Search Results (18)

We consider the macroscopic motion of the normal component of superfluid ³He-A in global thermodynamic equilibrium within the context of the Zubarev statistical operator method. We formulate the corresponding effective theory in the language of the functional integral. The effective Lagrangian comprising macroscopic motion of fermionic excitations is calculated explicitly for the emergent relativistic fermions of the superfluid ³He-A phase immersed in a non-trivial bosonic background due to a space- and time-dependent matrix-valued vierbein featuring nonzero torsion as well as the Nieh–Yan anomaly. We do not consider the dynamics of the superfluid component itself and thereby its backreaction effects due to normal component macroscopic flow. It is treated as an external background within which the emergent relativistic fermions of the normal component move. The matrix-valued vierbein formulation comprises an additional two-dimensional internal spin space for the two axially charged Weyl fermions living at the Fermi points, which may be replaced by one featuring a Dirac fermion doublet with a real-valued vierbein, an axial Abelian gauge field, and a spin connection gauge field mixing the Dirac and internal spin spaces. We carry out this change of description in detail and determine the constraints on the superfluid background as well as the the normal component motion as determined from the Zubarev statistical operator formalism in global thermodynamic equilibrium. As an application of the developed theory, we consider macroscopic rotation around the axis of pure integer mass vortices. The corresponding thermodynamic quantities of the normal component are analyzed. Our formulation incorporates both superfluid background flow and macroscopic motion flow of the normal component and thereby enables an analysis of their interrelation. Full article

We extend the Quantum Memory Matrix (QMM) framework, originally developed to reconcile quantum mechanics and general relativity by treating space–time as a dynamic information reservoir, to incorporate the full suite of Standard Model gauge interactions. In this discretized, Planck-scale formulation, each space–time cell possesses a finite-dimensional Hilbert space that acts as a local memory, or quantum imprint, for matter and gauge field configurations. We focus on embedding non-Abelian SU(3)_c (quantum chromodynamics) and SU(2)_L × U(1)_Y (electroweak interactions) into QMM by constructing gauge-invariant imprint operators for quarks, gluons, electroweak bosons, and the Higgs mechanism. This unified approach naturally enforces unitarity by allowing black hole horizons, or any high-curvature region, to store and later retrieve quantum information about color and electroweak charges, thereby preserving subtle non-thermal correlations in evaporation processes. Moreover, the discretized nature of QMM imposes a Planck-scale cutoff, potentially taming UV divergences and modifying running couplings at trans-Planckian energies. We outline major challenges, such as the precise formulation of non-Abelian imprint operators and the integration of QMM with loop quantum gravity, as well as possible observational strategies—ranging from rare decay channels to primordial black hole evaporation spectra—that could provide indirect probes of this discrete, memory-based view of quantum gravity and the Standard Model. Full article

We explore the dependence of vacuum energy on the boundary conditions for massive scalar fields in (2 + 1)-dimensional spacetimes. We consider the simplest geometrical setup given by a two-dimensional space bounded by two homogeneous parallel wires in order to compare it with the non-perturbative behaviour of the Casimir energy for non-Abelian gauge theories in (2 + 1) dimensions. Our results show the existence of two types of boundary conditions which give rise to two different asymptotic exponential decay regimes of the Casimir energy at large distances. The two families are distinguished by the feature that the boundary conditions involve or not interrelations between the behaviour of the fields at the two boundaries. Non-perturbative numerical simulations and analytical arguments show such an exponential decay for Dirichlet boundary conditions of SU(2) gauge theories. The verification that this behaviour is modified for other types of boundary conditions requires further numerical work. Subdominant corrections in the low-temperature regime are very relevant for numerical simulations, and they are also analysed in this paper. Full article

An attempt is made to describe from first principles the large-scale structure of the confining vacuum in quantum chromodynamics. Starting from our previous variational studies of the SU(2) pure gauge theory in an external Abelian chromomagnetic field and extending Feynman’s qualitative analysis in (2+1)-dimensional SU(2) gauge theory, we show that the SU(3) vacuum in three-space and one-time dimensions behaves like a disordered chromomagnetic condensate. Color confinement is assured by the presence of a mass gap together with the absence of color long-range correlations. We offer a clear physical picture for the formation of the flux tube between static quark charges that allows us to determine the color structure and the transverse profile of the flux-tube chromoelectric field. The transverse profile of the flux-tube chromoelectric field turns out to be in reasonable agreement with lattice data. We, also, show that our quantum vacuum allows for both the color and ordinary Meissner effect. We find that for massless quarks, the quantum vacuum can accommodate a finite non-zero density of fermion zero modes leading to the dynamical breaking of the chiral symmetry. Full article

