We point out the existence of a class of non-Gaussian yet free “quantum field theories” in 0+0 dimensions, based on a cubic action classified by simple Lie groups. A “three-pronged” version of the Wick theorem applies. (LPTHE-P03-01, hep-th/0302043) With the exception of a few integrable models in low dimension, much of what we know of quantum field theory relies on perturbation around a free t...

Finsler geometry motivates a generalization of the Riemannian structure of spacetime to include dependence of the spacetime metric and associated invariant tensor fields on the four-velocity coordinates as well as the spacetime coordinates of the observer. It is then useful to consider the tangent bundle of spacetime with spacetime in the base manifold and four-velocity space in the fiber. A ph...

Attempts to apply effective field theory (EFT) methods to nonrelativistic nucleon-nucleon (N N) scattering have raised questions about the nature and limitations of an EFT expansion when used nonperturbatively. We discuss the characteristics of a meaningful EFT analysis and compare them with traditional approaches to N N scattering. A key feature of an EFT treatment is a systematic expansion in...

Class field theory furnishes an intrinsic description of the abelian extensions of a number field which is in many cases not of an immediate algorithmic nature. We outline the algorithms available for the explicit computation of such extensions.

Supersymmetric theories are reviewed in the context of field theories. The gauge hierarchy problem in attempting the unification of all fundamental interactions is the strongest motivation of modern development of supersymmetry. Starting from the general notion of supersymmetry as a symmetry between bosons and fermions, we explain how the supersymmetry becomes a part of the space-time symmetry ...

The pioneering work of early non-relativistic quantum theory led to the understanding that quantum dynamics on Hilbert space is a comprehensive predictive framework for microscopic phenomena. From the Bohr atom, through the nonrelativistic quantum theory of Schrödinger and Heisenberg, and the relativistic Dirac equation for hydrogen, agreement between calculation and experiment improved rapidly...

Several theories of conscious first described about a decade ago, including the conscious electromagnetic information (CEMI) field theory, claimed that the substrate of consciousness is the brain’s electromagnetic (EM) field. These theories were prompted by the observation, in many diverse systems, that synchronous neuronal firing, which generates coherent EM fields, was a strong correlate of a...