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Specialized computational chemistry packages have permanently reshaped the landscape of chemical and materials science by providing tools to support and guide experimental efforts and for the prediction of atomistic and electronic properties. In this regard, electronic structure packages have played a special role by using first-principledriven methodologies to model complex chemical and materials processes. Over the last few decades, the rapid development of computing technologies and the tremendous increase in computational power have offered a unique chance to study complex transformations using sophisticated and predictive many-body techniques that describe correlated behavior of electrons in molecular and condensed phase systems at different levels of theory. In enabling these simulations, novel parallel algorithms have been able to take advantage of computational resources to address the polynomial scaling of electronic structure methods. In this paper, we briefly review the NWChem computational chemistry suite, including its history, design principles, parallel tools, current capabilities, outreach and outlook., Comment: This article appeared in volume 152, issue 18, page 184102 of the Journal of Chemical Physics. It can be found at https://doi.org/10.1063/5.0004997

The $(3 + 1)$-dimensional (generalized) Dirac equation is shown to have the same form as the equation expressing the condition that a given point lies on a given line in 3-dimensional projective space. The resulting Hamiltonian with a $\gamma_5$ mass term is not Hermitian, but is invariant under the combined transformation of parity reflection $\cal P$ and time reversal $\cal T$. When the $\cal PT$ symmetry is unbroken, the energy spectrum of the free spin-$\frac {1}{2}$ theory is real, with an appropriately shifted mass., Comment: 7 pages, LaTeX; version accepted for publication in Phys. Lett. B; revised version incorporates useful suggestions from an anonymous referee

Due to quantum fluctuations, spacetime is probably ``foamy'' on very small scales. We propose to detect this texture of spacetime foam by looking for core-halo structures in the images of distant quasars. We find that the Very Large Telescope interferometer will be on the verge of being able to probe the fabric of spacetime when it reaches its design performance. Our method also allows us to use spacetime foam physics and physics of computation to infer the existence of dark energy/matter, independent of the evidence from recent cosmological observations., Comment: LaTeX, 11 pages, 1 figure; version submitted to PRL; several references added; very useful comments and suggestions by Eric Perlman incorporated

Neutrices are additive groups of negligible functions that do not contain any constants except 0. Their calculus was developed by van der Corput and Hadamard in connection with asymptotic series and divergent integrals. We apply neutrix calculus to quantum field theory, obtaining finite renormalizations in the loop calculations. For renormalizable quantum field theories, we recover all the usual physically observable results. One possible advantage of the neutrix framework is that effective field theories can be accommodated. Quantum gravity theories appear to be more manageable., Comment: LateX, 19 pages

In general, quantum field theories (QFT) require regularizations and infinite renormalizations due to ultraviolet divergences in their loop calculations. Furthermore, perturbation series in theories like QED are not convergent series, but are asymptotic series. We apply neutrix calculus, developed in connection with asymptotic series and divergent integrals, to QFT,obtaining finite renormalizations. While none of the physically measurable results in renormalizable QFT is changed, quantum gravity is rendered more manageable in the neutrix framework., Comment: 10 pages; LaTeX; version to appear in J. Phys. A: Math. Gen. as a Letter to the Editor

Spacetime foam, also known as quantum foam, has its origin in quantum fluctuations of spacetime. Arguably it is the source of the holographic principle, which severely limits how densely information can be packed in space. Its physics is also intimately linked to that of black holes and computation. In particular, the same underlying physics is shown to govern the computational power of black hole quantum computers., Comment: 8 pages, LaTeX; Talk given by Jack Ng, in celebration of Paul Frampton's 60th birthday, at the Coral Gables Conference (in Fort Lauderdale, Florida on December 17, 2003). To appear in the Proceedings of the 2003 Coral Gables Conference

At Planck-scale, spacetime is "foamy" due to quantum fluctuations predicted by quantum gravity. Here we consider the possibility of using spacetime foam-induced phase incoherence of light from distant galaxies and gamma-ray bursters to probe Planck-scale physics. In particular, we examine the cumulative effects of spacetime fluctuations over a huge distance. Our analysis shows that they are far below what is required in this approach to shed light on the foaminess of spacetime., Comment: Minor changes; this version will appear in ApJ Letters