The equations of motion of an isospin-carrying particle in a Yang–Mills and gravitational field were first proposed in 1968 by Kerner, who considered geodesics in a Kaluza–Klein-type framework. Two years later, the flat space Kerner equations were completed by also considering the motion of the isospin by Wong, who used a field-theoretical approach. Their groundbreaking work was then followed by a long series of rediscoveries whose history is reviewed. The concept of isospin charge and the physical meaning of its motion are discussed. Conserved quantities are studied for Wu–Yang monopoles and diatomic molecules by using van Holten’s algorithm. Full article

In 1978, Friedberg and Lee introduced the phenomenological soliton bag model of hadrons, generalizing the MIT bag model developed in 1974 shortly after the formulation of QCD. In this model, quarks and gluons are confined due to coupling with a real scalar field $\rho$, which tends to zero outside some compact region $S\subset {\mathbb{R}}^3$ determined dynamically from the equations of motion. The gauge coupling in the soliton bag model runs as the inverse power of $\rho$, already at the semiclassical level. We show that this model arises naturally as a consequence of introducing the warped product metric $\mathrm{d}{s}_M^2+{\rho }^2\mathrm{d}{s}_G^2$ on the principal G-bundle $P(M,G)\cong M\times G$ with a non-Abelian group G over Minkowski space $M={\mathbb{R}}^{3,1}$. Confinement of quarks and gluons in a compact domain $S\subset {\mathbb{R}}^3$ is a consequence of the collapse of the bundle manifold $M\times G$ to M outside S due to shrinking of the group manifold G to a point. We describe the formation of such regions S as a dynamical process controlled by the order parameter field $\rho$. Full article

Non-Abelian gauge theories with composite fields are examined in the background field method. Generating functionals of Green’s functions for a Yang–Mills theory with composite and background fields are introduced, including the generating functional of vertex Green’s functions (effective action). The corresponding Ward identities are obtained, and the issue of gauge dependence is investigated. A gauge variation of the effective action is found in terms of a nilpotent operator depending on the composite and background fields. On-shell independence from the choice of gauge fixing for the effective action is established. In the study of the Ward identities and gauge dependence, finite field-dependent BRST transformations with a background field are introduced and employed on a systematic basis. On the one hand, this involves the consideration of (modified) Ward identities with a field-dependent anticommuting parameter, also depending on a non-trivial background. On the other hand, the issue of gauge dependence is studied with reference to a finite variation of the gauge Fermion. The concept of a joint introduction of composite and background fields to non-Abelian gauge theories is exemplified by the Gribov–Zwanziger theory, including the case of a local BRST-invariant horizon, and also by the Volovich–Katanaev model of two-dimensional gravity with dynamical torsion. Full article

In general relativity, an inertial frame can only be established in a small region of spacetime, and local inertial frames are mathematically represented by a tetrad field in gravity. The tetrad field is not unique due to the freedom to perform Lorentz transformations in local inertial frames, and there exists freedom to choose the local inertial frame at each spacetime point. The local Lorentz transformations are known as non-Abelian gauge transformations for the tetrad field, and to fix the gauge freedom corresponding to the Lorentz gauge ${\partial }^{\mu }{\mathcal{A}}_{\mu }=0$ and the Coulomb gauge ${\partial }^i{\mathcal{A}}_i=0$ in electrodynamics, the Lorentz gauge and Coulomb gauge for tetrad fields are proposed in the present work. Moreover, properties of the Lorentz gauge and the Coulomb gauge for tetrad fields are discussed to show their similarities to those in electromagnetic fields. Full article

Overlap fermion on the lattice has been shown to properly reproduce topological aspects of gauge fields. In this paper, we review the derivation of Overlap fermion formalism in a torus of three space-time dimensions. Using the formalism, we show how to use the Overlap fermion determinants in the massless and infinite mass limits to construct different continuum topological gauge actions, such as the level-k Chern–Simons action, “half-CS” term and the mixed Chern–Simons (BF) coupling, in a gauge-invariant lattice UV regulated manner. Taking special Abelian and non-Abelian background fields, we demonstrate numerically how the lattice formalism beautifully reproduces the continuum expectations, such as the flow of action under large gauge transformations. Full article

Within the earlier developed high-energy-$\overrightarrow{k}·\overrightarrow{p}$-Hamiltonian approach to describe graphene-like materials, the simulations of band structure, non-Abelian Zak phases and the complex conductivity of graphene have been performed. The quasi-relativistic graphene model with a number of flavors (gauge fields) $N_F=3$ in two approximations (with and without a pseudo-Majorana mass term) has been utilized as a ground for the simulations. It has been shown that Zak-phases set for the non-Abelian Majorana-like excitations (modes) in graphene represent the cyclic ${\mathbb{Z}}_{12}$ and this group is deformed into a smaller one ${\mathbb{Z}}_8$ at sufficiently high momenta due to a deconfinement of the modes. Simulations of complex longitudinal low-frequency conductivity have been performed with a focus on effects of spatial dispersion. A spatial periodic polarization in the graphene models with the pseudo Majorana charge carriers is offered. Full article

