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Kevin Cahill

Publications and source records attributed to Kevin Cahill.

51 records · Page 3Linked to original sources
arXiv1999

Elements of Supersymmetry

These notes are intended to provide an introduction to supersymmetry. The notes begin with supersymmetric quantum mechanics and the basic properties of spinor fields. The supersymmetry of simple theories of spin-zero and spin-one-half fields is discussed with emphasis upon the charges that generate the transformations of supersymmetry. Abelian and non-abelian supersymmetric gauge theories are characterized in their simpler and more general forms. Superfields are defined, and the concise notation they make possible is described. The minimal supersymmetric standard model is discussed with particular attention to the Higgs fields and the electro-weak superpotential.

hep-ph↗
arXiv1999

Condensates Break Chiral Symmetry

In the physical vacuum of QCD, the energy density of light-quark fields strongly coupled to slowly varying gluon fields can be negative. The states that drive this energy density lowest are condensates of pairs of quarks and antiquarks of nearly opposite momenta. These quark-antiquark condensates break chiral symmetry. They may also affect other features of hadronic physics, such as the range of the strong force and the confinement of color.

hep-ph↗
arXiv1998

Chiral Symmetry and Quark Confinement

In the physical vacuum of QCD, the energy density of light-quark fields strongly coupled to slowly varying gluon fields can be negative, and so a condensate of pairs of quarks and antiquarks of nearly opposite momenta forms which breaks chiral symmetry, confines quarks, and makes gluons massive.

hep-ph↗
arXiv1998

Noncompact, Gauge-Invariant Simulations of U(1), SU(2), and SU(3)

We have applied a new noncompact, gauge-invariant, Monte Carlo method to simulate the U(1), SU(2), and SU(3) gauge theories on 8^4 and 12^4 lattices. For U(1) the Creutz ratios of the Wilson loops agree with the exact results for beta > 0.5 after a renormalization of the charge. The SU(2) and SU(3) Creutz ratios robustly display quark confinement at beta = 0.5 and beta = 2, respectively. At much weaker coupling, the SU(2) and SU(3) Creutz ratios agree with perturbation theory after a renormalization of the coupling constant. For SU(3) without quarks, our lattice QCD parameter is Lambda_L = 130 +- 18$ MeV.

hep-lat↗
arXiv1996

Better Actions

We explain why compact U(1) confines and how to fix it. We show that plaquettes of negative trace carry most of the confinement signal in compact SU(2). We show how to perform noncompact gauge-invariant simulations without auxiliary fields. We suggest a way to simulate fermions without doublers.

hep-lat↗
arXiv1995

Lattice Fermions without Doublers

By placing fermions only on the even sites of a lattice, one may halve the momentum spectrum and construct a theory without doublers. The interaction is nonlocal. The fermion propagator is not a sparse matrix, but because the unwanted fermionic states are absent from the formalism, it is 256 times smaller than the usual propagator.

hep-lat↗
arXiv1995

Noncompact Gauge-Invariant Simulations of U(1), SU(2), and SU(3)

We have applied a new gauge-invariant, noncompact, Monte Carlo method to simulate the $U(1)$, $SU(2)$, and $SU(3)$ gauge theories on $8^4$ and $12^4$ lattices. The Creutz ratios of the Wilson loops agree with the exact results for $U(1)$ for $β\ge 0.5$ apart from a renormalization of the charge. The $SU(2)$ and $SU(3)$ Creutz ratios robustly display quark confinement at $β= 0.5$ and $β= 2$, respectively. At much weaker coupling, the $SU(2)$ and $SU(3)$ Creutz ratios agree with perturbation theory after a renormalization of the coupling constant. For $SU(3)$ the scaling window is near $ β= 2 $, and the relation between the string tension $σ$ and our lattice QCD parameter $ Λ_L $ is $\sqrtσ \approx 5 Λ_L$.

hep-lat↗
arXiv1994

Noncompact Gauge-Invariant Lattice Simulations

We have applied a new gauge-invariant, noncompact, Monte Carlo method to simulate $U(1)$, $SU(2)$, and $SU(3)$ gauge theories on $8^4$ and $12^4$ lattices. The Creutz ratios of the Wilson loops agree with the exact results for $U(1)$ for $β\ge 1$ apart from a renormalization of the charge. The $SU(2)$ and $SU(3)$ Creutz ratios robustly display quark confinement at $β= 0.5$ and $β= 1.5$, respectively. At much weaker coupling, the $SU(2)$ and $SU(3)$ Creutz ratios agree with perturbation theory after a renormalization of the coupling constant.

hep-lat↗
arXiv1994

Gauge-Invariant Noncompact Lattice Simulations

Three techniques for performing gauge-invariant, noncompact lattice simulations of nonabelian gauge theories are discussed. In the first method, the action is not itself gauge invariant, but a kind of lattice gauge invariance is restored by random compact gauge transformations during the successive sweeps of the simulation. This method has been applied to pure $SU(2)$ gauge theory on a $12^4$ lattice, and Wilson loops have been measured at strong coupling, $β=0.5$. These Wilson loops display a confinement signal not seen in simulations performed earlier with the same action but without the random gauge transformations. In the second method, the action is gauge symmetrized by integrations over the group manifold. The third method is based upon a new, noncompact form of the action that is exactly invariant under lattice gauge transformations. The action is a natural discretization of the classical Yang-Mills action.

hep-lat↗
arXiv1994

A More-Effective Potential

In theories with spontaneous symmetry breaking, the loop expansion of the effective potential is awkward. In such theories, the exact effective potential $V(ϕ_c,T)$ is real and convex (as a function of the classical field $ϕ_c$), but its perturbative series can be complex with a real part that is concave. These flaws limit the utility of the effective potential, particularly in studies of the early universe. A generalization of the effective potential is available that is real, that has no obvious convexity problems, and that can be computed in perturbation theory. For the theory with classical potential $V(ϕ) = (λ/4)(ϕ^2 - σ^2)^2$, this more-effective potential closely tracks the usual effective potential where the latter is real $|ϕ_c| \geq σ/\sqrt{3}$ and naturally extends it to $ϕ_c = 0$, revealing that the critical temperature at the one-loop level runs from $T_C \approx 1.81 σ$ for $λ= 0.1$ to $T_C \approx 1.74 σ$ for $λ= 1$.

hep-ph↗
arXiv1993

The Fourth Root of Gravity

By attaching basis vectors to the components of matter fields, one may render free action densities fully covariant. Both the connection and the tetrads are quadratic forms in these basis vectors. The metric of spacetime, which is quadratic in the tetrads, is then quartic in the basis vectors.

gr-qc↗
arXiv1992

A More Effective Potential

In theories with spontaneous symmetry breaking, the conventional effective potential possesses a defective loop expansion. For such theories, the exact effective potential $V(ϕ_c,T)$ is real and convex, but its perturbative series is complex and concave at small $ϕ_c$ and $T$. A more effective potential is available.

hep-ph↗