arXiv subjects
Publications and source records attributed to Roman V. Buniy.
The entanglement entropy in a quantum field theory between two regions of space has been shown in simple cases to be proportional to the volume of the hypersurface separating the regions. We prove that this is true for a free scalar field in an arbitrary geometry with purely spatial curvature and obtain a complete asymptotic expansion for the entropy.
It is well known that for a field theory with the Chern-Simons action, expectation values of Wilson line operators are topological invariants. The standard result is expressed in terms of the Gaussian linkings of closed curves defining the operators. We show how judicious choice of Wilson lines leads to higher order topological linkings.
Gaussian linking of a semiclassical path of a charged particle with a magnetic flux tube is responsible for the Aharonov-Bohm effect, where one observes interference proportional to the magnitude of the enclosed flux. We construct quantum mechanical wave functions where semiclassical paths can have second order linking to two magnetic flux tubes, and show there is interference proportional to the product of the two fluxes.
In classical mechanics, an action is defined only modulo additive terms which do not modify the equations of motion; in certain cases, these terms are topological quantities. We construct an infinite sequence of higher order topological actions and argue that they play a role in quantum mechanics, and hence can be accessed experimentally.
Attempts to derive the Born rule, either in the Many Worlds or Copenhagen interpretation, are unsatisfactory for systems with only a finite number of degrees of freedom. In the case of Many Worlds this is a serious problem, since its goal is to account for apparent collapse phenomena, including the Born rule for probabilities, assuming only unitary evolution of the wavefunction. For finite number of degrees of freedom, observers on the vast majority of branches would not deduce the Born rule. However, discreteness of the quantum state space, even if extremely tiny, may restore the validity of the usual arguments.
We extend previous work showing that violation of the null energy condition implies instability in a broad class of models, including gauge theories with scalar and fermionic matter as well as any perfect fluid. Simple examples are given to illustrate these results. The role of causality in our results is discussed. Finally, we extend the fluid results to more general systems in thermal equilibrium. When applied to the dark energy, our results imply that w is unlikely to be less than -1.
We provide exact solutions to the Einstein equations when the Universe contains vacuum energy plus a uniform arrangements of magnetic fields, strings, or domain walls. Such a universe has planar symmetry, i. e., it is homogeneous but, not isotropic. Further exact solutions are obtained when dust is included and approximate solutions are found for $w\not=0$ matter. These cosmologies also have planar symmetry. These results may eventually be used to explain some features in the WMAP data. The magnetic field case is the easiest to motivate and has the highest possibility of yielding reliable constraints on observational cosmology.
We show that Lorentzian (traversable) wormholes and time machines with semi-classical spacetimes are unstable due to their violation of the null energy condition (NEC). Semi-classicality of the energy-momentum tensor in a given quantum state (required for semi-classicality of the spacetime) implies localization of its wavefunction in phase space, leading to evolution according to the classical equations of motion. Previous results related to violation of the NEC then require that the configuration is unstable to small perturbations.
We show that violation of the null energy condition implies instability in a broad class of models, including classical gauge theories with scalar and fermionic matter as well as any perfect fluid. When applied to the dark energy, our results imply that $w = p / ρ$ is unlikely to be less than -1.
For a universe containing cosmological constant together with uniform arrangements of magnetic fields, strings, or domain walls, exact solutions to the Einstein equations are shown to lead to a universe with ellipsoidal expansion. The magnetic field case is the easiest to motivate and has the highest possibility of finding application in observational cosmology.
We argue that a systems of tightly knotted, linked, or braided flux tubes will have a universal mass-energy spectrum, since the length of fixed radius flux tubes depend only on the topology of the configuration. We motivate the discussion with plasma physics examples, then concentrate on the model of glueballs as knotted QCD flux tubes. Other applications will also be discussed.
For uniform arrangements of magnetic fields, strings, or domain walls (together with the cosmological constant and non-relativistic matter), exact solutions to the Einstein equations are shown to lead to a universe with ellipsoidal expansion. We argue the results can be used to explain some features in the WMAP data. The magnetic field case is the easiest to motivate and has the highest possibility of yielding reliable constraints on observational cosmology.
Systems of tightly knotted, linked, or braided flux tubes will have a universal mass-energy spectrum if the flux is quantized. We focus on a model of glueballs as knotted QCD flux tubes.
It has been proposed that propagation of cosmic rays at extreme-energy may be sensitive to Lorentz-violating metric fluctuations (``foam''). We investigate the changes in interaction thresholds for cosmic-rays and gamma-rays interacting on the CMB and IR backgrounds, for a class of stochastic models of spacetime foam. The strength of the foam is characterized by the factor (E/M_P)^a, where ``a'' is a phenomenological suppression parameter. We find that there exists a critical value of ``a'' (dependent on the particular reaction), below which the threshold energy can only be lowered, and above which the threshold energy may be raised, but at most by a factor of two. Thus, it does not appear possible in this class of models to extend cosmic-ray spectra significantly beyond their classical absorption energies. However, the lower thresholds resulting from foam may have signatures in the cosmic-ray spectrum. We also find that cosmic-ray energies cannot exceed the fundamental Planck scale, and so set a lower bound of 10^8 TeV on the context of this model for the scale of gravity. Finally, we comment in the apparent non-conservation of particle energy-momentum, and speculate on its re-emergence as dark energy in the foamy vacuum.
We show how the existence of non-trivial finite-energy time-dependent classical lumps is restricted by a generalized virial theorem. For simple model Lagrangians, bounds on energies follow.
We model the observed glueball mass spectrum in terms of energies for tightly knotted and linked QCD flux tubes. The data is fit well with one parameter. We predict additional glueball masses.
We consider an eight-dimensional local octonionic theory with the seven-sphere playing the role of the gauge group. Duality conditions for two- and four-forms in eight dimensions are related. Dual fields--octonionic instantons--solve an 8D generalization of the Yang-Mills equation. Modifying the ADHM construction of 4D instantons, we find general $k$-instanton 8D solutions which depends on $16k-7$ effective parameters.
Skew density matrices can be diagonalized to yield probability interpretation. The power-counting prediction of perturbative QCD is found consistent with recent CEBAF data on $F_2(Q^2)/F_1(Q^2)$