International Journal of Modern Physics A

Tom Kibble pioneered the idea that there were one or more symmetry breaking phase transitions in the very early universe, at which defects like monopoles, strings and domain walls would have formed. In the context of grand unified theories, or their extensions, this idea remains compelling: observing these defects would be one of the very few ways of directly confirming the theories. In contrast, inflationary theory invoked a strongly supercooled transition driving a period of exponential expansion which would sweep all such defects away. If inflation terminated slowly, quantum vacuum fluctuations would be amplified and stretched to cosmological scales, forming density variations of just the character required to explain the formation of galaxies. The ensuing paradigm has dominated cosmology for the last three decades. However, basic problems in the scenario remain unresolved. Extreme tuning both of the initial conditions and of the physical laws are required. There are many different versions, each with slightly different predictions. Finally, inflation brought with it the theory of a "multiverse" — a universe containing infinite number of different, infinite, universes — while providing no "measure" or means of calculating the probability of observing any one of them. I will discuss an alternative to inflation, in which the big bang was a bounce from a previous contracting epoch. The discovery of the Higgs boson at the LHC has provided new evidence for such a picture by showing that, within the minimal standard model, our current vacuum is metastable. This opens the door to a cyclic universe scenario in which the electroweak Higgs plays a central role.

The Dirac equation with scalar and vector potentials of equal magnitude is considered. For the two-dimensional harmonic oscillator superintegrable potential, the superintegrable potentials of E₈ (case (3b)), S₄ and S₂, the Schrödinger-like equations are studied. The quadratic algebras of these quasi-Hamiltonians are derived. By using the realization of the quadratic algebras in a deformed oscillator algebra, the structure function and the energy eigenvalues are obtained.

Using a Mathematica^TM code, we present a straightforward numerical analysis of the 384-dimensional solution space of signed permutation 4×4 matrices, which in sets of four, provide representations of the 𝒢ℛ(4, 4) algebra, closely related to the 𝒩 = 1 (simple) supersymmetry algebra in four-dimensional space–time. Following after ideas discussed in previous papers about automorphisms and classification of adinkras and corresponding supermultiplets, we make a new and alternative proposal to use equivalence classes of the (unsigned) permutation group S₄ to define distinct representations of higher-dimensional spin bundles within the context of adinkras. For this purpose, the definition of a dual operator akin to the well-known Hodge star is found to partition the space of these 𝒢ℛ(4, 4) representations into three suggestive classes.

We analyze the Markovian and non-Markovian stochastic quantization methods for a complex action quantum mechanical model analog to Maxwell–Chern–Simons electrodynamics in Weyl gauge. We show through analytical methods convergence to the correct equilibrium state for both methods. Introduction of a memory kernel generates a non-Markovian process which has the effect of slowing down oscillations that arise in the Langevin-time evolution towards equilibrium of complex-action problems. This feature of non-Markovian stochastic quantization might be beneficial in large-scale numerical simulations of complex action field theories on a lattice.

The modified Dirac equations describing massless and massive spin-1/2 particles violating the Lorentz invariance are considered. The equation for massless fermions with varying speed is formulated in the 16-component first-order form. The projection matrix, which is the density matrix, extracting solutions to the equation has been obtained. Exact solutions to the equation and energy spectrum for a massive neutrino are obtained in the presence of background matter. We have considered as subluminal as well as superluminal propagations of neutrinos. The bounds on the Lorentz invariance violation parameter from astrophysical observations by IceCube, OPERA, MINOS collaborations and by the SN1987A supernova are obtained for superluminal neutrinos.

In this paper, we present results based on a combination of four inclusive topology searches for supersymmetry (SUSY) from the CMS experiment, and use this to determine universal mass limits on gluino and third-generation squarks in the context of Natural-like SUSY spectra. This class of sparticle spectra is inspired by the argument of naturalness, which originates from both consideration of fine-tuning arguments, and the need to satisfy current experimental search constraints. The class of Natural-like SUSY spectra considered follows the typical Natural SUSY model made up of a gluino, third-generation squarks, and higgsino sparticles, but is extended to more complex spectra containing sleptons. We show that the limits obtained from the combination of inclusive topology searches are far more stable than those from individual searches, with respect to the assumed underlying complexity of the spectra, and hence these limits can be considered as universal mass limits on gluino and third-generation squarks, defined in the context of this broad class of Natural-like SUSY spectra. Furthermore, we present our results using a simple colour scheme that allows a straightforward interpretation of any Natural-like SUSY spectrum with our limits.

Complementing the final results of the 2011 searches based on 5 fb^-1 of integrated luminosity, with the first published results from 2012 searches using approximately 11 fb^-1, we find that gluinos with a mass of and third-generation top and bottom squarks with masses of are excluded for low masses of the lightest SUSY particle (LSP). These limits weaken to and , when the mass of the LSP is increased to several hundred GeV. Based on this result, we establish a prediction of how these limits might evolve when the full 2012 dataset is analysed, with both the CMS and ATLAS experiments combined. This outlook suggests that for low masses of the LSP, gluinos with a mass of and third-generation squarks with masses of are likely to be excluded. For high LSP masses, these limits are expected to decrease to and . Therefore, despite the fact that the LHC already probes a significant region of the SUSY parameter space, Natural SUSY scenarios based on rather stringent fine-tuning requirements may not be fully excluded by the data taken so far. This suggests that additional data is needed, to be recorded during the higher energy running of the LHC expected in 2015. The importance of combining relevant inclusive topology searches, in order to make the most universal interpretations possible, is a general recommendation for future experimental searches at the LHC.

The reason why the elementary-particle theory must be Lorentz invariant is investigated under the principle of quantum priority, which implies that the existence of any space–time manifold such as the Minkowski space should not be assumed logically prior to the formulation of quantum-theoretical framework. The consideration is based on the canonical operator formalism of quantum Einstein gravity, which is formulated without introducing any classical background space–time nor any particular metric signature. The Lorentz invariance of the elementary-particle theory is derived as a consequence of the spontaneous breakdown of general linear invariance on the basis of quantum Einstein gravity. The pseudo-Riemannian space–time can appear not as a consequence of the presence of gravitation, but as that of the spontaneous breakdown of translational invariance.

A self-adjoint dynamical time operator is introduced in Dirac's relativistic formulation of quantum mechanics and shown to satisfy a commutation relation with the Hamiltonian analogous to that of the position and momentum operators. The ensuing time-energy uncertainty relation involves the uncertainty in the instant of time when the wave packet passes a particular spatial position and the energy uncertainty associated with the wave packet at the same time, as envisaged originally by Bohr. The instantaneous rate of change of the position expectation value with respect to the simultaneous expectation value of the dynamical time operator is shown to be the phase velocity, in agreement with de Broglie's hypothesis of a particle associated wave whose phase velocity is larger than c. Thus, these two elements of the original basis and interpretation of quantum mechanics are integrated into its formal mathematical structure. Pauli's objection is shown to be resolved or circumvented. Possible relevance to current developments in electron channeling, in interference in time, in Zitterbewegung-like effects in spintronics, graphene and superconducting systems and in cosmology is noted.