Mario Serna

Riemannian gauge theory and charge quantization

In a traditional gauge theory, the matter fields a and the gauge fields Acμ are fundamental objects of the theory. The traditional gauge field is similar to the connection coefficient in the riemannian geometry covariant derivative, and the field-strength tensor is similar to the curvature tensor. In contrast, the connection in riemannian geometry is derived from the metric or an embedding space. Guided by the physical principal of increasing symmetry among the four forces, we propose a different construction. Instead of defining the transformation properties of a fundamental gauge field, we derive the gauge theory from an embedding of a gauge fiber F = n or F = n into a trivial, embedding vector bundle = N or = N where n

Advanced IR detector devices and concepts for remote sensing

>N>n. Our new action is symmetric between the gauge theory and the riemannian geometry. By expressing gauge-covariant fields in terms of the orthonormal gauge basis vectors, we recover a traditional, SO(n) or U(n) gauge theory. In contrast, the new theory has all matter fields on a particular fiber couple with the same coupling constant. Even the matter fields on a 1 fiber, which have a U(1) symmetry group, couple with the same charge of ±q. The physical origin of this unique coupling constant is a generalization of the general relativity equivalence principle. Because our action is independent of the choice of basis, its natural invariance group is GL(n,) or GL(n,). Last, the new action also requires a small correction to the general-relativity action proportional to the square of the curvature tensor.

The geometric origin of electric force

In the Advanced Detectors Research Group within the Space-Based Optical Sensing Center of Excellence in the Spacecraft Technology Division of the Air Force Research Laboratory’s Space Vehicles Directorate, we look to enhance existing detector technologies and develop new detector capabilities for future space-based surveillance missions. To that end, we present some ideas for tuning the wavelength response of detectors throughout the IR (using applied electric or magnetic fields or via a lateral biasing technique). We also present a concept for detecting the full polarization vector of a signal within a single pixel of a quantum well detector.

Unifying Geometrical Representations of Gauge Theory

Every textbook on quantumfield theory points out the formal, mathematical parallels between gauge theory and general relativity. In this paper, we make these parallels visual. The differential geometry behind general relativity can be visualized using an embedding space. We will use similar embedding techniques to show the spatial geometry associated with an electricfield. As one might expect from the Lagrangian, electricfields have time-changing geometry. This paper focuses on exposing the geometrical origin of electric force by using both a near-exact solution and a more simple, physically insightful, approximate solution.

Spaceship with a thruster -- one body, one force

We unify three approaches within the vast body of gauge-theory research that have independently developed distinct representations of a geometrical surface-like structure underlying the vector-potential. The three approaches that we unify are: those who use the compactified dimensions of Kaluza–Klein theory, those who use Grassmannian models (also called gauge theory embedding or

Measurement of gravitational time dilation: An undergraduate research project

CP^{N-1}

Polarimeter using quantum well stacks separated by gratings

CPN-1 models) to represent gauge fields, and those who use a hidden spatial metric to replace the gauge fields. In this paper we identify a correspondence between the geometrical representations of the three schools. Each school was mostly independently developed, does not compete with other schools, and attempts to isolate the gauge-invariant geometrical surface-like structures that are responsible for the resulting physics. By providing a mapping between geometrical representations, we hope physicists can now isolate representation-dependent physics from gauge-invariant physical results and share results between each school. We provide visual examples of the geometrical relationships between each school for