Related papers: Quantum Fields on the Light Front, Formulation in …
In loop quantum cosmology, Friedmann-LeMaitre-Robertson-Walker (FLRW) space-times arise as well-defined approximations to specific \emph{quantum} geometries. We initiate the development of a quantum theory of test scalar fields on these…
The paper is devoted to the Hamiltonian treatment of classical and quantum properties of Liouville field theory on a timelike strip in 2d Minkowski space. We give a complete description of classical solutions regular in the interior of the…
We introduce a nonperturbative, first principles numerical approach for solving time-dependent problems in quantum field theory, using light-front quantization. As a first application we consider QED in a strong background field, and the…
Light-Front Field Theory (LFFT) is a good candidate to describe bound states. In LFFT covariance is non-manifest. Burkardt and Langnau claim that, even for scattering amplitudes, rotational invariance is broken. We will take a different…
We propose a new formulation of lattice theory. It is given by a matrix form and suitable for satisfying Leibniz rule on lattice. The theory may be interpreted as a multi-flavor system. By realizing the difference operator as a commutator,…
The different forms of the Hamiltonian formulations of linearized General Relativity/spin-two theories are discussed in order to show their similarities and differences. It is demonstrated that in the linear model, non-covariant…
The canonical front form Hamiltonian for non-Abelian SU(N) gauge theory in 3+1 dimensions and in the light-cone gauge is mapped non-perturbatively on an effective Hamiltonian which acts only in the Fock space of a quark and an antiquark.…
Truncating quantum field theories to a dominant mode offers a non-perturbative approach to their solution. We consider here the interaction of charged scalar matter with a single mode of the electromagnetic field. The implied breaking of…
Basis Light-front Quantization has been proposed as a nonperturbative framework for solving quantum field theory. We apply this approach to Quantum Electrodynamics and explicitly solve for the light-front wave function of a physical…
We construct the classical and canonically quantized theories of a massless scalar field on a background lattice in which the number of points--and hence the number of modes--may grow in time. To obtain a well-defined theory certain…
Present models describing the interaction of quantum Maxwell and gravitational fields predict a breakdown of Lorentz invariance and a non standard dispersion relation in the semiclassical approximation. Comparison with observational data…
Covariant (polysymplectic) Hamiltonian field theory is formulated as a particular Lagrangian theory on a polysymplectic phase space that enables one to quantize it in the framework of familiar quantum field theory.
Modes with zero longitudinal light-front momentum (zero modes) do have roles to play in the analysis of light-front field theories. These range from improvements in convergence for numerical calculations to implications for the light-front…
We address the problem of nonperturbative calculations on the light front in quantum field theory regularized by Pauli-Villars method. As a preliminary step we construct light front Hamiltonians in (2+1)-dimensional $\lambda\phi^4$ model,…
The basic ideas in the theory of quantum mechanics on phase space are illustrated through an introduction of generalities, which seem to underlie most if not all such formulations and follow with examples taken primarily from kinematical…
A modification of the canonical quantization procedure for systems with time-dependent second-class constraints is discussed and applied to the quantization of the relativistic particle in a plane wave. The time dependence of constraints…
We analyze the properties of low-energy bound states in the transverse-field Ising model and in the XXZ model on the square lattice. To this end, we develop an optimized implementation of perturbative continuous unitary transformations. The…
Quantizing the gravitational field described by General relativity being a notorious difficult, unsolved and maybe meaningless problem I use in this essay a different strategy: I consider a linear theory in the framework of Special…
We show how to implement the background field method by means of canonical transformations and comment on the applications of the method to non-perturbative techniques in non-Abelian gauge theories. We discuss the case of the lattice in…
Symplectic quantization is a functional approach to quantum field theory that allows sampling of quantum fluctuations directly in Minkowski space time by means of a Hamiltonian dynamics in an intrinsic time $\tau$ which samples a…