In this review, we revisit our approach to constructing an effective theory for Abelian and Non-Abelian gauge theories in 4D. Our goal is to have an effective theory that provides a simple classical picture of the main qualitatively important features of these theories. We set out to ensure the presence of the massless photons—Goldstone bosons in Abelian theory and their disappearance in the Non-Abelian case—accompanied by the formation of confining strings between charged states. Our formulation avoids using vector fields and instead operates with the basic degrees of freedom that are the scalar fields of a nonlinear $\sigma$-model. The Mark 1 model we study turns out to have a large global symmetry group-the 2D diffeomorphism invariance in the Abelian limit, which is isomorphic to the group of all canonical transformations in the classical two dimensional phase space. This symmetry is not present in QED, and we eliminate it by “gauging” this infinite dimensional global group. Introducing additional modifications to the model (Mark 2), we are able to prove that the “Abelian” version is equivalent to the theory of a free photon. Achieving the desired property in the “Non-Abelian” regime turns out to be tricky. We are able to introduce a perturbation that leads to the formation of confining strings in our Mark 1 model. These strings have somewhat unusual properties, in that their profile does not decay exponentially away from the center of the string. In addition, the perturbation explicitly breaks the diffeomorphism invariance. Preserving this invariance in the gauged model as well as achieving confining strings in Mark 2 model remains an open question. Full article

It is by now well established that Dirac fermions coupled to non-Abelian gauge theories can undergo an Anderson-type localization transition. This transition affects eigenmodes in the lowest part of the Dirac spectrum, the ones most relevant to the low-energy physics of these models. Here we review several aspects of this phenomenon, mostly using the tools of lattice gauge theory. In particular, we discuss how the transition is related to the finite-temperature transitions leading to the deconfinement of fermions, as well as to the restoration of chiral symmetry that is spontaneously broken at low temperature. Other topics we touch upon are the universality of the transition, and its connection to topological excitations (instantons) of the gauge field and the associated fermionic zero modes. While the main focus is on Quantum Chromodynamics, we also discuss how the localization transition appears in other related models with different fermionic contents (including the quenched approximation), gauge groups, and in different space-time dimensions. Finally, we offer some speculations about the physical relevance of the localization transition in these models. Full article

A joint introduction of composite and background fields into non-Abelian quantum gauge theories is suggested based on the symmetries of the generating functional of Green’s functions, with the systematic analysis focused on quantum Yang–Mills theories, including the properties of the generating functional of vertex Green’s functions (effective action). For the effective action in such theories, gauge dependence is found in terms of a nilpotent operator with composite and background fields, and on-shell independence from gauge fixing is established. The basic concept of a joint introduction of composite and background fields into non-Abelian gauge theories is extended to the Volovich–Katanaev model of two-dimensional gravity with dynamical torsion, as well as to the Gribov–Zwanziger theory. Full article

Within the earlier developed high-energy- $\overrightarrow{k}·\overrightarrow{p}$ -Hamiltonian approach to describe graphene-like materials, the simulations of non-Abelian Zak phases and band structure of the quasi-relativistic graphene model with a number of flavors $N=3$ have been performed in approximations with and without gauge fields (flavors). It has been shown that a Zak-phases set for non-Abelian Majorana-like excitations (modes) in Dirac valleys of the quasi-relativistic graphene model is the cyclic group ${\mathbf{Z}}_{12}$ . This group is deformed into ${\mathbf{Z}}_8$ at sufficiently high momenta due to deconfinement of the modes. Since the deconfinement removes the degeneracy of the eightfolding valleys, Weyl nodes and antinodes emerge. We offer that a Majorana-like mass term of the quasi-relativistic model affects the graphene band structure in the following way. Firstly, the inverse symmetry emerges in the graphene model with Majorana-like mass term, and secondly the mass term shifts the location of Weyl nodes and antinodes into the region of higher energies. Full article

We show that a non-abelian global $SU{\left(2\right)}_R$ R-symmetry acting on the quartic part of the two Higgs Doublet Model leads, at tree-level, to an automatic alignment without decoupling. An example of phenomenologically viable model with this feature is the the low energy effective field theory of the Minimal Dirac Gaugino Supersymmetric Model in the limit where the adjoint scalars are decoupled. We discuss here how the $SU{\left(2\right)}_R$ can be identified with the R-symmetry of the $N=2$ supersymmetry in the gauge and Higgs sectors. We also review how the radiative corrections lead to a very small misalignment. Full article