Related papers: Quaternionic scalar field in the real Hilbert spac…

Within the framework of exterior algebra, the concept of time-like quaternions has been previously established. This paper advances beyond the existing structure by elucidating the procedure for constructing time-like quaternions with the…

A 4-dimensional Lorentzian static space-time is equivalent to 3-dimensional Euclidean gravity coupled to a massless Klein-field. By canonically quantizing the coupling model in the framework of loop quantum gravity, we obtain a quantum…

In this review paper we give a geometrical formulation of the field equations in the Lagrangian and Hamiltonian formalisms of classical field theories (of first order) in terms of multivector fields. This formulation enables us to discuss…

Using bi-spinor fields we write the pseudo-scalar and bi-spinor fields that are characterized by the field functions of coordinates of several particles, namely multi-particle fields. By applying the quantization procedure to these…

A Hamiltonian lattice formulation of lattice gauge theories opens the possibility for quantum simulations of the non-perturbative dynamics of QCD. By parametrizing the gauge invariant Hilbert space in terms of plaquette degrees of freedom,…

We present some striking global consequences of a model quaternionic quantum field theory which is locally complex. We show how making the quaternionic structure a dynamical quantity naturally leads to the prediction of cosmic strings and…

Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. We…

We generalize the unconstrained description of free massless higher spin fields previously developed in [Nucl.Phys. B 779 (2007) 155] to the case of free massive higher spin fields in a flat space of arbitrary dimension. The Lagrangian is…

We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three…

A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical…

It is shown how the theory of the fields can be constructed in a consistent way in quantized spaces. All constructions are connected with unitary irreducible representations of real forms of six dimensional rotation algebras O(1,5), O(2,4),…

We construct the non-standard Lagrangian, called the multiplicative form, of the homogeneous scalar field and fermion field through the inverse calculus of variations, which the equation of motion still satisfies the Klein-Gordon and Dirac…

Large-N field systems are considered from an unusual point of view. The Hamiltonian is presented in a third-quantized form analogously to the second-quantized formulation of the quantum theory of many particles. The semiclassical…

We apply the multisymplectic formulation of classical field theories [11, 12, 14] to describe the Einstein-Hilbert and the Einstein-Palatini (or metric-affine) Lagrangian models of General Relativity.

As established by Sol\`er, Quantum Theories may be formulated in real, complex or quaternionic Hilbert spaces only. St\"uckelberg provided physical reasons for ruling out real Hilbert spaces relying on Heisenberg principle. Focusing on this…

The scalar field theory with higher derivatives is considered in the first order formalism. The field equation of the forth order describes scalar particles possessing two mass states. The first order relativistic wave equation in the…

Conventional quantum field theory is a method for studying structureless elementary particles. Non-elementary particles, on the other hand, are those with internal structure or particles that are made up of elementary constituents like the…

Proceeding from the main principles of the non-unitary quantum theory of relativistic bi-Hamiltonian systems, a system of Lagrangian fields characterized by a certain dispersion law (mass spectrum of particles), interactions between them…

In our joint papers [FL1-FL2] we revive quaternionic analysis and show deep relations between quaternionic analysis, representation theory and four-dimensional physics. As a guiding principle we use representation theory of various real…

We discuss the quantization of an unstable field through the construction of a "one-particle Hilbert space." The system considered here is a neutral scalar field evolving over a globally hyperbolic static spacetime and subject to a…