Related papers: Convergent series for QCD
We consider the problem of digitalizing Euclidean line segments from $\mathbb{R}^d$ to $\mathbb{Z}^d$. Christ {\em et al.} (DCG, 2012) showed how to construct a set of {\em consistent digital segment} (CDS) for $d=2$: a collection of…
We give a mathematical construction of Euclidean quantum field theory on certain curved backgrounds. We focus on generalizing Osterwalder-Schrader quantization, as these methods have proved useful to establish estimates for interacting…
I present an introduction to the field of Quantum Chromodynamics (QCD) with emphasis on nucleon spin structure and perturbative methods. After a somewhat comprehensive overview of perturbative QCD, including the systematics of…
We analyze critically the renormalization of quantum fields in cosmological spacetimes, using non covariant ultraviolet cutoffs. We compute explicitly the counterterms necessary to renormalize the semiclassical Einstein equations, using…
We study properties of a scalar quantum field theory on two-dimensional noncommutative space-times. Contrary to the common belief that noncommutativity of space-time would be a key to remove the ultraviolet divergences, we show that field…
Bosonic quantum field theories, even when regularized using a finite lattice, possess an infinite dimensional Hilbert space and, therefore, cannot be simulated in quantum computers with a finite number of qubits. A truncation of the Hilbert…
We incorporate the concept of dimensional reduction at high energies within the perturbative formulation of quantum field theory. In this new framework, space and momentum integrations are modified by a weighting function incorporating an…
This paper presents a comprehensive review of both the theory and experimental successes of Quantum Chromodynamics, starting with its emergence as a well defined theory in 1972-73 and following developments and results up to the present…
Conformal symmetry provides a systematic approximation to QCD in both its perturbative and nonperturbative domains. One can use the AdS/CFT correspondence between Anti-de Sitter space and conformal gauge theories to obtain an analytically…
The aim of this review is to outline a full route from the fundamental principles of algebraic quantum field theory on curved spacetime in its present-day form to explicit phenomenological applications which allow for comparison with…
Conformal truncation is a powerful numerical method for solving generic strongly-coupled quantum field theories based on purely field-theoretic technics without introducing lattice regularization. We discuss possible speedups for performing…
The Euclidean quantum field theory for the fields $\phi_{\Delta x}(x)$, which depend on both the position $x$ and the resolution $\Delta x$, constructed in SIGMA 2 (2006), 046, hep-th/0604170, on the base of the continuous wavelet…
We construct a periodically time-dependent Hamiltonian with a phase transition in the quantum Hall universality class. One spatial dimension can be eliminated by introducing a second incommensurate driving frequency, so that we can study…
In QCD one can change the representation of the gauge group for quarks and/or the gauge group itself. Examples of such generalizations are: (a) supersymmetric Yang-Mills theory with gauge group SU(2) or SU(3); (b) QCD with SU(2) colour and…
There exists the problem to construct a quantum algebra of observables in lightcone QCD beyond the perturbative regime. It has recently established that the boundary gauge fields are crucial for a consistent construction of the classical…
A new application of quantum field theory is developed that gives a description of the internal dynamics of dressed elementary particles and predicts their masses. The fermionic and bosonic quantum fields are treated as interdependent…
We discuss a program suite for simulating Quantum Chromodynamics on a 4-dimensional space-time lattice. The basic Hybrid Monte Carlo algorithm is introduced and a number of algorithmic improvements are explained. We then discuss the…
Quantum cosmology is traditionally formulated in a minisuperspace setting, implicitly averaging fields over space to obtain homogeneous models. For universal reasons related to the uncertainty principle, quantum corrections then depend on…
This paper discusses the general structure of reflection positive Euclidean covariant distributions that can be used to construct Euclidean representations of relativistic quantum mechanical models of systems of a finite number of degrees…
Extended QCD (XQCD) proposed by Kaplan [1] is an interesting reformulation of QCD with additional bosonic auxiliary fields. While its partition function is kept exactly the same as that of original QCD, XQCD naturally contains properties of…