Explore the vast range of titles available.

Based on a highly regarded lecture course at Moscow State University, this is a clear and systematic introduction to gauge field theory. It is unique in providing the means to master gauge field theory prior to the advanced study of quantum mechanics. Though gauge field theory is typically included in courses on quantum field theory, many of its ideas and results can be understood at the classical or semi-classical level. Accordingly, this book is organized so that its early chapters require no special knowledge of quantum mechanics. Aspects of gauge field theory relying on quantum mechanics are introduced only later and in a graduated fashion--making the text ideal for students studying gauge field theory and quantum mechanics simultaneously. The book begins with the basic concepts on which gauge field theory is built. It introduces gauge-invariant Lagrangians and describes the spectra of linear perturbations, including perturbations above nontrivial ground states. The second part focuses on the construction and interpretation of classical solutions that exist entirely due to the nonlinearity of field equations: solitons, bounces, instantons, and sphalerons. The third section considers some of the interesting effects that appear due to interactions of fermions with topological scalar and gauge fields. Mathematical digressions and numerous problems are included throughout. An appendix sketches the role of instantons as saddle points of Euclidean functional integral and related topics. Perfectly suited as an advanced undergraduate or beginning graduate text, this book is an excellent starting point for anyone seeking to understand gauge fields.

Cosmology and particle physics are deeply interrelated. Among the common problems are dark energy, dark matter and baryon asymmetry of the Universe. We discuss these problems in general terms, and concentrate on several particular hypotheses. On the dark matter side, we consider weakly interacting massive particles and axions/axion-like particles as cold dark matter, sterile neutrinos and gravitinos as warm dark matter. On the baryon asymmetry side, we discuss electroweak baryogenesis as a still-viable mechanism. We briefly describe diverse experimental and observational approaches towards checking these hypotheses. We then turn to the earliest cosmology. We give arguments showing that the hot stage was preceded by another epoch at which density perturbations and possibly primordial gravity waves were generated. The best guess here is inflation, which is consistent with everything we know of density perturbations, but there are alternative scenarios. Future measurements of the properties of density perturbations and possible discovery of primordial gravity waves have strong potential in this regard.

We consider a class of generalized Galileon theories within General Relativity in space-times of more than two spatial dimensions. We show that these theories do not admit stable, static, spherically symmetric, asymptotically flat and traversable Lorentzian wormholes.

We discuss the possibility of constructing stable, static, spherically symmetric, asymptotically flat Lorentzian wormhole solutions in General Relativity coupled to a generalized Galileon field \\(\\pi\\). Assuming that Minkowski space-time is obtained at \\(\\partial \\pi =0\\), we find that there is tension between the properties of the energy-momentum tensor required to support a wormhole (violation of average null energy conditions) and stability of the Galileon perturbations about the putative solution (absence of ghosts and gradient instabilities). In 3-dimensional space-time, this tension is strong enough to rule out wormholes with above properties. In higher dimensions, including the most physically interesting case of 4-dimensional space-time, wormholes, if any, must have fairly contrived shapes.

In these lectures we first concentrate on the cosmological problems which, hopefully, have to do with the new physics to be probed at the LHC: the nature and origin of dark matter and generation of matter-antimatter asymmetry. We give several examples showing the LHC cosmological potential. These are WIMPs as cold dark matter, gravitinos as warm dark matter, and electroweak baryogenesis as a mechanism for generating matter-antimatter asymmetry. In the remaining part of the lectures we discuss the cosmological perturbations as a tool for studying the epoch preceeding the conventional hot stage of the cosmological evolution.

We give a mini-review of scalar field theories with second-derivative Lagrangians, whose field equations are second order. Some of these theories admit solutions violating the Null Energy Condition and having no obvious pathologies. We give a few examples of using these theories in cosmological setting and also in the context of the creation of a universe in the laboratory.

Null Energy Condition (NEC) can be violated in a consistent way in models with unconventional kinetic terms, notably, in Galileon theories and their generalizations. We make use of one of these, the scale-invariant kinetic braiding model, to discuss whether a universe can in principle be created by man-made processes. We find that even though the simplest models of this sort can have both healthy Minkowski vacuum and consistent NEC-violating phase, there is an obstruction for creating a universe in a straightforward fashion. To get around this obstruction, we design a more complicated model, and present a scenario for the creation of a universe in the laboratory.

We show that flat spectrum of small perturbations of field(s) is generated in a simple way in a theory of multi-component scalar field provided this theory is conformally invariant, it has some global symmetry and the quartic potential is negative. We suggest a mechanism of converting these field perturbations into adiabatic scalar perturbations with flat spectrum.

We address the question of whether or not fermions with twisted periodicity condition suppress the semiclassical decay of M^4xS^1 Kaluza--Klein vacuum. We consider a toy (1+1)-dimensional model with twisted fermions in cigar-shaped Euclidean background geometry and calculate the fermion determinant. We find that contrary to expectations, the determinant is finite. We consider this as an indication that twisted fermions do not stabilize the Kaluza--Klein vacuum.