Related papers: Implementing Unitarity in Perturbation Theory
The unitary S-matrix for the space-time non-commutative QED is constructed using the $\star$-time ordering which is needed in the presence of derivative interactions. Based on this S-matrix, perturbation theory is formulated and Feynman…
We prove the following result: if a $\mathbb{Q}$-Fano variety is uniformly K-stable, then it admits a K\"{a}hler-Einstein metric. We achieve this by modifying Berman-Boucksom-Jonsson's strategy with appropriate perturbative arguments and…
A classical result of Sz.-Nagy asserts that a Hilbert space contraction operator $T$ can be dilated to a unitary $\cU$. A more general multivariable setting for these ideas is the setup where (i) the unit disk is replaced by a domain…
Current quantum theories of an elementary free particle assume unitary space inversion and anti-unitary time reversal operators. In so doing robust classes of possible theories are discarded. The present work shows that consistent theories…
A Procedure is outlined that may be used as a starting point for a perturbative treatment of theories with permanent confinement. By using a counter term in the Lagrangian that renormalizes the infrared divergence in the Coulomb potential,…
Ostrogradsky instability generally appears in nondegenerate higher-order derivative theories and this issue can be resolved by removing any existing degeneracy present in such theories. We consider an action involving terms that are at most…
We have combined perturbative unitarity and renormalisation group equation arguments in order to find a dynamical way to constrain the space of the gauge couplings ($g'_1$, $\widetilde{g}$) of the so-called "Minimal $Z'$ Models". We have…
We introduce a prescriptive approach to generalized unitarity, resulting in a strictly-diagonal basis of loop integrands with coefficients given by specifically-tailored residues in field theory. We illustrate the power of this strategy in…
Feynman perturbation theory for nonabelian gauge theory in light-like gauge is investigated. A lattice along two space-like directions is used as a gauge invariant ultraviolet regularization. For preservation of the polinomiality of action…
We compare the non-linear matter power spectrum in real space calculated analytically from 3rd-order perturbation theory with N-body simulations at 1<z<6. We find that the perturbation theory prediction agrees with the simulations to better…
For many practical purposes, it is convenient to formulate unbroken non-abelian gauge theories like QCD in a color-flow basis. We present a new derivation of SU(N) interactions in the color-flow basis by extending the gauge group to…
We study $D$-dimensional elastic manifolds driven by ac-forces in a disordered environment using a perturbation expansion in the disorder strength and the mean-field approximation. We find, that for $D\le 4$ perturbation theory produces…
The validity of the tree-unitarity criterion for scattering amplitudes on the noncommutative space-time is considered, as a condition that can be used to shed light on the problem of unitarity violation in noncommutative quantum field…
The Riemann-Hilbert problem associated with the integrable PDE is used as a nonlinear transformation of the nearly integrable PDE to the spectral space. The temporal evolution of the spectral data is derived with account for arbitrary…
Constructions introduced by Dirac for singular Lagrangians are extended and reinterpreted to cover cases when kernel distributions are either nonintegrable or of nonconstant rank, and constraint sets need not be closed.
The constraints imposed by asymptotic freedom and analyticity on the large-order behavior of perturbation theory for the electromagnetic current-current correlation function are examined. By suitably applying the renormalization group, the…
The Feynman-Schwinger representation provides a convenient framework for the cal culation of nonperturbative propagators. In this paper we first investigate an analytically solvable case, namely the scalar QED in 0+1 dimension. With this…
Categorical quantum mechanics exploits the dagger compact closed structure of finite dimensional Hilbert spaces, and uses the graphical calculus of string diagrams to facilitate reasoning about finite dimensional processes. A significant…
We introduce N-parameter perturbation theory as a new tool for the study of non-linear relativistic phenomena. The main ingredient in this formulation is the use of the Baker-Campbell-Hausdorff formula. The associated machinery allows us to…
In this article, we study the quantum dynamics of a Klein-Gordon field on de-Sitter space. We prove time evolution is not unitarily implementable. We also consider a Klein-Gordon field perturbed by a local potential V. In this case we prove…