Quantum Gauge Research Articles

An Alternative to the Gauge Theoretic Setting

The standard formulation of quantum gauge theories results from the Lagrangian (functional integral) quantization of classical gauge theories. A more intrinsic quantum theoretical access in the spirit of Wigner’s representation theory shows that there is a fundamental clash between the pointlike localization of zero mass (vector, tensor) potentials and the Hilbert space (positivity, unitarity) structure of QT. The quantization approach has no other way than to stay with pointlike localization and sacrifice the Hilbert space whereas the approach built on the intrinsic quantum concept of modular localization keeps the Hilbert space and trades the conflict creating pointlike generation with the tightest consistent localization: semiinfinite spacelike string localization. Whereas these potentials in the presence of interactions stay quite close to associated pointlike field strengths, the interacting matter fields to which they are coupled bear the brunt of the nonlocal aspect in that they are string-generated in a way which cannot be undone by any differentiation. The new stringlike approach to gauge theory also revives the idea of a Schwinger-Higgs screening mechanism as a deeper and less metaphoric description of the Higgs spontaneous symmetry breaking and its accompanying tale about “God’s particle” and its mass generation for all the other particles.

Covariant Approach of the Dynamics of Particles in External Gauge Fields, Killing Tensors and Quantum Gravitational Anomalies

We give an overview of the first integrals of motion of particles in the presence of external gauge fields in a covariant Hamiltonian approach. The special role of St\"ackel-Killing and Killing-Yano tensors is pointed out. Some nontrivial examples involving Runge-Lenz type conserved quantities are explicitly worked out. A condition of the electromagnetic field to maintain the hidden symmetry of the system is stated. A concrete realization of this condition is given by the Killing-Maxwell system and exemplified with the Kerr metric. Quantum symmetry operators for the Klein-Gordon and Dirac equations are constructed from Killing tensors. The transfer of the classical conserved quantities to the quantum mechanical level is analyzed in connection with quantum anomalies.

Covariant Closed String Coherent States

We give the first construction of covariant coherent closed string states, which may be identified with fundamental cosmic strings. We outline the requirements for a string state to describe a cosmic string, and provide an explicit and simple map that relates three different descriptions: classical strings, light cone gauge quantum states, and covariant vertex operators. The resulting coherent state vertex operators have a classical interpretation and are in one-to-one correspondence with arbitrary classical closed string loops.

Quantum gauge fields and flat connections in 2-dimensional BF theory

The 2-dimensional BF theory is both a gauge theory and a topological Poisson σ-model corresponding to a linear Poisson bracket. In [3], Torossian discovered a connection which governs correlation functions of the BF theory with sources for the B-field. This connection is flat, and it is a close relative of the KZ connection in the WZW model. In this Letter, we show that flatness of the Torossian connection follows from (properly regularized) quantum equations of motion of the BF theory.

Contributions to the muon’s anomalous magnetic moment from a hidden sector

The measurement of the anomalous magnetic moment of the muon provides a stringent test of the standard model and of any physics that lies beyond it. There is currently a deviation of 3.1 σ between the standard model prediction for the muon’s anomalous magnetic moment and its experimental value. We calculate the contribution to the anomalous magnetic moment in theories where the muon couples to a particle in a hidden sector (that is, uncharged under the standard model) and a connector (which has nontrivial standard model gauge and hidden sector quantum numbers).

