Singularities of Scattering Amplitudes on Unphysical Sheets and Their Interpretation

The analytic structure of two-particle scattering amplitudes on the unphysical sheet of the Riemann surface reached by crossing the two-particle cut is discussed. The singularities of the amplitudes there are shown to be poles and their physical interpretation is studied. The way in which bound states appear on the physical sheet in the Mandelstam representation, both as isolated poles and as cuts, is traced in detail. The properties of partial wave amplitudes and of the full amplitude as a function of energy and angle and of energy and momentum transfer are discussed. Finally, a few remarks are made in connection with unstable states

Instability of a Nielsen-Olesen vortex embedded in the electroweak theory; 2, electroweak vortices and gauge equivalence

Vortex configurations in the electroweak gauge theory are investigated. Two gauge-inequivalent solutions of the field equations, the Z and W vortices, have previously been found. They correspond to embeddings of the abelian Nielsen-Olesen vortex solution into a U(1) subgroup of SU(2)xU(1). It is shown here that any electroweak vortex solution can be mapped into a solution of the same energy with a vanishing upper component of the Higgs field. The correspondence is a gauge equivalence for all vortex solutions except those for which the winding numbers of the upper and lower Higgs components add to zero. This class of solutions, which includes the W vortex, instead corresponds to a singular solution in the one-component gauge. The results, combined with numerical investigations, provide an argument against the existence of other vortex solutions in the gauge-Higgs sector of the Standard Model

Gravitational Wilson Loop in Discrete Quantum Gravity

Results for the gravitational Wilson loop, in particular the area law for large loops in the strong coupling region, and the argument for an effective positive cosmological constant discussed in a previous paper, are extended to other proposed theories of discrete quantum gravity in the strong coupling limit. We argue that the area law is a generic feature of almost all non-perturbative lattice formulations, for sufficiently strong gravitational coupling. The effects on gravitational Wilson loops of the inclusion of various types of light matter coupled to lattice quantum gravity are discussed as well. One finds that significant modifications to the area law can only arise from extremely light matter particles. The paper ends with some general comments on possible physically observable consequences.Comment: 39 pages, 10 figure

Coupling of Gravity to Matter via SO(3,2) Gauge Fields

We consider gravity from the quantum field theory point of view and introduce a natural way of coupling gravity to matter by following the gauge principle for particle interactions. The energy-momentum tensor for the matter fields is shown to be conserved and follows as a consequence of the dynamics in a spontaneously broken SO(3,2) gauge theory of gravity. All known interactions are described by the gauge principle at the microscopic level.Comment: 12 latex page

The geometric role of symmetry breaking in gravity

In gravity, breaking symmetry from a group G to a group H plays the role of describing geometry in relation to the geometry the homogeneous space G/H. The deep reason for this is Cartan's "method of equivalence," giving, in particular, an exact correspondence between metrics and Cartan connections. I argue that broken symmetry is thus implicit in any gravity theory, for purely geometric reasons. As an application, I explain how this kind of thinking gives a new approach to Hamiltonian gravity in which an observer field spontaneously breaks Lorentz symmetry and gives a Cartan connection on space.Comment: 4 pages. Contribution written for proceedings of the conference "Loops 11" (Madrid, May 2011

A Relation Between Gravity in (3+1)(3+1)--Dimensions and Pontrjagin Topological Invariant

A relation between the MacDowell-Mansouri theory of gravity and the Pontrjagin toplogical invariant in $(3+1)$ dimensions is discussed. This relation may be of especial interest in the quest of finding a mechanism to go from non-dynamical to dynamical gravity.Comment: 9 pages, Te

Surface van der Waals Forces in a Nutshell

Most often in chemical physics, long range van der Waals surface interactions are approximated by the exact asymptotic result at vanishing distance, the well known additive approximation of London dispersion forces due to Hamaker. However, the description of retardation effects that is known since the time of Casimir is completely neglected for lack of a tractable expression. Here we show that it is possible to describe surface van der Waals forces at arbitrary distances in one single simple equation. The result captures the long sought crossover from non-retarded (London) to retarded (Casimir) interactions, the effect of polarization in condensed media and the full suppression of retarded interactions at large distance. This is achieved with similar accuracy and the same material properties that are used to approximate the Hamaker constant in conventional applications. The results show that at ambient temperature, retardation effects significantly change the power law exponent of the conventional Hamaker result for distances of just a few nanometers.Comment: 6 pages + 4 figures + supplementary materia

Ring diagrams and electroweak phase transition in a magnetic field

Electroweak phase transition in a magnetic field is investigated within the one-loop and ring diagram contributions to the effective potential in the minimal Standard Model. All fundamental fermions and bosons are included with their actual values of masses and the Higgs boson mass is considered in the range $75 GeV \leq m_H \leq 115 GeV$. The effective potential is real at sufficiently high temperature. The important role of fermions and $W$-bosons in symmetry behaviour is observed. It is found that the phase transition for the field strengths $10^{23} - 10^{24}$G is of first order but the baryogenesis condition is not satisfied. The comparison with the hypermagnetic field case is done.Comment: 16 pages, Latex, changed for a mistake in the numerical par

Examples of Embedded Defects (in Particle Physics and Condensed Matter)

We present a series of examples designed to clarify the formalism of the companion paper `Embedded Vortices'. After summarising this formalism in a prescriptive sense, we run through several examples: firstly, deriving the embedded defect spectrum for Weinberg-Salam theory, then discussing several examples designed to illustrate facets of the formalism. We then calculate the embedded defect spectrum for three physical Grand Unified Theories and conclude with a discussion of vortices formed in the superfluid $^3$He-A phase transition.Comment: final corrections. latex fil

Point-form quantum field theory

We examine canonical quantization of relativistic field theories on the forward hyperboloid, a Lorentz-invariant surface of the form $x_\mu x^\mu = \tau^2$. This choice of quantization surface implies that all components of the 4-momentum operator are affected by interactions (if present), whereas rotation and boost generators remain interaction free -- a feature characteristic of Dirac's `` point-form\rq\rq of relativistic dynamics. Unlike previous attempts to quantize fields on space-time hyperboloids, we keep the usual plane-wave expansion of the field operators and consider evolution of the system generated by the 4-momentum operator. We verify that the Fock-space representations of the Poincar\'e generators for free scalar and spin-1/2 fields look the same as for equal-time quantization. Scattering is formulated for interacting fields in a covariant interaction picture and it is shown that the familiar perturbative expansion of the S-operator is recovered by our approach. An appendix analyzes special distributions, integrals over the forward hyperboloid, that are used repeatedly in the paper.Comment: 30 page