is to first construct the non-perturbative physical (reduced) Hamiltonian of the reduced phase space of fully gauge invariant observables and only then apply perturbation theory directly in terms of observables. The task to construct observables is then disentangled from perturbation theory, thus allowing to unambiguously develop perturbation theory to arbitrary orders. In this first paper of the series we outline and showcase this approach for spherical symmetry and second order in the perturbations for Einstein–Klein–Gordon–Maxwell theory. Details and generalizations to other matter and symmetry and higher orders will appear in subsequent companion papers. Full article

A renormalized group improved Schwarzschild black hole spacetime contains two quantum correction parameters. One parameter $\gamma$ represents the identification of cutoff of the distance scale, and another parameter $\mathsf{\Omega }$ stems from nonperturbative renormalization group theory. The two parameters are constrained by the data from the shadow of M87* central black hole. The dynamics of electrically charged test particles around the black hole are integrable. However, when the black hole is immersed in an external asymptotically uniform magnetic field, the dynamics are not integrable and may allow for the occurrence of chaos. Employing an explicit symplectic integrator, we survey the contributions of the two parameters to the chaotic dynamical behavior. It is found that a small change of the parameter $\gamma$ constrained by the shadow of M87* black hole has an almost negligible effect on the dynamical transition of particles from order to chaos. However, a small decrease in the parameter $\mathsf{\Omega }$ leads to an enhancement in the strength of chaos from the global phase space structure. A theoretical interpretation is given to the different contributions. The term with the parameter $\mathsf{\Omega }$ dominates the term with the parameter $\gamma$, even if the two parameters have same values. In particular, the parameter $\mathsf{\Omega }$ acts as a repulsive force, and its decrease means a weakening of the repulsive force or equivalently enhancing the attractive force from the black hole. On the other hand, there is a positive Lyapunov exponent that is universally given by the surface gravity of the black hole when $\mathsf{\Omega }\ge 0$ is small and the external magnetic field vanishes. In this case, the horizon would influence chaotic behavior in the motion of charged particles around the black hole surrounded by the external magnetic field. This point can explain why a smaller value of the renormalization group parameter would much easily induce chaos than a larger value. Full article

We derive a Nambu–Jona-Lasinio (NJL) model from a non-local gauge theory and show that it has confining properties at low energies. In particular, we present an extended approach to non-local QCD and a complete revision of the technique of Bender, Milton and Savage applied to non-local theories, providing a set of Dyson–Schwinger equations in differential form. In the local case, we obtain closed-form solutions in the simplest case of the scalar field and extend it to the Yang–Mills field. In general, for non-local theories, we use a perturbative technique and a Fourier series and show how higher-order harmonics are heavily damped due to the presence of the non-local factor. The spectrum of the theory is analysed for the non-local Yang–Mills sector and found to be in agreement with the local results on the lattice in the limit of the non-locality mass parameter running to infinity. In the non-local case, we confine ourselves to a non-locality mass that is sufficiently large compared to the mass scale arising from the integration of the Dyson–Schwinger equations. Such a choice results in good agreement, in the proper limit, with the spectrum of the local theory. We derive a gap equation for the fermions in the theory that gives some indication of quark confinement in the non-local NJL case as well. Confinement seems to be a rather ubiquitous effect that removes some degrees of freedom in the original action, favouring the appearance of new observable states, as seen, e.g., for quantum chromodynamics at lower energies. Full article

If a quantum field theory has a Landau pole, the theory is usually called ‘sick’ and dismissed as a candidate for an interacting UV-complete theory. In a recent study on the interacting 4d O(N) model at large N, it was shown that at the Landau pole, observables remain well-defined and finite. In this work, I investigate both relevant and irrelevant deformations of the said model at the Landau pole, finding that physical observables remain unaffected. Apparently, the Landau pole in this theory is benign. As a phenomenological application, I compare the O(N) model to QCD by identifying ${\Lambda }_{\overline{\mathrm{MS}}}$ with the Landau pole in the O(N) model. Full article