Gauge invariance and quantization of Yang-Mills theories in extra dimensions

The gauge structure of the four-dimensional effective theory arising from a pure $S{U}_{5}(N)$ Yang-Mills theory in five dimensions compactified on the orbifold ${S}^{1}/{Z}_{2}$ is reexamined on the basis of Becchi-Rouet-Stora-Tyutin symmetry. In this context, the two scenarios that can arise are analyzed: if the gauge parameters propagate in the bulk, the excited Kaluza-Klein (KK) modes are gauge fields, but they are matter vector fields if these parameters are confined in the 3-brane. In the former case, it is shown that the four-dimensional theory is gauge invariant only if the compactification is carried out by using curvatures instead of gauge fields as fundamental objects. Then, it is shown that the four-dimensional theory is governed by two types of gauge transformations, one determined by the KK zero modes of the gauge parameters, ${\ensuremath{\alpha}}^{(0)a}$, and another by the excited KK modes, ${\ensuremath{\alpha}}^{(n)a}$. The Dirac method and the proper solution of the master equation in the context of the field-antifield formalism are employed to show that the theory is subject to first-class constraints. A gauge-fixing procedure to quantize the KK modes ${A}_{\ensuremath{\mu}}^{(n)a}$ that is covariant under the first type of gauge transformations, which embody the standard gauge transformations of $S{U}_{4}(N)$, is introduced through gauge-fixing functions transforming in the adjoint representation of this group. The ghost sector induced by these gauge-fixing functions is derived on the basis of the Becchi-Rouet-Stora-Tyutin formalism. The effective quantum Lagrangian that links the interactions between light physics (zero modes) and heavy physics (excited KK gauge modes) is presented. Concerning the radiative corrections of the excited KK modes on the light Green's functions, the predictive character of this Lagrangian at the one-loop level is stressed. In the case of the gauge parameters confined to the 3-brane, the known result in the literature is reproduced with some minor variants, although it is emphasized that the exited KK modes are not gauge fields but matter fields that transform under the adjoint representation of $S{U}_{4}(N)$. The Dirac method is employed to show that this theory is subject to both first- and second-class constraints, which arise from the zero and excited KK modes, respectively.

Curvature function and coarse graining

A classic theorem in the theory of connections on principal fiber bundles states that the evaluation of all holonomy functions gives enough information to characterize the bundle structure (among those sharing the same structure group and base manifold) and the connection up to a bundle equivalence map. This result and other important properties of holonomy functions have encouraged their use as the primary ingredient for the construction of families of quantum gauge theories. However, in these applications often the set of holonomy functions used is a discrete proper subset of the set of holonomy functions needed for the characterization theorem to hold. We show that the evaluation of a discrete set of holonomy functions does not characterize the bundle and does not constrain the connection modulo gauge appropriately. We exhibit a discrete set of functions of the connection and prove that in the abelian case their evaluation characterizes the bundle structure (up to equivalence), and constrains the connection modulo gauge up to “local details” ignored when working at a given scale. The main ingredient is the Lie algebra valued curvature function \documentclass[12pt]{minimal}\begin{document}$F_S (A)$\end{document}FS(A) defined below. It covers the holonomy function in the sense that \documentclass[12pt]{minimal}\begin{document}$\exp {F_S (A)} = {\rm Hol}(l= \partial S , A)$\end{document}expFS(A)= Hol (l=∂S,A).

Quantum gauge models without (classical) Higgs mechanism

We examine the status of massive gauge theories, such as those usually obtained by spontaneous symmetry breakdown, from the viewpoint of causal (Epstein-Glaser) renormalization. The BRS formulation of gauge invariance in this framework, starting from canonical quantization of massive (as well as massless) vector bosons as fundamental entities, and proceeding perturbatively, allows one to rederive the reductive group symmetry of interactions, the need for scalar fields in gauge theory, and the covariant derivative. Thus the presence of higgs particles is explained without recourse to a Higgs(-Englert-Brout-Guralnik-Hagen-Kibble) mechanism. Along the way, we dispel doubts about the compatibility of causal gauge invariance with grand unified theories.

Appearance of gauge fields and forces beyond the adiabatic approximation

We investigate the origin of quantum geometric phases, gauge fields and forces beyond the adiabatic regime. In particular, we extend the notions of geometric magnetic and electric forces discovered in studies of the Born–Oppenheimer approximation to arbitrary quantum systems described by matrix-valued quantum Hamiltonians. The results are illustrated by several physical relevant examples.

LHC signals for coset electroweak gauge bosons in warped/composite pseudo-Goldstone boson Higgs models

The framework of a warped extra dimension with the Standard Model (SM) fields propagating in it is a very well-motivated extension of the SM since it can address both the Planck-weak and flavor hierarchy problems of the SM. Within this framework, solution to the little hierarchy problem motivates extending the SM electroweak (EW) 5D gauge symmetry in such a way that its breakdown to the SM delivers the SM Higgs boson. We study signals at the large hadron collider (LHC) for the extra EW (called coset) gauge bosons, a fundamental ingredient of this framework. The coset gauge bosons, due to their unique EW gauge quantum numbers [doublets of SU(2)_L], do not couple at leading order to two SM particles. We find that, using the associated production of the charged coset gauge bosons via their coupling to SM bottom quark and a (light) KK top quark, the LHC can have a 3\sigma reach of \sim 2 (2.6) TeV for the coset gauge boson masses with \sim 100 (1000) fb^{-1} luminosity. Since current theoretical framework(s) suggest an {\em indirect} lower limit on coset gauge boson masses of >3 TeV, luminosity or energy upgrade of LHC is likely to be crucial in observing these states.

