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Register a new userDark matter, Elko fields and Weinbergs quantum field theory formalism
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The Elko quantum field was introduced by Ahluwalia and Grumiller, who proposed it as a candidate for dark matter. We study the Elko field in Weinbergs formalism for quantum field theory. We prove that if one takes the symmetry group to be the full Poincare group then the Elko field is not a quantum field in the sense of Weinberg. This confirms results of Ahluwalia, Lee and Schritt, who showed using a different approach that the Elko field does not transform covariantly under rotations and hence has a preferred axis.
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The Casimir effect for {mass dimension one fermion fields (sometimes called Elko)} in $3+1$ dimension is obtained using Dirichlet boundary conditions. It is shown the existence of a repulsive force four times greater than the case of the scalar field. The precise reason for such differences are highlighted and interpreted, as well as the right parallel of the Casimir effect due to scalar and fermionic fields.
We here provide further details on the construction and properties of mass dimension one quantum fields based on Elko expansion coefficients. We show that by a judicious choice of phases, the locality structure can be dramatically improved. In the process we construct a fermionic dark matter candidate which carries not only an unsuppressed quartic self interaction but also a preferred axis. Both of these aspects are tentatively supported by the data on dark matter.
The Elko field of Ahluwalia and Grumiller is a quantum field for massive spin-1/2 particles. It has been suggested as a candidate for dark matter. We discuss our attempts to interpret the Elko field as a quantum field in the sense of Weinberg. Our work suggests that one should investigate quantum fields based on representations of the full Poincare group which belong to one of the non-standard Wigner classes.
We discuss the renormalisation of the initial value problem in quantum field theory using the two-particle irreducible (2PI) effective action formalism. The nonequilibrium dynamics is renormalised by counterterms determined in equilibrium. We emphasize the importance of the appropriate choice of initial conditions and go beyond the Gaussian initial density operator by defining self-consistent initial conditions. We study the corresponding time evolution and present a numerical example which supports the existence of a continuum limit for this type of initial conditions.
The holomorphic Coulomb gas formalism is a set of rules for computing minimal model observables using free field techniques. We attempt to derive and clarify these rules using standard techniques of QFT. We begin with a careful examination of the timelike linear dilaton. Although the background charge $Q$ breaks the scalar fields continuous shift symmetry, the exponential of the action is invariant under a discrete shift because $Q$ is imaginary. Gauging this symmetry makes the dilaton compact and introduces winding modes into the spectrum. One of these winding operators corresponds to the BRST current first introduced by Felder. The cohomology of this BRST charge isolates the irreducible representations of the Virasoro algebra within the linear dilaton Fock space, and the supertrace in the BRST complex reproduces the minimal model partition function. The model at the radius $R=sqrt{pp}$ has two marginal operators corresponding to the Dotsenko-Fateev screening charges. Deforming by them, we obtain a model that might be called a BRST quotiented compact timelike Liouville theory. The Hamiltonian of the zero-mode quantum mechanics is not Hermitian, but it is $PT$-symmetric and exactly solvable. Its eigenfunctions have support on an infinite number of plane waves, suggesting an infinite reduction in the number of independent states in the full QFT. Applying conformal perturbation theory to the exponential interactions reproduces the Coulomb gas calculations of minimal model correlators. In contrast to spacelike Liouville, these resonance correlators are finite because the zero mode is compact. We comment on subtleties regarding the reflection operator identification, as well as naive violations of truncation in correlators with multiple reflection operators inserted. This work is part of an attempt to understand the relationship between JT gravity and the $(2,p)$ minimal string.
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