We give a geometrical derivation of the Dirac equation by considering a spin-1/2 particle travelling with the speed of light in a cubic spacetime lattice. The mass of the particle acts to flip the multi-component wavefunction at the lattice sites. Starting with a difference equation for the case of one spatial and one time dimensions, we generalize the approach to higher dimensions. Interactions with external electromagnetic and gravitational fields are also considered. One logical interpretation is that only at the lattice sites is the spin-1/2 particle aware of its mass and the presence of external fields., Comment: 9 pages, LaTeX, version accepted for publication in Phys. Lett. A

We have argued that quantum mechanics and general relativity give a lower bound $\delta l \gtrsim l^{1/3} l_P^{2/3}$ on the measurement uncertainty of any distance $l$ much greater than the Planck length $l_P$. Recently Baez and Olson have claimed that one can go below this bound by attaching the measuring device to a massive elastic rod. Here we refute their claim. We also reiterate (and invite our critics to ponder on) the intimate relationship and consistency between black hole physics (including the holographic principle) and our bound on distance measurements., Comment: 4 pages, aastex

Why does the physical 4-dimensional space have a 3 + 1 signature rather than a 4 + 0 or a 2 + 2 for its metric? We give a simple explanation based largely on a group-theoretic argument a la Wigner. Applied to flat spaces of higher dimensions the same approach indicates that metrics with more than one time dimension are physically unacceptable because the corresponding irreducible unitary representations are infinite dimensional (besides the trivial representation)., Comment: 8 Latex pages

A threshold anomaly refers to a theoretically expected energy threshold that is not observed experimentally. Here we offer an explanation of the threshold anomalies encountered in the ultra-high energy cosmic ray events and the TeV-gamma ray events, by arguing that energy-momentum uncertainties due to quantum gravity, too small to be detected in low-energy regime, can affect particle kinematics so as to raise or even eliminate the energy thresholds. A possible modification of the energy-momentum dispersion relation, giving rise to time-of-flight differences between photons of different energies from gamma ray bursts, is also discussed., Comment: minor changes in text and references

A recent paper (gr-qc/9909017) criticizes our work on the structure of spacetime foam. Its authors argue that the quantum uncertainty limit for the position of the quantum clock in a gedanken timing experiment, obtained by Wigner and used by us, is based on unrealistic assumptions. Here we point out some flaws in their argument. We also discuss their other comments and some other issues related to our work, including a simple connection to the holographic principle. We see no reason to change our cautious optimism on the detectability of spacetime foam with future refinements of modern gravitational-wave interferometers like LIGO/VIRGO and LISA., Comment: 13 pages; in the concluding section, a simple connection to the holographic principle is pointed out; two new references, and minor changes in the text and abstract; this new version of the paper will appear in Phys. Lett. B

Recent astrophysical observations seem to indicate that the cosmological constant is small but nonzero and positive. The old cosmological constant problem asks why it is so small; we must now ask, in addition, why it is nonzero (and is in the range found by recent observations), and why it is positive. In this essay, we try to kill these three metaphorical birds with one stone. That stone is the unimodular theory of gravity, which is the ordinary theory of gravity, except for the way the cosmological constant arises in the theory. We argue that the cosmological constant becomes dynamical, and eventually, in terms of the cosmic scale factor $R(t)$, it takes the form $\Lambda(t) = \Lambda(t_0)(R(t_0)/R(t))^2$, but not before the epoch corresponding to the redshift parameter $z \sim 1$., Comment: A discussion on the form of the cosmological constant (inversely proportional to the square of the cosmic scale factor) after the epoch corresponding to the redshift $z \sim 1$ is added. Two new references are added. This version of the paper will appear in Int. J. Mod. Phys. D

By analyzing a gedanken experiment designed to measure the distance $l$ between two spatially separated points, we find that this distance cannot be measured with uncertainty less than $(ll_P^2)^{1/3}$, considerably larger than the Planck scale $l_P$ (or the string scale in string theories), the conventional wisdom uncertainty in distance measurements. This limitation to space-time measurements is interpreted as resulting from quantum fluctuations of space-time itself. Thus, at very short distance scales, space-time is "foamy." This intrinsic foaminess of space-time provides another source of noise in the interferometers. The LIGO/VIRGO and LISA generations of gravity-wave interferometers, through future refinements, are expected to reach displacement noise levels low enough to test our proposed degree of foaminess in the structure of space-time. We also point out a simple connection to the holographic principle which asserts that the number of degrees of freedom of a region of space is bounded by the area of the region in Planck units., Comment: 15 pages, TeX, A simple connection to the holographic principle is added, minor changes in the text and abstract, and some changes in the References; this new version will appear in the third "Haller" issue in Foundations of Physics