Novel TeV-scale seesaw mechanism with Dirac mediators

We propose novel tree level seesaw mechanism with TeV-scale vectorlike Dirac mediators that produce Majorana masses of the known neutrinos. The gauge quantum number assignment to the Dirac mediators allows them to belong to a weak triplet and a five-plet of non-zero hypercharge. The latter leads to new seesaw formula mν∼v6/M5, so that the empirical masses mν∼10−1 eV can be achieved by M∼TeV new states. There is a limited range of the parameter space with M⩽a few100 GeV where the tree level contribution dominates over the respective loop contributions and the proposed mechanism is testable at the LHC. We discuss specific signatures for Dirac type heavy leptons produced by Drell–Yan fusion at the LHC.

Non-perturbative Effective Action in Gauge Theories and Quantum Gravity

We use our recently developed algebraic methods for the calculation of the heat kernel on homogeneous bundles over symmetric spaces to evaluate the non-perturbative low-energy effective action in quantum general relativity and Yang-Mills gauge theory in curved space. We obtain an exact integral repesentation for the effective action that generates all terms in the standard asymptotic epxansion of the effective action without derivatives of the curvatures effectively summing up the whole infinite subseries of all quantum corrections with low momenta.

Production of isolated Higgs particle at the Large Hadron Collider

Theoretical predictions are presented for the process p+p→A+H+B, where H is the Higgs particle and A (B) is a group of particles that mostly goes down one (the other) beam pipe. These predictions are obtained using results from relativistic quantum gauge field theory and the fact that, for the Large Hadron Collider (LHC), the center-of-mass energy ≫ Higgs mass ≫ proton mass. The average transverse momentum of the produced Higgs particle is of the order of 1 GeV/c. This process leads naturally to the concept of considering the LHC as a Pomeron Collider.

Time-Dependent Variational Approach to the Non-Abelian Pure Gauge Theory: Its Application to Evaluation of the Shear Viscosity of Quantum Gluonic Matter

The time-dependent variational approach to the pure Yang-Mills gauge theory, especially a color su(3) gauge theory, is formulated in the functional Schroedinger picture with a Gaussian wave functional approximation. The equations of motion for the quantum gauge fields are formulated in the Liouville-von Neumann form. This variational approach is applied in order to derive the transport coefficients, such as the shear viscosity, for the pure gluonic matter by using the linear response theory. As a result, the contribution to the shear viscosity from the quantum gluons is zero up to the lowest order of the coupling g in the quantum gluonic matter.

Super-horizon cosmic string correlations

When gauged cosmic strings form in a symmetry-breaking phase transition, the gauge field configuration at the time becomes imprinted in the spatial string distribution by the flux trapping mechanism. Causality and flux conservation suggest that quantum and thermal gauge field fluctuations give rise to long-range super-horizon correlations in the string network. Classical field theory simulations in the Abelian Higgs model confirm this finding. In contrast, the Kibble-Zurek mechanism, which most cosmic string studies are based on, only gives rise to short-distance, subhorizon correlations. These results may have implications for cosmology, and it may also be possible to test them in superconductor experiments.

Quarks in Coulomb gauge perturbation theory

Coulomb gauge quantum chromodynamics within the first order functional formalism is considered. The quark contributions to the Dyson-Schwinger equations are derived and one-loop perturbative results for the two-point functions are presented.

A Gauge Model for Quantum Mechanics on a Stratified Space

In the Hamiltonian approach on a single spatial plaquette, we construct a quantum (lattice) gauge theory which incorporates the classical singularities. The reduced phase space is a stratified K\"ahler space, and we make explicit the requisite singular holomorphic quantization procedure on this space. On the quantum level, this procedure furnishes a costratified Hilbert space, that is, a Hilbert space together with a system which consists of the subspaces associated with the strata of the reduced phase space and of the corresponding orthoprojectors. The costratified Hilbert space structure reflects the stratification of the reduced phase space. For the special case where the structure group is $\mathrm{SU}(2)$, we discuss the tunneling probabilities between the strata, determine the energy eigenstates and study the corresponding expectation values of the orthoprojectors onto the subspaces associated with the strata in the strong and weak coupling approximations.

