Heat-kernel expansion and counterterms of the Faddeev–Popov determinant in Coulomb and Landau gauge

The Faddeev–Popov determinant of Landau gauge in d dimensions and Coulomb gauge in d+1 dimensions is calculated in the heat-kernel expansion up to next-to-leading order. The UV-divergent parts in d=3,4 are isolated and the counterterms required for a non-perturbative treatment of the Faddeev–Popov determinant are determined.     

Faddeev–Jackiw quantization of the higher derivative Chern–Simons gauge theory in the first-order formalism

We analyse the physical constraints of the higher derivative Chern–Simons gauge model by means of Faddeev–Jackiw symplectic approach in the first-order formalism. Within such framework, we systematically determine the zero-mode structure of the corresponding symplectic matrix. In addition, we calculate the Faddeev–Jackiw quantum brackets by choosing appropriate gauge-fixing conditions and evaluate the determinant of the non-singular symplectic matrix as well as the transition-amplitude. Finally, we present a detailed Hamiltonian analysis using Dirac–Bergmann algorithm method and show that the Dirac brackets coincide with the FJ brackets when all the second-class constraints are treated as zero equations.     

Harada–Tsutsui gauge recovery procedure: From Abelian gauge anomalies to the Stueckelberg mechanism

Revisiting a path-integral procedure developed by Harada and Tsutsui for recovering gauge invariance from anomalous effective actions, it is shown that there are two ways to achieve gauge symmetry: one already presented by the authors, which is shown to preserve the anomaly in the sense of standard current conservation law, and another one which is anomaly-free, preserving current conservation. It is also shown that the application of the Harada–Tsutsui technique to other models which are not anomalous but do not exhibit gauge invariance allows the identification of the gauge invariant formulation of the Proca model, also done by the referred authors, with the Stueckelberg model, leading to the interpretation of the gauge invariant map as a generalization of the Stueckelberg mechanism.     

On the infrared scaling solution of SU(N) Yang–Mills theories in the maximally Abelian gauge

An improved method for extracting infrared exponents from functional equations is presented. The generalizations introduced allow for an analysis of quite complicated systems such as Yang–Mills theory in the maximally Abelian gauge. Assuming the absence of cancellations in the appropriately renormalized integrals the only consistent scaling solution yields an infrared enhanced diagonal gluon propagator in support of the Abelian dominance hypothesis. This is explicitly shown for SU(2) and subsequently verified for SU(N), where additional interactions exist. We also derive the most infrared divergent scaling solution possible for vertex functions in terms of the propagators’ infrared exponents. We provide general conditions for the existence of a scaling solution for a given system and comment on the cases of linear covariant gauges and ghost–anti-ghost symmetric gauges.     

Faddeev–Jackiw quantization of an Abelian and non-Abelian exotic action for gravity in three dimensions

A detailed Faddeev–Jackiw quantization of an Abelian and non-Abelian exotic action for gravity in three dimensions is performed. We obtain for the theories under study the constraints, the gauge transformations, the generalized Faddeev–Jackiw brackets and we perform the counting of physical degrees of freedom. In addition, we compare our results with those found in the literature where the canonical analysis is developed, in particular, we show that both the generalized Faddeev–Jackiw brackets and Dirac’s brackets coincide to each other. Finally we discuss some remarks and prospects.     

Supercurrent coupling in the Faddeev–Skyrme model

Motivated by the sigma model limit of multicomponent Ginzburg–Landau theory, a version of the Faddeev–Skyrme model is considered in which the scalar field is coupled dynamically to a one-form field called the supercurrent. This coupled model is investigated in the general setting where physical space M$M$ is an oriented Riemannian manifold and the target space N$N$ is a Kähler manifold, and its properties are compared with the usual, uncoupled Faddeev–Skyrme model. In the case N=S²$N=S^2$, it is shown that supercurrent coupling destroys the familiar topological lower energy bound of Vakulenko and Kapitanski when M=R³$M={\mathbb{R}}^3$, and the less familiar linear bound when M$M$ is a compact 3-manifold. Nonetheless, local energy minimizers may still exist. The first variation formula is derived and used to construct three families of static solutions of the model, all on compact domains. In particular, a coupled version of the unit charge hopfion on a three-sphere of arbitrary radius is found. The second variation formula is derived, and used to analyze the stability of some of these solutions. In particular, it is shown that, in contrast to the uncoupled model, the coupled unit hopfion on the three-sphere of radius R$R$ is unstable   for all R$R$. This gives an explicit, exact example of supercurrent coupling destabilizing a stable solution of the usual Faddeev–Skyrme model, and casts doubt on the conjecture of Babaev, Faddeev and Niemi that knot solitons should exist in the low energy regime of two-component superconductors.     

Representation of an interaction in the formalism of operator BRST quantization for the standard electroweak theory in the Rξ gauge

An operator BRST quantization of the spontaneously broken SU(2)×U(1) electroweak theory is carried out in the R gauge. A representation is found for the interaction.Leninist Communist Youth League, Tomsk Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 79–83, July, 1992.     

