Rigid Gauge Research Articles

Dirac sigma models from gauging

Abstract The G/G WZW model results from the WZW-model by a standard procedure of gauging. G/G WZW models are members of Dirac sigma models, which also contain twisted Poisson sigma models as other examples. We show how the general class of Dirac sigma models can be obtained from a gauging procedure adapted to Lie algebroids in the form of an equivariantly closed extension. The rigid gauge groups are generically infinite dimensional and a standard gauging procedure would give a likewise infinite number of 1-form gauge fields; the proposed construction yields the requested finite number of them. Although physics terminology is used, the presentation is kept accessible also for a mathematical audience.

Dynamical Locality of the Free Scalar Field

Dynamical locality is a condition on a locally covariant physical theory, asserting that kinematic and dynamical notions of local physics agree. This condition was introduced in [arXiv:1106.4785], where it was shown to be closely related to the question of what it means for a theory to describe the same physics on different spacetimes. In this paper, we consider in detail the example of the free minimally coupled Klein--Gordon field, both as a classical and quantum theory (using both the Weyl algebra and a smeared field approach). It is shown that the massive theory obeys dynamical locality, both classically and in quantum field theory, in all spacetime dimensions $n\ge 2$ and allowing for spacetimes with finitely many connected components. In contrast, the massless theory is shown to violate dynamical locality in any spacetime dimension, in both classical and quantum theory, owing to a rigid gauge symmetry. Taking this into account (equivalently, working with the massless current) dynamical locality is restored in all dimensions $n\ge 2$ on connected spacetimes, and in all dimensions $n\ge 3$ if disconnected spacetimes are permitted. The results on the quantized theories are obtained using general results giving conditions under which dynamically local classical symplectic theories have dynamically local quantizations.

Water temperature and concentration measurements within the expanding blast wave of a high explosive

We present an application of absorption spectroscopy to directly measure temperature and concentration histories of water vapor within the expansion of a high explosive detonation. While the approach of absorption spectroscopy is well established, the combination of a fast, near-infrared array, broadband light source, and rigid gauge allow the first application of time-resolved absorption measurements in an explosive environment. The instrument is demonstrated using pentaerythritol tetranitrate with a sampling rate of 20 kHz for 20 ms following detonation. Absorption by water vapor is measured between 1335 and 1380 nm. Water temperatures are determined by fitting experimental transmission spectra to a simulated database. Water mole fractions are deduced following the temperature assignment. The sources of uncertainty and their impact on the results are discussed. These measurements will aid the development of chemical-specific reaction models and the predictive capability in technical fields including combustion and detonation science.

A search for non-perturbative dualities of local N = 2 Yang - Mills theories from Calabi - Yau 3-folds

The generalization of the rigid special geometry of the vector multiplet quantum moduli space to the case of supergravity is discussed through the notion of a dynamical Calabi - Yau 3-fold. Duality symmetries of this manifold are connected with the analogous dualities associated with the dynamical Riemann surface of the rigid theory. N = 2 rigid gauge theories are reviewed in a framework ready for comparison with the local case. As a byproduct we give in general the full duality group (quantum monodromy) for an arbitrary rigid SU(r+1) gauge theory, extending previous explicit constructions for the r = 1,2 cases. In the coupling to gravity, R-symmetry and monodromy groups of the dynamical Riemann surface, whose structure we discuss in detail, are embedded into the symplectic duality group associated with the moduli space of the dynamical Calabi - Yau 3-fold.

Bose-Einstein condensation for interacting scalar fields in curved spacetime.

We consider the model of self-interacting complex scalar fields with a rigid gauge invariance under an arbitrary gauge group $G$. In order to analyze the phenomenon of Bose-Einstein condensation finite temperature and the possibility of a finite background charge is included. Different approaches to derive the relevant high-temperature behaviour of the theory are presented.

Body fixed frame, rigid gauge rotations and largeN random fields in QCD

The "body fixed frame" with respect to local gauge transformations is introduced. Rigid gauge "rotations" in QCD and their \Sch equation are studied for static and dynamic quarks. Possible choices of the rigid gauge field configuration corresponding to a nonvanishing static colormagnetic field in the "body fixed" frame are discussed. A gauge invariant variational equation is derived in this frame. For large number N of colors the rigid gauge field configuration is regarded as random with maximally random probability distribution under constraints on macroscopic--like quantities. For the uniform magnetic field the joint probability distribution of the field components is determined by maximizing the appropriate entropy under the area law constraint for the Wilson loop. In the quark sector the gauge invariance requires the rigid gauge field configuration to appear not only as a background but also as inducing an instantaneous quark-quark interaction. Both are random in the large N limit.

Rigid quantization of the Skyrmion

We present a detailed discussion of the rigid quantization scheme for rotating skyrmions. We pay special attention to ordering problems and their repercussion on the pion-baryon coupling. We derive the pion-baryon vertex in the rigid gauge and discuss the baryon form factor. We show that the “radiation problem” for rotating skyrmions is due to neglect of operator ordering and restriction to K = 0 waves.

Rigid gauge symmetry in the SU(2) Higgs model without gauge fixing

A nonlocal order parameter is introduced for the spontaneous breakdown of rigid gauge symmetry in lattice Higgs models without fixing the gauge. At zero and finite temperatures, numerical result from the SU(2) Higgs model suggests the existence of an underlying phase transition, which coincides with the Higgs transition but extends beyond its end point to separate the Higgs and the confinement region completely.

Automorphic field theory-some mathematical issues

The general structure of field theories on multiply connected spaces is presented using the universal covering space concept. Restriction to rigid gauge theories allows the use of representation theory to answer several relevant mathematical questions.