Related papers: Causal Perturbative Quantum Field Theory and the S…
We introduce the historical development and physical idea behind topological Yang-Mills theory and explain how a physical framework describing subatomic physics can be used as a tool to study differential geometry. Further, we emphasize…
We apply the effective field theory approach to the coupled metric-inflaton system, in order to investigate the impact of higher dimension operators on the spectrum of scalar and tensor perturbations in the short-wavelength regime. In both…
We consider in detail the problem of gauge dependence that exists in relativistic perturbation theory, going beyond the linear approximation and treating second and higher order perturbations. We first derive some mathematical results…
A doublet of three-dimensional Dirac fermions can effectively describe the low energy spectrum of a fermionic cubic lattice. We employ this fermion doubling to encode a non-Abelian SU(2) charge in the fundamental representation. We…
We present a reformulation of SU(2) Yang-Mills theory in the maximal Abelian gauge, where the non-Abelian gauge field components are exactly integrated out at the expense of a new Abelian tensor field. The latter can be treated in a…
Quantum gravity coupled to scalar massive matter fields is investigated within the framework of causal perturbation theory. One-loop calculations include matter loop graviton self-energy and matter self-energy and yield ultraviolet finite…
We analyze perturbative aspects of gauged matrix models, including those where classically the gauge symmetry is partially broken. Ghost fields play a crucial role in the Feynman rules for these vacua. We use this formalism to elucidate the…
We generalize classical Yang-Mills theory by extending nonlinear constitutive equations for Maxwell fields to non-Abelian gauge groups. Such theories may or may not be Lagrangian. We obtain conditions on the constitutive equations…
We develop a general framework for quantum field theory on noncommutative spaces, i.e., spaces with quantum group symmetry. We use the path integral approach to obtain expressions for $n$-point functions. Perturbation theory leads us to…
These lectures present some basic facts in field theory necessary to understand the quantum theory of the Standard Model of weak and electromagnetic interactions.
We discuss the evaluation of observables in two-dimensional conformal field theory using the topological membrane description. We show that the spectrum of anomalous dimensions can be obtained perturbatively from the topologically massive…
We present a general method for constructing consistent quantum field theories with global symmetries. We start from a free non-interacting quantum field theory with given global symmetries and we determine all consistent perturbative…
We show, in great detail, how the perturbative tools of quantum field theory allow one to rigorously obtain: a ``categorified'' Faa di Bruno type formula for multiple composition, an explicit formula for reversion and a proof of…
A recent construction of the electroweak theory, based on perturbative quantum gauge invariance alone, is extended to the case of more generations of fermions with arbitrary mixing. The conditions implied by second order gauge invariance…
We study the transformation law of quantum fields in super Yang-Mills theory quantized in the Wess-Zumino gauge. It can be derived from a local version of generalized Slavnov-Taylor identities for general Green functions. Under suitable…
This paper presents relevant modern mathematical formulations for (classical) gauge field theories, namely, ordinary differential geometry, noncommutative geometry, and transitive Lie algebroids. They provide rigorous frameworks to describe…
Using the closed-time-path formalism, we construct perturbative frameworks, in terms of quasiparticle picture, for studying quasiuniform relativistic quantum field systems near equilibrium and non-equilibrium quasistationary systems. We…
Linear cosmological perturbation theory is pivotal to a theoretical understanding of current cosmological experimental data provided e.g. by cosmic microwave anisotropy probes. A key issue in that theory is to extract the gauge invariant…
We determine the most general form of the interaction between the gravitational field and an arbitrary Yang-Mills system of fields (massless and massive). We work in the perturbative quantum framework of the causal approach (of Epstein and…
Recent years have seen noteworthy progress in the mathematical formulation of quantum field theory and perturbative string theory. We give a brief survey of these developments. It serves as an introduction to the more detailed collection…