Topological approach to examine the singularity of the axial-vector current in an Abelian gauge field theory （QED）

A topological way to distinguish divergences of the Abelian axial-vector current in quantum field theory is proposed. By using the properties of the Atiyah-Singer index theorem, the nomtrivial Jacobian factor of the integration measure in the path-integral formulation of the theory is connected with the topological properties of the gauge field. The singularity of the fermion current related to the topological character can be correctly examined in a gauge background.     

Fermion zero modes in Painlevé-Gullstrand black hole

The Painlevé-Gullstrand metric of a black hole allows one to discuss the fermion zero modes inside the hole. The statistical mechanics of the fermionic microstates can be responsible for the black hole thermodynamics. These fermion zero modes also lead to quantization of the horizon area.     

On the issue of zero point energy in Bose–Einstein condensates

Following on our earlier work in this area, here we examine in some detail the physical mechanism involved in the Bose–Einstein condensation process. In particular we emphasise the significance of the zero value of the chemical potential at and below the critical temperature. The molar zero-point energy (ZPE) for an ideal gas of He⁴ atoms in our new analysis is estimated and found to be very close to that calculated for an ideal Fermi gas of He³ atoms under the same conditions. This gives numerical support to our theory. We also show how the theory is consistent with the presence of a density maximum in liquid He⁴.     

Stable computation of the functional variation of the Dirichlet–Neumann operator

This paper presents an accurate and stable numerical scheme for computation of the first variation of the Dirichlet–Neumann operator in the context of Euler’s equations for ideal free-surface fluid flows. The Transformed Field Expansion methodology we use is not only numerically stable, but also employs a spectrally accurate Fourier/Chebyshev collocation method which delivers high-fidelity solutions. This implementation follows directly from the authors’ previous theoretical work on analyticity properties of functional variations of Dirichlet–Neumann operators. These variations can be computed in a number of ways, but we establish, via a variety of computational experiments, the superior effectiveness of our new approach as compared with another popular Boundary Perturbation algorithm (the method of Operator Expansions).     

Numerical computation of the helical Chandrasekhar–Kendall modes

A new formulation is presented for numerically computing the helical Chandrasekhar–Kendall modes in an axisymmetric torus. It explicitly imposes ? · B = 0 and yields a standard matrix eigenvalue problem, which can then be solved by standard matrix eigenvalue techniques. Numerical implementation and computational results are shown for an axisymmetric torus typical of reversed field pinch and spherical tokamak.     

Structure of zero modes in a model of the discrete (2+1)-dimensional nonlinear Schrödinger equation

The structure of the zero modes in a discrete (2+1)-dimensional model of the gauge-invariant nonlinear Schrödinger equation is studied. Including the compactification of the Chern-Simons gauge fields eliminates the difficulties with the continuous model [L. A. Abramyan and A. P. Protogenov, JETP Lett. 64, 859 (1996); L. A. Abramyan, V. I. Berezhiani, and A. P. Protogenov, Phys. Rev. E 56, 6026 (1997)] and leads to a prediction of the existence of a transition region characterized by a hierarchical sequence of collapses which are enumerated by the Chern-Simons coefficient. Using the zero modes in calculating the dependence of the critical power N on the Chern-Simons coefficient, we have found that the transition region lies in the interval 11.703≤N≤12.01.     

Study of supersolidity in the two-dimensional Hubbard–Holstein model

We derive an effective Hamiltonian for the two-dimensional Hubbard–Holstein model in the regimes of strong electron–electron and strong electron–phonon interactions by using a nonperturbative approach. In the parameter region where the system manifests the existence of a correlated singlet phase, the effective Hamiltonian transforms to a t₁ ? V ₁ ? V ₂ ? V ₃ Hamiltonian for hard-core-bosons on a checkerboard lattice. We employ quantum Monte Carlo simulations, involving stochastic-series-expansion technique, to obtain the ground state phase diagram. At filling 1∕8, as the strength of off-site repulsion increases, the system undergoes a first-order transition from a superfluid to a diagonal striped solid with ordering wavevector \(\vec{Q}\) = (π∕4, 3π∕4) or (π∕4, 5π∕4). Unlike the one-dimensional situation, our results in the two-dimensional case reveal a supersolid phase (corresponding to the diagonal striped solid) around filling 1∕8 and at large off-site repulsions. Furthermore, for small off-site repulsions, we witness a valence bond solid at one-fourth filling and tiny phase-separated regions at slightly higher fillings.     

Center-of-mass quantization of excitons and Fabry–Perot modes of the polariton in ZnSe epilayers

Reflectance properties of ZnSe epilayers grown on GaAs substrates are studied at 80 K. Oscillation features are observed in the region of exciton resonance which are significantly different depending on the epilayer thickness L. For optically thin layers with thickness in the range of several tens of nanometer, reflectance oscillations appear above the light-hole (lh) exciton, while for optically thick layers with thickness in the range of a micrometer, reflectance oscillations appear between 1s and 2s excitons. These oscillations are interpreted as the quantized levels of the exciton center-of-mass motion in the lower branch of the polariton for optically thin layers and Fabry–Perot modes in the upper branch of the polariton for optically thick layers, respectively. The reflectance data are analyzed in the frame work of a dielectric function with a polariton dispersion.