On localization properties of Fourier transforms of hyperfunctions

In [A.G. Smirnov, Fourier transformation of Sato's hyperfunctions, Adv. Math. 196 (2005) 310–345] the author introduced a new generalized function space U ( R k ) which can be naturally interpreted as the Fourier transform of the space of Sato's hyperfunctions on R k . It was shown that all Gelfand–Shilov spaces S α ′ 0 ( R k ) ( α > 1 ) of analytic functionals are canonically embedded in U ( R k ) . While the usual definition of support of a generalized function is inapplicable to elements of S α ′ 0 ( R k ) and U ( R k ) , their localization properties can be consistently described using the concept of carrier cone introduced by Soloviev [M.A. Soloviev, Towards a generalized distribution formalism for gauge quantum fields, Lett. Math. Phys. 33 (1995) 49–59; M.A. Soloviev, An extension of distribution theory and of the Paley–Wiener–Schwartz theorem related to quantum gauge theory, Comm. Math. Phys. 184 (1997) 579–596]. In this paper, the relation between carrier cones of elements of S α ′ 0 ( R k ) and U ( R k ) is studied. It is proved that an analytic functional u ∈ S α ′ 0 ( R k ) is carried by a cone K ⊂ R k if and only if its canonical image in U ( R k ) is carried by K.

Hamiltonian approach to 1 + 1 dimensional Yang–Mills theory in Coulomb gauge

We study the Hamiltonian approach to 1 + 1 dimensional Yang–Mills theory in Coulomb gauge, considering both the pure Coulomb gauge and the gauge where in addition the remaining constant gauge field is restricted to the Cartan algebra. We evaluate the corresponding Faddeev–Popov determinants, resolve Gauss’ law and derive the Hamiltonians, which differ in both gauges due to additional zero modes of the Faddeev–Popov kernel in the pure Coulomb gauge. By Gauss’ law the zero modes of the Faddeev–Popov kernel constrain the physical wave functionals to zero colour charge states. We solve the Schrödinger equation in the pure Coulomb gauge and determine the vacuum wave functional. The gluon and ghost propagators and the static colour Coulomb potential are calculated in the first Gribov region as well as in the fundamental modular region, and Gribov copy effects are studied. We explicitly demonstrate that the Dyson–Schwinger equations do not specify the Gribov region while the propagators and vertices do depend on the Gribov region chosen. In this sense, the Dyson–Schwinger equations alone do not provide the full non-abelian quantum gauge theory, but subsidiary conditions must be required. Implications of Gribov copy effects for lattice calculations of the infrared behaviour of gauge-fixed propagators are discussed. We compute the ghost–gluon vertex and provide a sensible truncation of Dyson–Schwinger equations. Approximations of the variational approach to the 3 + 1 dimensional theory are checked by comparison to the 1 + 1 dimensional case.

Universal structure of subleading infrared poles in gauge theory amplitudes

We study the origin of subleading soft and collinear poles of form factors and amplitudes in dimensionally-regulated massless gauge theories. In the case of form factors of fundamental fields, these poles originate from a single function of the coupling, denoted G(alpha_s), depending on both the spin and gauge quantum numbers of the field. We relate G(alpha_s) to gauge-theory matrix elements involving the gluon field strength. We then show that G(alpha_s) is the sum of three terms: a universal eikonal anomalous dimension, a universal non-eikonal contribution, given by the coefficient B_delta (alpha_s) of delta(1 - z) in the collinear evolution kernel, and a process-dependent short-distance coefficient function, which does not contribute to infrared poles. Using general results on the factorization of soft and collinear singularities in fixed-angle massless gauge theory amplitudes, we conclude that all such singularities are captured by the eikonal approximation, supplemented only by the knowledge of B_delta (alpha_s). We explore the consequences of our results for conformal gauge theories, where in particular we find a simple exact relation between the form factor and the cusp anomalous dimension.