Search Results (68)

It is revealed that the material derivative of a variable in gravity field is its directional derivative, from which and energy/complementary-energy conservations with exterior derivatives, two sets of gauge equations of Newton’s dynamic gravity field are derived, which has same mathematical structure with the gauge ones for the Maxwell equations in electromagnetic fields, revealing that gravity force and curl momentum in Newton’s gravity field, respectively, play the roles like the electric $\mathit{E}$ and the magnetic $\mathit{B}$ of the Maxwell equations in the electromagnetic field. The gravity tensor of Newton’s gravitational field is constructed, and an example is given to validate it. This finding allows Newton’s gravity to be governed by a gauge theory, addressing the historic issue that “Newton’s gravitation is an exception to the Yang–Mills gauge theory”. Full article

We present the invariant structure of a Holomorphic Unified Field Theory in which gravity and gauge interactions arise from a single geometric framework. The theory is formulated using a product principal bundle, with one connection, and curvature equipped with a Hermitian field on a complexification of spacetime. From a single $\mathrm{Diff}\left(M\right)\times G$-invariant action, variation yields the Einstein and Yang–Mills equations together with their paired Bianchi identities. A compatibility condition is implemented either definitionally or through an auxiliary penalty functional. It enforces that the antisymmetric part of our Hermitian field is the gauge field’s exact curvature on the real slice. Full article

We expand our previous study of replicated gauge configurations in lattice SU($N_c$) Yang–Mills theory—employing Bloch’s theorem from condensed matter physics—to construct gauge-fixed field configurations on significantly larger lattices than the original, or primitive, one. We present a comprehensive discussion of the general gauge-fixing problem, identifying advantages of the replicated-lattice approach. In particular, the consideration of Bloch waves leads us to a visualization of the extended gauge-fixed configurations in terms of (color) magnetization domains. Moreover, we are able to explore features of the method to optimize the evaluation of gauge fields in momentum space, furthering our knowledge of the “allowed momenta”, an issue that has hindered wider applications of this approach up to now. Interestingly, our analysis yields both a better conceptual understanding of the problem and a more efficient way to compute the desired large-volume observables. 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

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

For the deconfinement phase of an SU(2) Yang–Mills theory, we compute the axion mass $m_A$ by appealing to the Veneziano–Witten formula. The topological susceptibility $\chi$ arises (i) from a precisely computable thermal ground-state contribution due to a center of a relevant (anti)caloron, and (ii) from contributions due to free thermal quasi-particles in the effective theory. Both (i) and (ii) are derived by using standard Euclidean thermal field theory techniques. While contribution (i) is positive and $\propto T^4$, contribution (ii) is negative, as demanded by reflection positivity, but negligible compared to contribution (i). As a consequence, practically from the critical temperature $T_c$ onward, a real-valued axion mass $m_A\left(T\right)=\sqrt{{\displaystyle \frac{2}{3}}}\pi {\displaystyle \frac{T^2}{M_P}}$ emerges when the Peccei–Quinn scale is assumed to be the Planck mass $M_P$, independently of the Yang–Mills scale that the axion associates with. We discuss why our results deviate from those found in the dilute instanton gas and interacting instanton liquid approximations, and from results obtained in lattice simulations. Assuming the universe is dark sector to be based on such ultralight axion species, which are nonrelativistic for $T\ll M_P$, we investigate the cosmological conditions for their global Bose condensation as the very early universe cooled to temperatures of the order of ${10}^9$eV. Full article

In this letter, we highlight the structure and main properties of an abstract approach to quantum cosmology and gravity, dubbed $SU(\infty )$-QGR. Beginning from the concept of the Universe as an isolated quantum system, the main axiom of the model is the existence of an infinite number of mutually commuting observables. Consequently, the Hilbert space of the Universe represents $SU(\infty )$ symmetry. This Universe as a whole is static and topological. Nonetheless, quantum fluctuations induce local clustering in its quantum state and divide it into approximately isolated subsystems representing $G\times SU(\infty )$, where G is a generic finite-rank internalsymmetry. Due to the global $SU(\infty )$ each subsystem is entangled to the rest of the Universe. In addition to parameters characterizing the representation of G, quantum states of subsystems depend on four continuous parameters: two of them characterize the representation of $SU(\infty )$, a dimensionful parameter arises from the possibility of comparing representations of $SU(\infty )$ by different subsystems, and the fourth parameter is a measurable used as time registered by an arbitrary subsystem chosen as a quantum clock. It introduces a relative dynamics for subsystems, formulated by a symmetry-invariant effective Lagrangian defined on the (3+1)D space of the continuous parameters. At lowest quantum order, the Lagrangian is a Yang–Mills field theory for both $SU(\infty )$ and internal symmetries. We identify the common $SU(\infty )$ symmetry and its interaction with gravity. Consequently, $SU(\infty )$-QGR predicts a spin-1 mediator for quantum gravity (QGR). Apparently, this is in contradiction with classical gravity. Nonetheless, we show that an observer who is unable to detect the quantumness of gravity perceives its effect as curvature of the space of average values of the continuous parameters. We demonstrate Lorentzian geometry of this emergent classical spacetime. Full article

