Massive Degeneracy and Goldstone Bosons: A Challenge for the Light Cone

Wherein it is argued that the light front formalism has problems dealing with Goldstone symmetries. It is further argued that the notion that in hadron condensates can explain Goldstone phenomena is false.Comment: 7 pages, 5 figures, Invited Talk at Light Cone 2010, Valencia Spai

CORE: Frustrated Magnets, Charge Fractionalization and QCD

I explain how to use a simple method to extract the physics of lattice Hamiltonian systems which are not easily analyzed by exact or other numerical methods. I will then use this method to establish the relationship between QCD and a special class of generalized, highly frustrated anti-ferromagnets.Comment: Invited talk at Light-Cone 2004, 16 pages, 10 figure

A Different Look at Dark Energy and the Time Variation of Fundamental Constants

This paper makes the simple observation that a fundamental length, or cutoff, in the context of Friedmann-Lema\^itre-Robertson-Walker (FRW) cosmology implies very different things than for a static universe. It is argued that it is reasonable to assume that this cutoff is implemented by fixing the number of quantum degrees of freedom per co-moving volume (as opposed to a Planck volume) and the relationship of the vacuum-energy of all of the fields in the theory to the cosmological constant (or dark energy) is re-examined. The restrictions that need to be satisfied by a generic theory to avoid conflicts with current experiments are discussed, and it is shown that in any theory satisfying these constraints knowing the difference between $w$ and minus one allows one to predict $\dot{w}$. It is argued that this is a robust result and if this prediction fails the idea of a fundamental cutoff of the type being discussed can be ruled out. Finally, it is observed that, within the context of a specific theory, a co-moving cutoff implies a predictable time variation of fundamental constants. This is accompanied by a general discussion of why this is so, what are the strongest phenomenological limits upon this predicted variation, and which limits are in tension with the idea of a co-moving cutoff. It is pointed out, however, that a careful comparison of the predicted time variation of fundamental constants is not possible without restricting to a particular model field-theory and that is not done in this paper.Comment: 7 page

Adaptive Perturbation Theory I: Quantum Mechanics

Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that heretofore were not believed to be obtainable by such methods. The novel feature of adaptive perturbation theory is that it decomposes a given Hamiltonian, $H$, into an unperturbed part and a perturbation in a way which extracts the leading non-perturbative behavior of the problem exactly. This paper introduces the method in the context of the pure anharmonic oscillator and then goes on to apply it to the case of tunneling between both symmetric and asymmetric minima. It concludes with an introduction to the extension of these methods to the discussion of a quantum field theory. A more complete discussion of this issue will be given in the second paper in this series. This paper will show how to use the method of adaptive perturbation theory to non-perturbatively extract the structure of mass, wavefunction and coupling constant renormalization.Comment: 21 pages, 4 figures, uses psfig.sty. This paper is being replaced to add references to previously published work which I became aware of after posting the original pape