1,527 research outputs found

### Geometrization of the Dirac theory of the electron

Using the concept of parallel displacement of a half vector, the Dirac equations are generally written in invariant form. The energy tensor is formed and both the macroscopic and quantum mechanic equations of motion are set up. The former have the usual form: divergence of the energy tensor equals the Lorentz force and the latter are essentially identical with those of the geodesic line

### Phase transitions in spinor quantum gravity on a lattice

We construct a well-defined lattice-regularized quantum theory formulated in
terms of fundamental fermion and gauge fields, the same type of degrees of
freedom as in the Standard Model. The theory is explicitly invariant under
local Lorentz transformations and, in the continuum limit, under
diffeomorphisms. It is suitable for describing large nonperturbative and
fast-varying fluctuations of metrics. Although the quantum curved space turns
out to be on the average flat and smooth owing to the non-compressibility of
the fundamental fermions, the low-energy Einstein limit is not automatic: one
needs to ensure that composite metrics fluctuations propagate to long distances
as compared to the lattice spacing. One way to guarantee this is to stay at a
phase transition.
We develop a lattice mean field method and find that the theory typically has
several phases in the space of the dimensionless coupling constants, separated
by the second order phase transition surface. For example, there is a phase
with a spontaneous breaking of chiral symmetry. The effective low-energy
Lagrangian for the ensuing Goldstone field is explicitly
diffeomorphism-invariant. We expect that the Einstein gravitation is achieved
at the phase transition. A bonus is that the cosmological constant is probably
automatically zero.Comment: 37 pages, 12 figures Discussion of dimensions and of the
Berezinsky--Kosterlitz--Thouless phase adde

### Accuracy of Electronic Wave Functions in Quantum Monte Carlo: the Effect of High-Order Correlations

Compact and accurate wave functions can be constructed by quantum Monte Carlo
methods. Typically, these wave functions consist of a sum of a small number of
Slater determinants multiplied by a Jastrow factor. In this paper we study the
importance of including high-order, nucleus-three-electron correlations in the
Jastrow factor. An efficient algorithm based on the theory of invariants is
used to compute the high-body correlations. We observe significant improvements
in the variational Monte Carlo energy and in the fluctuations of the local
energies but not in the fixed-node diffusion Monte Carlo energies. Improvements
for the ground states of physical, fermionic atoms are found to be smaller than
those for the ground states of fictitious, bosonic atoms, indicating that
errors in the nodal surfaces of the fermionic wave functions are a limiting
factor.Comment: 9 pages, no figures, Late

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