Based on the thermal phase structure of pure SU(2) quantum Yang–Mills theory, we describe the electron at rest as an extended particle, a droplet of radius $r_0\sim a_0$, where $a_0$ is the Bohr radius. This droplet is of vanishing pressure and traps a monopole within its bulk at a temperature of $T_c=7.95$ keV. The monopole is in the Bogomolny–Prasad–Sommerfield (BPS) limit. It is interpreted in an electric–magnetically dual way. Utilizing a spherical mirror-charge construction, we approximate the droplet’s charge at a value of the electromagnetic fine-structure constant $\alpha$ of ${\alpha }^{-1}\sim 134$ for soft external probes. It is shown that the droplet does not exhibit an electric dipole or quadrupole moment due to averages of its far-field electric potential over monopole positions. We also calculate the mixing angle ${\theta }_{\mathrm{W}}\sim 30°$, which belongs to deconfining phases of two SU(2) gauge theories of very distinct Yang–Mills scales (${\Lambda }_{\mathrm{e}}=3.6$ keV and ${\Lambda }_{\mathrm{CMB}}\sim {10}^{-4}$ eV). Here, the condition that the droplet’s bulk thermodynamics is stable determines the value of ${\theta }_W$. The core radius of the monopole, whose inverse equals the droplet’s mass in natural units, is about 1% of $r_0$. Full article

The Moyal-Higher-Spin (MHS) formalism, involving fields dependent on spacetime and auxiliary coordinates, is an approach to studying higher-spin (HS)-like models. To determine the particle content of the MHS model of the Yang–Mills type, we calculate the quartic Casimir operator for on-shell MHS fields, finding it to be generally non-vanishing, indicative of infinite/continuous spin degrees of freedom. We propose an on-shell basis for these infinite/continuous spin states. Additionally, we analyse the content of a massive MHS model. Full article

Topological susceptibility of the SU(3) gluon plasma is calculated by accounting for both factorized and non-factorized contributions to the two-point correlation function of topological-charge densities. It turns out that, while the factorized contribution keeps this correlation function non-positive away from the origin, the non-factorized contribution makes it positive at the origin, in accordance with the reflection positivity condition. Matching the obtained result for topological susceptibility to its lattice value at the deconfinement critical temperature, we fix the parameters of the quartic cumulant of gluonic field strengths, and calculate the contribution of that cumulant to the string tension. This contribution reduces the otherwise too large value of the string tension, which stems from the quadratic cumulant, making it much closer to the standard phenomenological value. Full article

In this paper, we review some recent findings related to the Casimir effect. Initially, the thermal corrections to the vacuum Casimir energy density are calculated, for a quantum scalar field, whose modes propagate in the (3+1)-dimensional Euclidean spacetime, subject to a nontrivial compact boundary condition. Next, we analyze the Casimir effect induced by two parallel plates placed in a weak gravitational field background. Finally, we review the three-dimensional wormhole solutions sourced by the Casimir density and pressures associated with the quantum vacuum fluctuations of the Yang-Mills field. Full article

$U\left(n\right)$ is a semi-direct product group characterized by nontrivial homomorphisms mapping $U\left(1\right)$ into the automorphism group of $SU\left(n\right)$. For $U\left(3\right)$, there are three nontrivial homomorphisms that induce three separate defining representations. In a toy model of $U\left(3\right)$ Yang–Mills (endowed with a suitable inner product) coupled to massive fermions, this renders three distinct covariant derivatives acting on a single matter field. Employing a $\mathrm{mod}3$ permutation induced by a large gauge transformation acting on the defining representation vector space, the three covariant derivatives and one matter field can alternatively be expressed as a single covariant derivative acting on three distinct species of matter fields possessing the same $U\left(3\right)$ quantum numbers. One can interpret this as three species of matter fields in the defining representation. 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

This article reviews recent progress in computational quantum gravity caused by the framework that efficiently computes Feynman’s rules. The framework is implemented in the FeynGrav package, which extends the functionality of the widely used FeynCalc package. FeynGrav provides all the tools to study quantum gravitational effects within the standard model. We review the framework, provide the theoretical background for the efficient computation of Feynman rules, and present the proof of its completeness. We review the derivation of Feynman rules for general relativity, Horndeski gravity, Dirac fermions, Proca field, electromagnetic field, and $SU\left(N\right)$ Yang–Mills model. We conclude with a discussion of the current state of the FeynGrav package and discuss its further development. Full article